Wikiversity:Colloquium

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== Motivation and emotion - Student editing ==

We are underway with [[Motivation and emotion]] this semester (Aug - Nov), which will see ~150 students signing up to and edting [[Motivation and emotion/Book/2026]]. Please be friendly and help them out as they learn their way around.

Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:16, 10 August 2026 (UTC)

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

Currently, only waiting for four days is required for a user to become autoconfirmed. I am proposing that we include a minimum edit count of 10 edits (akin to Wikipedia) especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:01, 23 August 2026 (UTC)
: [[Wikiversity:Autoconfirmed users]]
: Are you suggesting an additional requirement? i.e., 4 days + 10 edits?
: How is it adjusted? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:57, 5 September 2026 (UTC)
:: Yes. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 01:30, 6 September 2026 (UTC)
:As a newly volunteered member, it doesn't seem unreasonable to me to require a certain number of edits to establish my bona fides. [[User:Cfm490|Cfm490]] ([[User talk:Cfm490|discuss]] • [[Special:Contributions/Cfm490|contribs]]) 17:53, 5 September 2026 (UTC)

== Bartending Course on Wikiversity ==

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

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

== Writing news here ==

I'm bringing up this discussion again because I think it is beneficial to the project since Wikinews is gone, thank you. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 03:17, 1 September 2026 (UTC)
: Given that the community consensus here was not to replicate WikiNews within Wikiversity, I suggest thinking differently e.g., in terms of specific news-related projects you are interested in that have educational objectives that satisfy Wikiversity's mission. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:46, 5 September 2026 (UTC)</text>
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&lt;!-- MESSAGES GO BELOW --&gt;

== Motivation and emotion - Student editing ==

We are underway with [[Motivation and emotion]] this semester (Aug - Nov), which will see ~150 students signing up to and edting [[Motivation and emotion/Book/2026]]. Please be friendly and help them out as they learn their way around.

Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:16, 10 August 2026 (UTC)

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

Currently, only waiting for four days is required for a user to become autoconfirmed. I am proposing that we include a minimum edit count of 10 edits (akin to Wikipedia) especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:01, 23 August 2026 (UTC)
: [[Wikiversity:Autoconfirmed users]]
: Are you suggesting an additional requirement? i.e., 4 days + 10 edits?
: How is it adjusted? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:57, 5 September 2026 (UTC)
:: Yes. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 01:30, 6 September 2026 (UTC)
:As a newly volunteered member, it doesn't seem unreasonable to me to require a certain number of edits to establish my bona fides. [[User:Cfm490|Cfm490]] ([[User talk:Cfm490|discuss]] • [[Special:Contributions/Cfm490|contribs]]) 17:53, 5 September 2026 (UTC)

== Bartending Course on Wikiversity ==

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

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

== Writing news here ==

I'm bringing up this discussion again because I think it is beneficial to the project since Wikinews is gone, thank you. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 03:17, 1 September 2026 (UTC)
: Given that the community consensus here was not to replicate WikiNews within Wikiversity, I suggest thinking differently e.g., in terms of specific news-related projects you are interested in that have educational objectives that satisfy Wikiversity's mission. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:46, 5 September 2026 (UTC)

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

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

== Motivation and emotion - Student editing ==

We are underway with [[Motivation and emotion]] this semester (Aug - Nov), which will see ~150 students signing up to and edting [[Motivation and emotion/Book/2026]]. Please be friendly and help them out as they learn their way around.

Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:16, 10 August 2026 (UTC)

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

Currently, only waiting for four days is required for a user to become autoconfirmed. I am proposing that we include a minimum edit count of 10 edits (akin to Wikipedia) especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:01, 23 August 2026 (UTC)
: [[Wikiversity:Autoconfirmed users]]
: Are you suggesting an additional requirement? i.e., 4 days + 10 edits?
: How is it adjusted? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:57, 5 September 2026 (UTC)
:: Yes. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 01:30, 6 September 2026 (UTC)
:As a newly volunteered member, it doesn't seem unreasonable to me to require a certain number of edits to establish my bona fides. [[User:Cfm490|Cfm490]] ([[User talk:Cfm490|discuss]] • [[Special:Contributions/Cfm490|contribs]]) 17:53, 5 September 2026 (UTC)

== Bartending Course on Wikiversity ==

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

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

== Writing news here ==

I'm bringing up this discussion again because I think it is beneficial to the project since Wikinews is gone, thank you. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 03:17, 1 September 2026 (UTC)
: Given that the community consensus here was not to replicate WikiNews within Wikiversity, I suggest thinking differently e.g., in terms of specific news-related projects you are interested in that have educational objectives that satisfy Wikiversity's mission. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:46, 5 September 2026 (UTC)

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

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

:I am also in favor of this and we did discuss it pretty recently and came to a consensus on extending IA rights and lowering the administrative overhead, but not allowing indefinite at this juncture. From my perspective, since we discussed this so recently and nothing seems to have changed much, I personally would recommend holding off for a couple of years or until/unless there is some critical new information. Again, I would continue to support indef IA rights were it to come up again and think that at least two is also a sensible proposal. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:32, 6 September 2026 (UTC)</text>
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&lt;!-- MESSAGES GO BELOW --&gt;

== Motivation and emotion - Student editing ==

We are underway with [[Motivation and emotion]] this semester (Aug - Nov), which will see ~150 students signing up to and edting [[Motivation and emotion/Book/2026]]. Please be friendly and help them out as they learn their way around.

Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:16, 10 August 2026 (UTC)

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

Currently, only waiting for four days is required for a user to become autoconfirmed. I am proposing that we include a minimum edit count of 10 edits (akin to Wikipedia) especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:01, 23 August 2026 (UTC)
: [[Wikiversity:Autoconfirmed users]]
: Are you suggesting an additional requirement? i.e., 4 days + 10 edits?
: How is it adjusted? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:57, 5 September 2026 (UTC)
:: Yes. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 01:30, 6 September 2026 (UTC)
:As a newly volunteered member, it doesn't seem unreasonable to me to require a certain number of edits to establish my bona fides. [[User:Cfm490|Cfm490]] ([[User talk:Cfm490|discuss]] • [[Special:Contributions/Cfm490|contribs]]) 17:53, 5 September 2026 (UTC)

== Bartending Course on Wikiversity ==

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

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

== Writing news here ==

I'm bringing up this discussion again because I think it is beneficial to the project since Wikinews is gone, thank you. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 03:17, 1 September 2026 (UTC)
: Given that the community consensus here was not to replicate WikiNews within Wikiversity, I suggest thinking differently e.g., in terms of specific news-related projects you are interested in that have educational objectives that satisfy Wikiversity's mission. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:46, 5 September 2026 (UTC)

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

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

:I am also in favor of this and we did discuss it pretty recently and came to a consensus on extending IA rights and lowering the administrative overhead, but not allowing indefinite at this juncture. From my perspective, since we discussed this so recently and nothing seems to have changed much, I personally would recommend holding off for a couple of years or until/unless there is some critical new information. Again, I would continue to support indef IA rights were it to come up again and think that at least two is also a sensible proposal. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:32, 6 September 2026 (UTC)
::Responding to myself so that I don't derail: I would be interested/willing to be an indef IA. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:36, 6 September 2026 (UTC)</text>
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&lt;!-- MESSAGES GO BELOW --&gt;

== Motivation and emotion - Student editing ==

We are underway with [[Motivation and emotion]] this semester (Aug - Nov), which will see ~150 students signing up to and edting [[Motivation and emotion/Book/2026]]. Please be friendly and help them out as they learn their way around.

Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:16, 10 August 2026 (UTC)

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

Currently, only waiting for four days is required for a user to become autoconfirmed. I am proposing that we include a minimum edit count of 10 edits (akin to Wikipedia) especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:01, 23 August 2026 (UTC)
: [[Wikiversity:Autoconfirmed users]]
: Are you suggesting an additional requirement? i.e., 4 days + 10 edits?
: How is it adjusted? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:57, 5 September 2026 (UTC)
:: Yes. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 01:30, 6 September 2026 (UTC)
:As a newly volunteered member, it doesn't seem unreasonable to me to require a certain number of edits to establish my bona fides. [[User:Cfm490|Cfm490]] ([[User talk:Cfm490|discuss]] • [[Special:Contributions/Cfm490|contribs]]) 17:53, 5 September 2026 (UTC)

== Bartending Course on Wikiversity ==

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

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

== Writing news here ==

I'm bringing up this discussion again because I think it is beneficial to the project since Wikinews is gone, thank you. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 03:17, 1 September 2026 (UTC)
: Given that the community consensus here was not to replicate WikiNews within Wikiversity, I suggest thinking differently e.g., in terms of specific news-related projects you are interested in that have educational objectives that satisfy Wikiversity's mission. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:46, 5 September 2026 (UTC)

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

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

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

== Motivation and emotion - Student editing ==

We are underway with [[Motivation and emotion]] this semester (Aug - Nov), which will see ~150 students signing up to and edting [[Motivation and emotion/Book/2026]]. Please be friendly and help them out as they learn their way around.

Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:16, 10 August 2026 (UTC)

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

Currently, only waiting for four days is required for a user to become autoconfirmed. I am proposing that we include a minimum edit count of 10 edits (akin to Wikipedia) especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:01, 23 August 2026 (UTC)
: [[Wikiversity:Autoconfirmed users]]
: Are you suggesting an additional requirement? i.e., 4 days + 10 edits?
: How is it adjusted? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:57, 5 September 2026 (UTC)
:: Yes. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 01:30, 6 September 2026 (UTC)
:As a newly volunteered member, it doesn't seem unreasonable to me to require a certain number of edits to establish my bona fides. [[User:Cfm490|Cfm490]] ([[User talk:Cfm490|discuss]] • [[Special:Contributions/Cfm490|contribs]]) 17:53, 5 September 2026 (UTC)

== Bartending Course on Wikiversity ==

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

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

== Writing news here ==

I'm bringing up this discussion again because I think it is beneficial to the project since Wikinews is gone, thank you. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 03:17, 1 September 2026 (UTC)
: Given that the community consensus here was not to replicate WikiNews within Wikiversity, I suggest thinking differently e.g., in terms of specific news-related projects you are interested in that have educational objectives that satisfy Wikiversity's mission. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:46, 5 September 2026 (UTC)

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

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

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

== Motivation and emotion - Student editing ==

We are underway with [[Motivation and emotion]] this semester (Aug - Nov), which will see ~150 students signing up to and edting [[Motivation and emotion/Book/2026]]. Please be friendly and help them out as they learn their way around.

Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:16, 10 August 2026 (UTC)

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

Currently, only waiting for four days is required for a user to become autoconfirmed. I am proposing that we include a minimum edit count of 10 edits (akin to Wikipedia) especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:01, 23 August 2026 (UTC)
: [[Wikiversity:Autoconfirmed users]]
: Are you suggesting an additional requirement? i.e., 4 days + 10 edits?
: How is it adjusted? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:57, 5 September 2026 (UTC)
:: Yes. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 01:30, 6 September 2026 (UTC)
:As a newly volunteered member, it doesn't seem unreasonable to me to require a certain number of edits to establish my bona fides. [[User:Cfm490|Cfm490]] ([[User talk:Cfm490|discuss]] • [[Special:Contributions/Cfm490|contribs]]) 17:53, 5 September 2026 (UTC)
:I agree that adding an edit count requirement is a reasonable expectation before the user can become autoconfirmed. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 18:56, 6 September 2026 (UTC)

== Bartending Course on Wikiversity ==

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

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

== Writing news here ==

I'm bringing up this discussion again because I think it is beneficial to the project since Wikinews is gone, thank you. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 03:17, 1 September 2026 (UTC)
: Given that the community consensus here was not to replicate WikiNews within Wikiversity, I suggest thinking differently e.g., in terms of specific news-related projects you are interested in that have educational objectives that satisfy Wikiversity's mission. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:46, 5 September 2026 (UTC)

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

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

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

We are underway with [[Motivation and emotion]] this semester (Aug - Nov), which will see ~150 students signing up to and edting [[Motivation and emotion/Book/2026]]. Please be friendly and help them out as they learn their way around.

Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:16, 10 August 2026 (UTC)

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

Currently, only waiting for four days is required for a user to become autoconfirmed. I am proposing that we include a minimum edit count of 10 edits (akin to Wikipedia) especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:01, 23 August 2026 (UTC)
: [[Wikiversity:Autoconfirmed users]]
: Are you suggesting an additional requirement? i.e., 4 days + 10 edits?
: How is it adjusted? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:57, 5 September 2026 (UTC)
:: Yes. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 01:30, 6 September 2026 (UTC)
:As a newly volunteered member, it doesn't seem unreasonable to me to require a certain number of edits to establish my bona fides. [[User:Cfm490|Cfm490]] ([[User talk:Cfm490|discuss]] • [[Special:Contributions/Cfm490|contribs]]) 17:53, 5 September 2026 (UTC)
:I agree that adding an edit count requirement is a reasonable expectation before the user can become autoconfirmed. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 18:56, 6 September 2026 (UTC)
:+ 1 —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:40, 6 September 2026 (UTC)

== Bartending Course on Wikiversity ==

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

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

== Writing news here ==

I'm bringing up this discussion again because I think it is beneficial to the project since Wikinews is gone, thank you. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 03:17, 1 September 2026 (UTC)
: Given that the community consensus here was not to replicate WikiNews within Wikiversity, I suggest thinking differently e.g., in terms of specific news-related projects you are interested in that have educational objectives that satisfy Wikiversity's mission. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:46, 5 September 2026 (UTC)

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

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

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

== Motivation and emotion - Student editing ==

We are underway with [[Motivation and emotion]] this semester (Aug - Nov), which will see ~150 students signing up to and edting [[Motivation and emotion/Book/2026]]. Please be friendly and help them out as they learn their way around.

Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:16, 10 August 2026 (UTC)

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

Currently, only waiting for four days is required for a user to become autoconfirmed. I am proposing that we include a minimum edit count of 10 edits (akin to Wikipedia) especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:01, 23 August 2026 (UTC)
: [[Wikiversity:Autoconfirmed users]]
: Are you suggesting an additional requirement? i.e., 4 days + 10 edits?
: How is it adjusted? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:57, 5 September 2026 (UTC)
:: Yes. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 01:30, 6 September 2026 (UTC)
:As a newly volunteered member, it doesn't seem unreasonable to me to require a certain number of edits to establish my bona fides. [[User:Cfm490|Cfm490]] ([[User talk:Cfm490|discuss]] • [[Special:Contributions/Cfm490|contribs]]) 17:53, 5 September 2026 (UTC)
:I agree that adding an edit count requirement is a reasonable expectation before the user can become autoconfirmed. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 18:56, 6 September 2026 (UTC)
:+ 1 —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:40, 6 September 2026 (UTC)
:'''Weak support''' Generally reasonable, but I would caution that we should really make this clear for those instances where professors have students edit here and make it frictionless for them to get autoconfirmed status. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 19:42, 6 September 2026 (UTC)

== Bartending Course on Wikiversity ==

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

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

== Writing news here ==

I'm bringing up this discussion again because I think it is beneficial to the project since Wikinews is gone, thank you. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 03:17, 1 September 2026 (UTC)
: Given that the community consensus here was not to replicate WikiNews within Wikiversity, I suggest thinking differently e.g., in terms of specific news-related projects you are interested in that have educational objectives that satisfy Wikiversity's mission. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:46, 5 September 2026 (UTC)

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

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

:I am also in favor of this and we did discuss it pretty recently and came to a consensus on extending IA rights and lowering the administrative overhead, but not allowing indefinite at this juncture. From my perspective, since we discussed this so recently and nothing seems to have changed much, I personally would recommend holding off for a couple of years or until/unless there is some critical new information. Again, I would continue to support indef IA rights were it to come up again and think that at least two is also a sensible proposal. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:32, 6 September 2026 (UTC)
::Responding to myself so that I don't derail: I would be interested/willing to be an indef IA. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:36, 6 September 2026 (UTC)
: I made [[Wikiversity:Candidates for Interface Adminship]]. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 18:24, 6 September 2026 (UTC)</text>
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&lt;quiz&gt;
1111111-000000=1111111
90+10=100
&lt;/quiz&gt;
final work

&lt;quiz&gt;
10-2=8
212+8+220

&lt;quiz&gt;
22-1=21
23+21(11)=354</text>
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&lt;table class=&quot;ambox&quot; style=&quot;background-color: #e8f0fe;{{Text default color}}; border-left: 5px solid #1a73e8; border-collapse: collapse; width: 100%; margin: 1em 0; padding: 0.5em 1em; border: 1px solid #a8c7fa; border-left-width: 5px;&quot;&gt;&lt;tr&gt;&lt;td style=&quot;padding: 0.5em 0 0.5em 1.2em; vertical-align: middle; width: 40px;&quot;&gt;[[File:Exquisite-khelpcenter.png|40px]]&lt;/td&gt;&lt;td style=&quot;padding: 0.5em 1.2em; vertical-align: middle;&quot;&gt;'''This article discusses a legacy technology.''' ActionScript is officially deprecated and no longer actively used or supported following the **End-of-Life (EOL) of Adobe Flash Player on 31 December 2020**. Content built using ActionScript has been **blocked from running in Flash Player since 12 January 2021**, and all major web browsers have completely removed support in favour of open standards like [[TypeScript]], [[JavaScript_Programming|Javascript]] and WebAssembly.&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;


{{rightTOC}}
Welcome to Adobe Flash [[w:ActionScript|ActionScript]]! I'm glad you've decided to try and learn ActionScript, it is truly a wonderful programming language with plenty of potential in the domain of interactive media.

Firstly, I would like to introduce myself, as teachers do. I am Raven Storm, a young Canadian programmer who has been working in ActionScript for over three years. I have plenty of free time that I've turned into a lot of experience. As an active member of the WikiMedia community, I would like to contribute in whatever way I can by creating this basic tutorial.

So let's get started, shall we?

==Prerequisites==

Since ActionScript is a basic scripting language, there is no real need for any programming experience prior to this tutorial. Basic knowledge of HTML and computers in general are a plus!

==[[Portal:Learning Projects|Learning Projects]]==
Learning materials and [[Portal:Learning Projects|learning projects]] are located in the main Wikiversity namespace. Simply make a [[link]] to the name of the learning project (learning projects are independent pages in the [[Wikiversity:Namespaces|main namespace]]) and start writing!  
* ...
===ActionScript tutorial===
This tutorial will cover everything you need to get started. There are plenty of tutorials out there that cover complex and specific engines created in ActionScript: this is not (yet) a congolomeration of these tutorials (see websites like [http://www.kirupa.com/ Kirupa.com], [http://www.flashkit.com/tutorials/ Flashkit Tutorials], [http://www.actionscript.org/resources/categories/Tutorials/ ActionScript.org Tutorials]) but an introduction to ActionScript so that you can understand those tutorials!
*[[ActionScript:Introduction]]

==Enrolled==

Please sign below if you are participating in this topic. Use 4 tildes (~) to sign.
*[[User:Ravenstorm|Ravenstorm]] 01:20, 27 September 2006 (UTC)
*[[User:88.207.191.72|88.207.191.72]] 17:55, 27 March 2007 (UTC)
*--[[User:Xora K Joken|Xora]] 18:34, 9 April 2007 (UTC)
*--[[User:Kortex|Kortex]] 20:54, 14 December 2007 (UTC)
*--[[User:Cecil|Cecil]] 00:29, 11 May 2008 (UTC)
*--[[User:Gazooks113|Gazooks113]] 01:35, 28 November 2008 (UTC)
*''Eternal.hazard''
*--Thomas Bebbington[[Special:Contributions/97.118.217.119|97.118.217.119]] 06:23, 29 November 2008 (UTC)
*--k.krishnakanth reddy
*[[User:Hughveal|Hughveal]] ([[User talk:Hughveal|discuss]] • [[Special:Contributions/Hughveal|contribs]]) 16:28, 11 March 2014 (UTC)[[User:hughveal|hughveal]]12:27, 11 March 2014 (UTC)

==See also==
*[[b:Programming:Action script|Programming:Action script]] - at Wikibooks

[[Category:Flash ActionScript]]
[[Category:Adobe]]</text>
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== Introductory Ancient Greek Language ==
[[Image:Socrates Louvre.jpg|thumb|right|200px|Σωκράτης]]
[[Image:Bust Athena Velletri Glyptothek Munich 213.jpg|thumb|right|200px|Ἀθηνᾶ]]
Welcome to the course &quot;Introductory Ancient Greek Language&quot;, part of [[Topic:Foreign Language Learning|Foreign Language Learning]] and [[School:Language and Literature|Language and Literature school]], and the 1st course within [[Greek classics]].

Greek was the ''lingua franca'' of the Mediterranean world from the rise of the Hellenic states after the Persian War until the rise of Rome. Its basis as the uniting factor of the Greek city-states makes knowledge of the language and its history vital to an understanding of the rise of Greek culture in the Western World.

This course will prepare students to read Classical Greek texts by building a solid foundation in rudimentary grammar and vocabulary, as well as give a broad overview of its history. It will begin on a very basic level, so if you have some experience, you may choose to move on to a more advanced course, or assist in lesson plans with this one. However, even a seasoned reader of Greek may benefit from a basic review.

If you're coming here with no experience of the Ancient Greek language, then congratulations on your choice to begin learning it! You are in for an exciting adventure that will not only give you knowledge of a new language, but a new way of thinking, opening doors to understanding the roots of philosophy, science, and Western thought.

The course will be divided into several important divisions, each one hopefully no longer than four lessons followed by a review. The goal is to prepare the student with a foundation in Classical Greek, on which he or she can later build a higher fluency.

== Student Questions ==
If you happen to become stumped or just have a general question out of curiosity, then feel free to message any recent active member involved in creating this course. I intend to add much more to this page, but I don't have a huge amount of time to work on it. I am looking into adding some exercises for translation and adding some study guide outlines to later pages.

== History ==
* [[w:Neolithic_Greece|Lesson 1]] - Neolithic Greece
* [[w:Aegean_civilization|Lesson 2]] - Bronze Age Greece
* [[w:Ancient_Greece|Lesson 3]] - Ancient Greece
* [[w:Hellenistic period|Lesson 4]] - Hellenistic Greece
* [[Introductory Ancient Greek Language/History/Review|Review]]

== Grammar ==
===Alphabet, Breathings, Accents, Articles===
After having completed these first four lessons, the student would be able to read and write with Greek characters.  Some vocabulary will be introduced, but the goal will be to familiarize yourself with understanding the alphabet in order to begin learning the language.
* [[Introductory Ancient Greek Language/Lesson 1|Lesson 1]] - The Alphabet
* [[Introductory Ancient Greek Language/Lesson 2|Lesson 2]] - Breathings and Accents
* [[Introductory Ancient Greek Language/Lesson 3|Lesson 3]] - The Definite Article
* [[Introductory Ancient Greek Language/Lesson 4|Lesson 4]] - Pronouns
* [[Introductory Ancient Greek Language/Lesson 5|Lesson 5]] - Conjunctions
* [[Introductory Ancient Greek Language/Review|Review]]

===Introduction to Verbs and Nouns===
* [[Introductory Ancient Greek Language/Lesson 6|Lesson 6]] - Present, Active and Middle-Passive, Indicative
* [[Introductory Ancient Greek Language/Lesson 7|Lesson 7]] - First, Second, and Third Noun Declensions
* [[Introductory Ancient Greek Language/Lesson 8|Lesson 8]] - Basic Prepositions, Negation
* [[Introductory Ancient Greek Language/Lesson 9|Lesson 9]] - Present Indicative of &quot;To Be&quot;
* [[Introductory Ancient Greek Language/Review 2|Review]]

===Verb Forms of the Active Indicative===
* [[Introductory Ancient Greek Language/Lesson 10|Lesson 10]] - Imperfect, Active, Indicative
* [[Introductory Ancient Greek Language/Lesson 11|Lesson 11]] - Future, Active, Indicative
* [[Introductory Ancient Greek Language/Lesson 12|Lesson 12]] - Aorist (1st and 2nd), Active, Indicative
* [[Introductory Ancient Greek Language/Lesson 13|Lesson 13]] - Perfect, Active, Indicative
* [[Introductory Ancient Greek Language/Lesson 14|Lesson 14]] - Pluperfect, Active, Indicative
* [[Introductory Ancient Greek Language/Review 3|Review]] 

===Introduction to Adjectives===
* [[Introductory Ancient Greek Language/Lesson 15|Lesson 15]] - 2-1-2 Adjectives
* [[Introductory Ancient Greek Language/Lesson 16|Lesson 16]] - 3-1-3 Adjectives
* [[Introductory Ancient Greek Language/Lesson 17|Lesson 17]] - Participles
* [[Introductory Ancient Greek Language/Review 4|Review]] 

===More Moods ===
* [[Introductory Ancient Greek Language/Lesson 18|Lesson 18]] - Subjunctive
* [[Introductory Ancient Greek Language/Lesson 19|Lesson 19]] - Optative
* [[Introductory Ancient Greek Language/Lesson 20|Lesson 20]] - Imperative
* [[Introductory Ancient Greek Language/Lesson 21|Lesson 21]] - Infinitive
* [[Introductory Ancient Greek Language/Review 5|Review]] 

===Advanced Syntax===
* [[Introductory Ancient Greek Language/Lesson 22|Lesson 22]] - The Genitive Absolute
* [[Introductory Ancient Greek Language/Lesson 23|Lesson 23]] - Conditional Clauses
* [[Introductory Ancient Greek Language/Lesson 24|Lesson 24]] - Particles
* [[Introductory Ancient Greek Language/Review 6|Review]] 

== Vocabulary ==
===Unit 1: Basics===
* [[Introductory Ancient Greek Language/Vocabulary/Lesson 1|Lesson 1]] - Basic Sentences
* [[Introductory Ancient Greek Language/Vocabulary/Lesson 2|Lesson 2]] - Numbers 1 to 100
* [[Introductory Ancient Greek Language/Vocabulary/Lesson 3|Lesson 3]] - Days of the Week (Attic Calendar)
* [[Introductory Ancient Greek Language/Vocabulary/Lesson 4|Lesson 4]] - Time and Weather
* [[Introductory Ancient Greek Language/Vocabulary/Lesson 5|Lesson 5]] - 100 Common Verbs
* [[Introductory Ancient Greek Language/Vocabulary/Quiz 1|Quiz]]

===Unit 2: Nature===
* 

===Unit 3: Science===
*

===Unit 4: Mathematics===
*

== Resources ==
* [[Enabling Greek Characters on Your Keyboard|Typing Greek Text]]
* [[An Ancient Greek Word List]]
* [[wikt:Category:Ancient Greek lemmas|Wiktionary's Word List]]
* [[wikibooks:Ancient Greek|Ancient Greek in Wikibooks]]

== Literature ==
* [https://archive.org/details/newtestamentino00west/page/6/mode/2up| The Greek New Testament]
* [https://archive.org/details/septuagintversio1879bren/page/n15/mode/2up| The Septuagint]
* [https://archive.org/details/platosrepublicgr01plat/page/n23/mode/2up| The Republic]
* [https://archive.org/details/JL_Heiberg___EUCLIDS_ELEMENTS_OF_GEOMETRY/page/n5/mode/2up| Euclid's Elements]
* [https://archive.org/details/iliadmurray01homeuoft/page/n11/mode/2up| The Iliad]
* [https://archive.org/details/homersodysseyedi01home/page/n11/mode/2up| The Odyssey]

Please place any questions or concerns on the discuss page for this portal or message me directly via my talk page,
I only recently took up this project after finding it alone for so long, so I'd love to hear your input or address any questions you may have. [[User:Wobblywatch|Wobblywatch]] ([[User talk:Wobblywatch|discuss]] • [[Special:Contributions/Wobblywatch|contribs]]) 00:23, 8 April 2019 (UTC)
[[Category:Language introductions]][[Category:Ancient Greek Language]][[el:Τμήμα:Αρχαία Ελληνικά]]</text>
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    <title>Introductory Ancient Greek Language/Lesson 5</title>
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      <text bytes="4996" sha1="cb2lq6xbl97aq9mfrf4koh47v68qmzh" xml:space="preserve">== Conjunctions ==
A conjunction is an '''uninflected''' linguistic form that '''joins''' together sentences, '''clauses''', phrases, or words.

Greek conjunctions work like those in English, but they are used much more often and in a more subtle way. Greek tends to connect sentences and clauses rather than separate them. While in English we often mark the end of a sentence with a period, Greek prefers to use conjunctions such as &quot;and&quot;, &quot;but&quot;, or &quot;therefore&quot; to chain ideas.

===AND===
* καί: Used to connect words, clauses, and sentences as a conjunction. If used as an adverb, καί means even, also.
* τε (enclitic): Like καί, τε is used to link clauses and sentences. However, τε rarely links individual words in Greek prose. τε…καί in a sentence is a slightly weaker version of καί…καί, both…and. As a monosyllabic enclitic, τε rarely has an accent.
* δέ: This little word is used most often to delineate, and slightly contrast, a clause or sentence from the one that precedes it. How to translate this slight contrast depends upon context. Sometimes and works well, other times but. At still other times it is difficult to distinguish between the two, and the word is best left untranslated.
* μέν…δέ: Together, these two words mark a contrast between one word or clause, marked by μέν, and another, marked by δέ. It’s sometimes translated as on the one hand (μέν)…on the other hand (δέ). In other contexts, the μέν is best left untranslated, and the δέ translated as and or but. Often, however, μέν…δέ is not translated in English.
In Attic Greek, conjunctions that always follow the word that they link are called postpositive, which can never be the first word in a sentence. All the and words are postpositive except for καί. As a result of the frequency of postpositive conjunctions, the second word—or third, if it follows a noun with a definite article—is a conjunction in a clause or sentence. Consider the following examples: 
* χρήματα καὶ ὑπάρχοντα δίδομεν → We give money and property.
* δίδομεν τὰ σπέρματα καὶ δίδοτε τὸ ὕδωρ. → We give the seeds and you give the water.
* τὰ σπέρματα δίδομεν, ὑπάρχοντα δὲ δίδοτε. → We give the seeds and you give property.
* τὰ σπέρματα μὲν δίδομεν, ὕδωρ δὲ δίδοτε. → We give the seeds and you give water.
===AND…NOT===
* οὔτε/μήτε: and…not
**οὔτε is used with indicative verbs.
** μήτε is used with infinitives.
** Note that they are simply combinations of οὐ and μή with τε.
===BUT===
* ἀλλά: This conjunction expresses an opposition (but, yet) to a previous clause or sentence. It represents a stronger contrast than δέ.
* δέ: Depending on the context, this postpositive word can be translated as but. See discussion, above.
* μέν…δέ: Depending on the context, the postpositive μέν is left untranslated, and the δέtranslated as but. See discussion, above.
===OR===
* ἤ: Note the breathing mark and accent, which distinguishes this little word from ἡ, the feminine definite article.
* εἴτε… εἴτε: either…or
* μήτε… μήτε: neither…nor (with infinitives)
* οὔτε… οὔτε: neither…nor (with indicative verbs)
===BECAUSE===
* γάρ (postpositive)
* ὅτι
===THEREFORE===
* ἄρα
* διό
* οὖν (postpositive)
* τοίνυν (postpositive)
===OTHER IMPORTANT CONJUNCTIONS:===
* εἰ (εἴπερ): if
* ἐάν: if (w/subjunctive verbs)
* ἐπεί: after, since, when
* ἕως: until, while
* ἵνα: so that (w/subjunctive verbs)
* μέχρι: until
* ὅθεν: from where
* ὅτε: when
* πρίν: until (w/indicative verbs); before (w/ infinitive verbs)
* ὡς: like, because, while, where
==Elision==
It is common for the final vowel of a conjunction to be elided before a word beginning with a vowel—elision. Note the elisions of each second sentence in the following examples:
* εἴτε τὰ χρήματα οὐ δίδομεν, εἴτε τὰ ὑπάρχοντα οὐ δίδοτε.
* εἴτ’ οὐ δίδομεν τὰ χρήματα, εἴτ’ οὐ δίδοτε τὰ ὑπάρχοντα.
** Either we don’t give the money or you don’t give the property.
* οὐκ ἀποδίδοτε, ἄρα χρήματα οὐ δίδομεν.
* οὐκ ἀποδίδοτε, ἄρ’ οὐ δίδομεν χρήματα.
** You do not give (it) back, so/therefore we do not give money.
* ὅτε χρήματα ἀποδίδοτε, ὑπάρχοντα δίδομεν.
* ὅτ’ ἀποδίδοτε χρήματα, ὑπάρχοντα δίδομεν.
** When you give money back, we give property.
Note: ὅτι never elides, so ὅτ’ always = ὅτε.


[[Category:Lessons]]
[[el:Κλίσεις ρημάτων/Αρχαία Ελληνικά/Οριστική Ενεργητικής/Ενεστώτας]]</text>
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      <comment>/* Definition of  Electrical current */ Fuck this honestly.</comment>
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{{science}}
{{secondary}}
{{Lesson}}
{{75%done}}
&lt;big&gt;Welcome to this lesson on Electrical Current.&lt;/big&gt;
{{clear}}
==Purpose==
In this lesson, the flow of electrons, electrical current, is described and characterized in contexts of voltage, resistance, and simple, useful electric components.

==Definition of  Electrical current==  
An '''electric current''' is a flow of [[electric charge]].  In electric circuits this charge is often carried by moving [[electron]]s in a [[wire]]. Electric current is denoted by I and is measured in the unit amperes (A).

[[file:Ampere coulomb.svg|thumb|left|movement of electrons in a conductor]]An electrical current (or currents) is the movement of electrons in a conductor. Since electrons need not be bound to atoms, it is important to exclude atoms, conductors, resistors, and what have you in our definition of current flow.  
&lt;math&gt;I = \frac{Q}{t} &lt;/math&gt; where Q is charge (units of Coulombs), t is time. An amp is equal to one coulomb per second.  
{{clear}}
[[image:Electron_flow_in_a_conductor.svg|thumb|left|voltage movement of electrons]]A voltage or electromotive force causes movement of electrons in a conductor.
: Ohm's law &lt;math&gt;E = I R   &lt;/math&gt;
Hence, &lt;math&gt;I = \frac{E}{R}&lt;/math&gt; where E is voltage (volts), I is current (amps), and R is resistance (ohms).
{{clear}}

[[File:Solenoid-1.png|thumb|left|movement of electrons in a coil conductor]]Magnetic flux linkage: 
:&lt;math&gt;B = L I&lt;/math&gt;
Hence,
:&lt;math&gt;I = \frac{B}{L}&lt;/math&gt; . &lt;math&gt;\phi = -\frac{B}{L}&lt;/math&gt;
&lt;br&gt;
&lt;br&gt;
NOTE: One coulomb equals the charge on -6.2415 × 10^18 electrons (note that electrons are negatively charged).  
{{clear}}

==Electron flow excitement==

So, when electrons flow through a material, they cause anything from an insignificant quantity to a catastrophic amount of vibrational energy or heat to be created.

===Current carriers===
 Insulators do not normally allow electron flow.  
To overcome that effect, voltage would have to be raised tremendously high.  For a spark to cross the insulating gap of air between his finger and the office door, the cube farmer would have to build up thousands of volts of static potential. However, there is only the air there to be heated and so it simply has too few bits of matter to support heating.  Vacuum, as you already surmised, has only the electrons themselves and only during the course of their passage.   

 Semiconductors will begin conducting after only a little voltage 'encourages' the flow.  

Before, it acts like an insulator.  After, it acts like a conductor.  Resistors are designed to resist the flow of electrons.  They may be of many materials and, in fact, even conductors display the same characteristics, but to a far smaller extent.  Resistors are manufactured as identified components in circuitry.  Not surprisingly, the filaments in electric lights, electric stove coils, blow dryer elements and space heater coils are also resistors.  

 Conductors allow electrons to flow quite freely.  
They do, however, present some resistance to current flow.  Thus, you can cause them to heat up by 1) passing more than the designed current or 2) insulating them so that the tiny heat that is normally generated has nowhere to go and builds up to a potentially disastrous temperature.  

 Superconductors are conductors with the characteristic of passing electrons with negligible heating and resistance.  

The current state of technology insists that they be cooled to a very low temperature.  Should room temperature superconductors ever be created, there would be no power wasted over the (currently resistive) power lines between our power plants, and our cities and towns.  That would cut carbon emissions, well, a whole lot.

==Hot and hotter==
In a lightbulb, that heat becomes so great that the tungsten filament glows white hot.  Stove and blow dryer elements can glow red-hot.  A space heater may not glow but it can still burn the dickens out of you if you are not careful.  Light generated is directly related to temperature.  If two objects give off the same color of light, they share identical temperatures.  

The amount of heat energy disspated into the surrounding is considered heat energy loss can be calculated as
:&lt;math&gt;P_R = I^2 R(T)&lt;/math&gt;
:&lt;math&gt;R(T) = R_o+nT&lt;/math&gt; For Conductor
:&lt;math&gt;R(T) = R_oe^{nT}&lt;/math&gt; For Semi conductor

==Experimentation in current carriers==

Experimentation is used to determine a substance's resistance characteristics with regard to current flow.  Experimental results show that increasing the conductor size decreases its resistance proportionately.  So, double the cross-section of a wire and you halve its resistance.  

The unit of current is the Ampere or Amp for short.  It is defined as a specific number of electrons flowing across a specific point per unit time.  

==Current, Power and mathematic equations==
We have spent a great deal of time talking about current and its thermal effects.  Let's consider what we know.  When voltage goes up in a circuit, current goes up.  If I double the voltage and the resistance remains constant, I double the current.  I also double the vibrations I'm causing so I double the amount of heat I am adding.  

In other words, doubling voltage doubles the power generated in the form of heat.  This leads us to an equation.  Power equals Current times Voltage.  The symbol for Power is P, the symbol for Current is I, and the symbol for voltage is E.  We have 
:&lt;math&gt;P_V = \frac{W}{Q} \frac{Q}{t} = I V&lt;/math&gt;

As I double the resistance, I halve the current when constant voltage is applied.  Resistance and current are inversely related.  As I double the voltage, the current doubles as well.  In point of fact, Voltage equals Current times Resistance or E = I * R.  

Look up the definition of an Amp.  Calculate the value of 50 amps in the terms you found.  Provide at least three correct   answers.  
For extra credit, write a paper on Tesla (the inventor, not the band).  If you plagiarize Wiki, you will be found out.

==Reference==
* [[Wikipedia:Electric current|Electric current]]

[[Category:Physics]]
[[Category:Electronic engineering]]
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{{science}}
{{secondary}}
{{Lesson}}
{{75%done}}
&lt;big&gt;Welcome to this lesson on Electrical Current.&lt;/big&gt;
{{clear}}
==Purpose==
In this lesson, the flow of electrons, electrical current, is described and characterized in contexts of voltage, resistance, and simple, useful electric components.

==Definition of  Electrical current==  
An '''electric current''' is a flow of [[electric charge]].  In electric circuits this charge is often carried by moving [[electron]]s in a [[wire]]. Electric current is denoted by I and is measured in the unit amperes (A).

[[file:Ampere coulomb.svg|thumb|left|movement of electrons in a conductor]]An electrical current is the movement of electrons in a conductor. Since electrons need not be bound to atoms, it is important to exclude atoms, conductors, resistors, and what have you in our definition of current flow.  
&lt;math&gt;I = \frac{Q}{t} &lt;/math&gt; where Q is charge (units of Coulombs), t is time. An amp is equal to one coulomb per second.  
{{clear}}
[[image:Electron_flow_in_a_conductor.svg|thumb|left|voltage movement of electrons]]A voltage or electromotive force causes movement of electrons in a conductor.
: Ohm's law: &lt;math&gt;E = I R   &lt;/math&gt;
Hence, &lt;math&gt;I = \frac{E}{R}&lt;/math&gt; where E is voltage (volts), I is current (amps), and R is resistance (ohms).
{{clear}}

[[File:Solenoid-1.png|thumb|left|movement of electrons in a coil conductor]] 
:&lt;math&gt;B = L I&lt;/math&gt;
Hence,
:&lt;math&gt;I = \frac{B}{L}&lt;/math&gt; . &lt;math&gt;\phi = -\frac{B}{L}&lt;/math&gt;
&lt;br&gt;
&lt;br&gt;
NOTE: One coulomb equals the charge on -6.2415 × 10^18 electrons (note that electrons are negatively charged).  
{{clear}}

==Electron flow excitement==

So, when electrons flow through a material, they cause anything from an insignificant quantity to a catastrophic amount of vibrational energy or heat to be created.

===Current carriers===
 Insulators do not normally allow electron flow.  
To overcome that effect, voltage would have to be raised tremendously high.  For a spark to cross the insulating gap of air between his finger and the office door, the cube farmer would have to build up thousands of volts of static potential. However, there is only the air there to be heated and so it simply has too few bits of matter to support heating.  Vacuum, as you already surmised, has only the electrons themselves and only during the course of their passage.   

 Semiconductors will begin conducting after only a little voltage 'encourages' the flow.  

Before, it acts like an insulator.  After, it acts like a conductor.  Resistors are designed to resist the flow of electrons.  They may be of many materials and, in fact, even conductors display the same characteristics, but to a far smaller extent.  Resistors are manufactured as identified components in circuitry.  Not surprisingly, the filaments in electric lights, electric stove coils, blow dryer elements and space heater coils are also resistors.  

 Conductors allow electrons to flow quite freely.  
They do, however, present some resistance to current flow.  Thus, you can cause them to heat up by 1) passing more than the designed current or 2) insulating them so that the tiny heat that is normally generated has nowhere to go and builds up to a potentially disastrous temperature.  

 Superconductors are conductors with the characteristic of passing electrons with negligible heating and resistance.  

The current state of technology insists that they be cooled to a very low temperature.  Should room temperature superconductors ever be created, there would be no power wasted over the (currently resistive) power lines between our power plants, and our cities and towns.  That would cut carbon emissions, well, a whole lot.

==Hot and hotter==
In a lightbulb, that heat becomes so great that the tungsten filament glows white hot.  Stove and blow dryer elements can glow red-hot.  A space heater may not glow but it can still burn the dickens out of you if you are not careful.  Light generated is directly related to temperature.  If two objects give off the same color of light, they share identical temperatures.  

The amount of heat energy disspated into the surrounding is considered heat energy loss can be calculated as
:&lt;math&gt;P_R = I^2 R(T)&lt;/math&gt;
:&lt;math&gt;R(T) = R_o+nT&lt;/math&gt; For Conductor
:&lt;math&gt;R(T) = R_oe^{nT}&lt;/math&gt; For Semi conductor

==Experimentation in current carriers==

Experimentation is used to determine a substance's resistance characteristics with regard to current flow.  Experimental results show that increasing the conductor size decreases its resistance proportionately.  So, double the cross-section of a wire and you halve its resistance.  

The unit of current is the Ampere or Amp for short.  It is defined as a specific number of electrons flowing across a specific point per unit time.  

==Current, Power and mathematic equations==
We have spent a great deal of time talking about current and its thermal effects.  Let's consider what we know.  When voltage goes up in a circuit, current goes up.  If I double the voltage and the resistance remains constant, I double the current.  I also double the vibrations I'm causing so I double the amount of heat I am adding.  

In other words, doubling voltage doubles the power generated in the form of heat.  This leads us to an equation.  Power equals Current times Voltage.  The symbol for Power is P, the symbol for Current is I, and the symbol for voltage is E.  We have 
:&lt;math&gt;P_V = \frac{W}{Q} \frac{Q}{t} = I V&lt;/math&gt;

As I double the resistance, I halve the current when constant voltage is applied.  Resistance and current are inversely related.  As I double the voltage, the current doubles as well.  In point of fact, Voltage equals Current times Resistance or E = I * R.  

Look up the definition of an Amp.  Calculate the value of 50 amps in the terms you found.  Provide at least three correct   answers.  
For extra credit, write a paper on Tesla (the inventor, not the band).  If you plagiarize Wiki, you will be found out.

==Reference==
* [[Wikipedia:Electric current|Electric current]]

[[Category:Physics]]
[[Category:Electronic engineering]]
[[Category:Unused Electronic engineering content]]</text>
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    <title>BCP/Waldsteinia fragarioides</title>
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'''''Waldsteinia fragarioides'''''
{{Bloom clock plant top|
| Scientific name = Waldsteinia fragarioides
| Common name = Appalachian Barren Strawberry
| main image = Waldsteinia fragarioides 15 (5097400745).jpg
| main image caption = Yellow flowering plant showing the distinct 5-parted flowers and trifoliate leaf structure of the North American native species.
| Habit = Clump-forming rhizomatous perennial
| Flower Structure = Pentamerous symmetry with 5 yellow petals and 5 sepals; lacks an epicalyx.
| Foliage = Glossy green trifoliate leaves with crenate margins and wedge-shaped leaflets.
| Stem = Leafless flowering stalks (peduncles) arising directly from basal clusters.
| Scent = None
| Growing Conditions = Partial shade to full shade; moist, organic-rich well-drained soils.
| Fruit = Collection of dry achenes.
| Life Cycle = Perennial
| Similar Plants = Waldsteinia ternata (creeping above-ground runners, has epicalyx), Waldsteinia geoides (simple lobed leaves).
| Included Subclasses =
| Global temperate seasons = {{bcpgt/4}}, {{bcpgt/5}}
| Higher taxa = 
| Cookbook link = 
| General information = 
| Higher key = 
| Lower key = 
| Image needed = 
| version tracking for top template (for robotic use) = 8.11.17
}}
&lt;noinclude&gt;
&lt;!----------------EXTRA IMAGES AND REGIONAL DATA  ----------------------------&gt;
{{bloom clock plant middle|
| image 1 = Waldsteinia fragarioides.png
| image 1 caption = Illustration
| image 2 = Waldsteinia fragarioides WFNY-099.jpg
| image 2 caption = 1918 image showing the low, ground-hugging basal foliage.
| image 3 = 
| image 3 caption = 
| Southeastern Pennsylvania = {{bcp/sepa/gp}} {{bcpm/sepa/4}}, {{bcpm/sepa/5}}
| London, England = 
| New Hampshire = 
| Southwest Oregon = 
| Central Pennsylvania = 
| Prague = 
| Central Bohemia = 
| South Bohemia = 
| Manchester, England = 
| Western Bohemia = 
| Victoria, Australia = 
| Moravia-Silesia = 
| Czech name = 
| Aurora, Colorado = 
| New Region 6 = 
| New Region 7 = 
| New Region 8 = 
| New Region 9 = 
| New Region 10 = 
| New Region 11 = 
| New Region 12 = 
| New Region 13 = 
| New Region 14 = 
| New Region 15 = 
| version tracking for middle template (for robotic use) = 8.5.12
}}
&lt;!---- TAXONOMY AND IDENTIFICATION (ADDITIONAL FIELDS MAY BE AVAILABLE ON THE CURRENT TEMPLATE VERSION) ----&gt;
{{bloom clock plant bottom|
| taxa level (genus, species, variety, color) =  species
| color variants profiled = 
| white flowers = 
| pink flowers = 
| red flowers = 
| orange flowers = 
| yellow flowers = y
| green flowers = 
| blue flowers = 
| purple flowers = 
| brown flowers = 
| black flowers = 
| insect pollinated = y
| wind pollinated = 
| bird pollinated = 
| water pollinated = 
| self pollinated = 
| herbaceous = y
| woody = 
| forb = y
| shrub = 
| tree = 
| vine = 
| emergent aquatic = 
| submerged aquatic = 
| floating aquatic = 
| graminoid = 
| monocot = 
| dicot = y
| conifer = 
| family = Rosaceae
| genus = Waldsteinia
| species = fragarioides
| armed (yes if armed) = 
| leaf complexity (simple, pinnately compound, palmately compound, trifoliate) = trifoliate
| leaf arrangement (opposite, alternate, whorled, basal only, none) = basal only
| fruits present when flowering (yes if possible) = 
| leaves absent when flowering (yes if possible) = 
| lobes (pinnate, palmate, none) = none
| deciduous/evergreen/semi-evergreen = evergreen
| petiolate/sessile = petiolate
| leaf veination (pinnate, palmate, linear) = palmate
| version tracking for bottom template (for robotic use) = 8.11.17
}}

{{bloom clock plant hardiness|
| USDA 1 = 
| USDA 2 = 
| USDA 3 = 
| USDA 4 = y
| USDA 5 = y
| USDA 6 = y
| USDA 7 = y
| USDA 8 = y
| USDA 9 = 
| USDA 10 = 
| USDA 11 = 
| tropical = 
| dry soil = 
| wet soil = 
| full sun = 
| part sun = y
| shade = y
| version tracking for hardiness template (for robotic use) = 8.11.17
}}

{{bcp-8.11.17}}

&lt;/noinclude&gt;</text>
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    <title>Continuum mechanics/Stress-strain relation for thermoelasticity</title>
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| colspan=&quot;2&quot; style=&quot;width:80%; horizontal-align:right; vertical-align:top; border:1px solid Sienna; background-color:White;{{Text default color}};&quot; |
&lt;div style=&quot;border-bottom:1px solid Sienna; background-color:Wheat;{{Text default color}}; padding:0.2em 0.5em 0.2em 0.5em; font-size:100%; font-weight:bold;&quot;&gt;
Relation between Cauchy stress and Green strain
&lt;/div&gt;
&lt;div style=&quot;padding:2em 5em 0em 3em;&quot;&gt; 

Show that, for thermoelastic materials, the Cauchy stress can be expressed in terms of the Green strain as
:&lt;math&gt;
    \boldsymbol{\sigma} = \rho~\boldsymbol{F}\cdot\frac{\partial e}{\partial \boldsymbol{E}}\cdot\boldsymbol{F}^T ~.
  &lt;/math&gt;
&lt;/div&gt;
|}

'''Proof:'''

Recall that the Cauchy stress is given by
:&lt;math&gt;
  \boldsymbol{\sigma} = \rho~\frac{\partial e}{\partial \boldsymbol{F}}\cdot\boldsymbol{F}^T 
  \qquad \implies \qquad
  \sigma_{ij} = \rho~\frac{\partial e}{\partial F_{ik}}F^T_{kj} 
              = \rho~\frac{\partial e}{\partial F_{ik}}F_{jk}  ~.
&lt;/math&gt;
The Green strain &lt;math&gt;\boldsymbol{E} = \boldsymbol{E}(\boldsymbol{F}) = \boldsymbol{E}(\boldsymbol{U})&lt;/math&gt; and 
&lt;math&gt;e = e(\boldsymbol{F},\eta) = e(\boldsymbol{U},\eta)&lt;/math&gt;.  Hence, using the chain rule,
:&lt;math&gt;
  \frac{\partial e}{\partial \boldsymbol{F}} = \frac{\partial e}{\partial \boldsymbol{E}}:\frac{\partial \boldsymbol{E}}{\partial \boldsymbol{F}}
  \qquad \implies \qquad
  \frac{\partial e}{\partial F_{ik}} = \frac{\partial e}{\partial E_{lm}}~\frac{\partial E_{lm}}{\partial F_{ik}} ~.
&lt;/math&gt;
Now,
:&lt;math&gt;
  \boldsymbol{E} = \frac{1}{2}(\boldsymbol{F}^T\cdot\boldsymbol{F} - \boldsymbol{\mathit{1}}) 
  \qquad \implies \qquad
  E_{lm} = \frac{1}{2}(F^T_{lp}~F_{pm} - \delta_{lm}) 
         = \frac{1}{2}(F_{pl}~F_{pm} - \delta_{lm}) ~.
&lt;/math&gt;
Taking the derivative with respect to &lt;math&gt;\boldsymbol{F}&lt;/math&gt;, we get
:&lt;math&gt;
  \frac{\partial \boldsymbol{E}}{\partial \boldsymbol{F}} = \frac{1}{2}\left(\frac{\partial \boldsymbol{F}^T}{\partial \boldsymbol{F}}\cdot\boldsymbol{F} +
       \boldsymbol{F}^T\cdot\frac{\partial \boldsymbol{F}}{\partial \boldsymbol{F}}\right)
  \qquad \implies \qquad
  \frac{\partial E_{lm}}{\partial F_{ik}} = \frac{1}{2}\left(\frac{\partial F_{pl}}{\partial F_{ik}}~F_{pm} +
       F_{pl}~\frac{\partial F_{pm}}{\partial F_{ik}}\right) ~.
&lt;/math&gt;
Therefore,
:&lt;math&gt;
  \boldsymbol{\sigma} = \frac{1}{2}~\rho~\left[\frac{\partial e}{\partial \boldsymbol{E}}:
      \left(\frac{\partial \boldsymbol{F}^T}{\partial \boldsymbol{F}}\cdot\boldsymbol{F} +
       \boldsymbol{F}^T\cdot\frac{\partial \boldsymbol{F}}{\partial \boldsymbol{F}}\right)\right]\cdot\boldsymbol{F}^T 
  \qquad \implies \qquad
  \sigma_{ij} = \frac{1}{2}~\rho~\left[\frac{\partial e}{\partial E_{lm}}
      \left(\frac{\partial F_{pl}}{\partial F_{ik}}~F_{pm} +
       F_{pl}~\frac{\partial F_{pm}}{\partial F_{ik}}\right)\right]~F_{jk} ~.
&lt;/math&gt;
Recall,
:&lt;math&gt;
  \frac{\partial \boldsymbol{A}}{\partial \boldsymbol{A}} \equiv \frac{\partial A_{ij}}{\partial A_{kl}} = 
  \delta_{ik}~\delta_{jl} \qquad \text{and} \qquad
  \frac{\partial \boldsymbol{A}^T}{\partial \boldsymbol{A}} \equiv \frac{\partial A_{ji}}{\partial A_{kl}} = 
  \delta_{jk}~\delta_{il} ~.
&lt;/math&gt;
Therefore,
:&lt;math&gt;
  \sigma_{ij} = \frac{1}{2}~\rho~\left[\frac{\partial e}{\partial E_{lm}}
      \left(\delta_{pi}~\delta_{lk}~F_{pm} +
       F_{pl}~\delta_{pi}~\delta_{mk}\right)\right]~F_{jk} 
   = \frac{1}{2}~\rho~\left[\frac{\partial e}{\partial E_{lm}}
      \left(\delta_{lk}~F_{im} +
       F_{il}~\delta_{mk}\right)\right]~F_{jk} 
&lt;/math&gt;
or, 
:&lt;math&gt;
  \sigma_{ij} = \frac{1}{2}~\rho~\left[\frac{\partial e}{\partial E_{km}}~F_{im} +
       \frac{\partial e}{\partial E_{lk}}~F_{il}\right]~F_{jk} 
  \qquad \implies \qquad
  \boldsymbol{\sigma} = \frac{1}{2}~\rho~\left[\boldsymbol{F}\cdot\left(\frac{\partial e}{\partial \boldsymbol{E}}\right)^T +
       \boldsymbol{F}\cdot\frac{\partial e}{\partial \boldsymbol{E}}\right]\cdot\boldsymbol{F}^T 
&lt;/math&gt;
or,
:&lt;math&gt;
  \boldsymbol{\sigma} = \frac{1}{2}~\rho~\boldsymbol{F}\cdot\left[\left(\frac{\partial e}{\partial \boldsymbol{E}}\right)^T +
       \frac{\partial e}{\partial \boldsymbol{E}}\right]\cdot\boldsymbol{F}^T ~.
&lt;/math&gt;
From the symmetry of the Cauchy stress, we have
:&lt;math&gt;
   \boldsymbol{\sigma} = (\boldsymbol{F}\cdot\boldsymbol{A})\cdot\boldsymbol{F}^T \qquad \text{and} \qquad
   \boldsymbol{\sigma}^T = \boldsymbol{F}\cdot(\boldsymbol{F}\cdot\boldsymbol{A})^T = \boldsymbol{F}\cdot\boldsymbol{A}^T\cdot\boldsymbol{F}^T 
   \qquad \text{and} \qquad \boldsymbol{\sigma} = \boldsymbol{\sigma}^T \implies \boldsymbol{A} = \boldsymbol{A}^T ~.
&lt;/math&gt;
Therefore, 
:&lt;math&gt;
   \frac{\partial e}{\partial \boldsymbol{E}} = \left(\frac{\partial e}{\partial \boldsymbol{E}}\right)^T
&lt;/math&gt;
and we get
:&lt;math&gt;
  {
  \boldsymbol{\sigma} = ~\rho~\boldsymbol{F}\cdot\frac{\partial e}{\partial \boldsymbol{E}}\cdot\boldsymbol{F}^T ~.
  }
&lt;/math&gt;


{{subpage navbar}}

[[Category:Continuum mechanics]]</text>
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==Brezhoneg Tri/Lesson 1:Possession==
===You will learn===

*How to say &quot;I have&quot;
*How to ask &quot;Have you got something&quot;

===Kentell/Lesson===

In English, you say the verb &quot;to have&quot; to say you have something.&lt;br&gt;
In Breton, the literal translation is ''There is ___ to-me''
&lt;br&gt;&lt;br&gt;
'''Emañ ... din.''' or '''Emañ din ... .''' 
&lt;br&gt;&lt;br&gt;
*'''Emañ''' - ''there is''&lt;br&gt;
*'''din''' - ''to-me''&lt;br&gt;
&lt;br&gt;
&lt;br&gt;
*''to-me'' - '''din'''
*''to-you'' - '''dit'''
*''to-him'' - '''dezhañ'''
*''to-her'' - '''dezhi'''
*''to-us'' -  '''deomp'''
*''to-you'' (pl.) - '''deoc'h'''
*''to-them'' -  '''dezho'''
&lt;br&gt;
Then when placed with '''Emañ''' ''there is'' they become:&lt;br&gt;

*'''Emañ ____ din'''   -  ''There is ____ to me'' = ''I have ____''
*'''Emañ ____ dit'''    -  ''There is ____ to you'' = ''You have ____''
*'''Emañ ____ dezhañ'''  -  ''There is ____ to him'' = ''He has ____''
*'''Emañ ____ dezhi'''  -  ''There is ____ to her'' = ''She has ____''
*'''Emañ ____ deomp'''    -  ''There is ____ to us'' = ''We have ____''
*'''Emañ ____ deoc'h'''  -  ''There is ____ to you'' (pl.) = ''You'' (pl.) ''has ____''
*'''Emañ ____ dezho'''  -  ''There is ____ to them'' = ''they have ____''

&lt;br&gt;If you wish to ask ''Do you have?'' you make the form as in other questions&lt;br&gt;

*'''Eus _____ dit?''' - ''Is there ____ to you?'' = ''Do you have ____?''

===Skouer/Examples===

*'''Ur pluen 'zo dit? Ez eus. Emañ ur pluen din.'''
**''Is there a pen to-you? There is. There is a pen to-me''
***''Do you have a pen? Yes, I have a pen.'' 

===Poelladennoù/Exercises===

Make up 5 examples of your own, using the format shown above. 


|}

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[[Category: Breton]]</text>
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== You will learn ... / {{font|color=blue|Te a zesk ...}} ==
* Vocabulary
** Going out
** Bonfire, music and dance
** In a tavern
** Let's go back home ...

== Goueliañ / Going out ==

==== A-raok mont / Before leaving ====
{|width=&quot;100%&quot; border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; style=&quot;background:transparent;color:inherit;border-collapse:collapse&quot;
|-
!style=&quot;width:50%;&quot;|Brezhoneg!!style=&quot;width:50%;&quot;|English
|-
| Da belec'h ez aimp da nozhvezhiñ fenoz ?
| Where do we go out tonight ?
|-
| Nozhvezhiñ
| To go out (lit. &quot;''to spend the evening''&quot;)
|-
| Deomp e kêr da nozhvezhiñ.
| Let's find some place in town.
|-
| Amañ e-kichen.
| Close around here.
|-
| War an aod.
| On the shore.
|-
| Du-hont.
| Overthere.
|-
| Deomp da Vrest / da Wiseni / da Naoned / da Roazhon.
| Let's go to Brest / to Guisseni / to Nantes / to Rennes.
|-
| Deomp d'ober un tamm tro d'ar fest-noz.
| Let's go and see the fest-noz for a while.
|-
| d'ar c'hoariva.
| to the theater.
|-
| d'ar sinema.
| to the movie.
|-
| d'ar voest-noz / d'an toull-noz.
| to the night-club.
|-
| d'ar sonadeg.
| to the concert.
|-
| d'ar gouel-meur (liester : gouelioù-meur).
| to the festival (plural : festivals).
|-
| d'an Erer Kozh.
| to the festival &quot;Erer Kozh&quot; (in French &quot;''Festival des vieilles charrues''&quot;, a music festival that happens every year in Carhaix).
|-
| da Yaouvezhioù ar Porzh.
| to the &quot;Port Thursdays&quot; (in French &quot;''Jeudis du Port''&quot;, musical evenings that happen every summertime thursday in Brest) .
|-
| da Ouel Erwan.
| to the Saint Yves feast (in French &quot;Fest-Yves&quot;, equivalent to &quot;Saint Patrick&quot;).
|-
| Da nav eur e krogo.
| It will start at nine PM.
|-
| Piv 'zo oc'h aozañ ?
| Who organizes ?
|-
| Ha penaos ez imp di ?
| And how do we get there ?
|-
| War droad.
| By foot.
|-
| Gant ar c'harr (-tan).
| By car (lit. ''Karr-tan'' = Car-fire).
|-
| O c'hoari biz-meud.
| Hitch-hiking.
|-
| Gant un taksi.
| By taxi.
|-
| Piv a zeuy ganimp ? Pipi, Fañch ha Soaz.
| Who will come with us ? Peter, Francis and Francoise.
|-
| Piv a vlenio fenoz ?
| Who will drive tonight
|-
| Plijadur 'vo !
| We will have a good time !
|}

==== Mont e-barzh / At entrance ====
{| border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; style=&quot;width:100%;background:transparent;color:inherit;border-collapse:collapse&quot;
|-
!style=&quot;width:50%;&quot;|Brezhoneg!!style=&quot;width:50%;&quot;|English
|-
| Pegement eo mont e-barzh ?
| How much is the entrance ?
|-
| 5 € eo mont e-barzh.
| It's 5 €.
|-
| Ne goust netra mont e-barzh.
| Entrance is free.
|-
| Evit mann eo.
| It's for free.
|-
| Lakaet e vo ur siell dimp.
| They will mark us with a stamp.
|}

==== En em gavout ha kejañ gant tud / Meeting people ====
{| border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; style=&quot;width:100%;background:transparent;color:inherit;border-collapse:collapse&quot;
|-
!style=&quot;width:50%;&quot;|Brezhoneg!!style=&quot;width:50%;&quot;|English
|-
| Penaos emañ ar bed ganeoc’h ?
| How are you? (''Lit.'': “How is the world with you?”)
|-
|colspan=&quot;2&quot;|[[Image:Penaos eman ar bed ganeoch.ogg|Sound]]
|-
| Mat kenañ !
| Fine!
|-
| Mat awalc’h. 
| Well enough. / Okay.
|-
| Dreist ! Brutal !
| Grand! / Excellent!
|-
|colspan=&quot;2&quot;|[[Image:Mat ar jeu.ogg|Sounds]]
|-
| Erru out a-benn ar fin !
| Now, here you are finally !
|-
| Sell 'ta piv 'zo aze !
| Look who's coming !
|-
| Pell 'zo n'em boa ket gwelet ac'hanout !
| It's been some time since I last saw you !
|-
| Plijadur am eus o welout ac'hanout adarre !
| I'm happy to see you again !
|-
| Penaos 'mañ kont ganit abaoe ar wech all ?
| How are you since last time ?
|-
| En em bleud on !
| I'm in good shape !
|-
| Petra eo da vicher ? / Petore micher eo da hini ?
| What is your job ?
|-
| Baraer on.
| I am a baker.
|-
| Dilabour on.
| I am on the dole.
|-
| Kelenner / Martolod / Studier / Ijinour / Teknikour / Muziker
| Teacher / Sailor / Student / Engineer / Technician / Musician
|-
| War ma leve.
| Retired.
|-
| Brav eo an amzer.
| We have a nice weather.
|}

=== Bonfire, music and dance ===

==== Tantad ha tan-harvest / Bonfire and firework ====
{| border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; style=&quot;width:100%;background:transparent;color:inherit;border-collapse:collapse&quot;
|-
!style=&quot;width:50%;&quot;|Brezhoneg!!style=&quot;width:50%;&quot;|English
|-
| An tantad
| The bonfire
|-
| Kaer eo an tantad evit ar bloaz-mañ !
| The bonfire is beautiful this year !
|-
| An tan-arvest
| The firework
|-
|}

==== Ar sonerezh / Music ====
{| border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; style=&quot;width:100%;background:transparent;color:inherit;border-collapse:collapse&quot;
|-
!style=&quot;width:50%;&quot;|Brezhoneg!!style=&quot;width:50%;&quot;|English
|-
| Piv eo an arzourien ?
| Who are the artists ?
|-
| Piv 'zo o kanañ ?
| Who is singing ?
|-
| Piv 'zo o seniñ ?
| Who is playing music ?
|-
| Mona 'zo o son gitar / Mona 'zo o seniñ gitar
| Mona is playing gitar
|-
| Nolwenn 'zo o kanañ
| Nolwenn is singing
|-
| Suzanna zo o c'hoari gitar-bout
| Suzanna plays bass
|-
| Anna-Laora a zo ouzh e zaboulin
| Anna-Laora is near her drum
|-
| Gwilhom a lak e zikadrakoù da strakal
| William plays his &quot;castagnets&quot;
|-
| Bouzarus e' ar sonerezh !
| The music is deafening !
|-
| Re greñv e' ar muzik !
| The music is too loud !
|-
| Kae da lâret da baotr ar sono izelaat ar son !
| Go and tell to the sound technician to lower the sound !
|-
| Pebezh kanerien vat int !
| How good are the singers !
|-
| Pebezh sonerien vat int !
| How good are the musicians !
|-
| War al leurenn emañ ar strollad &quot;Pop-Korn&quot;
| The group &quot;Pop-Corn&quot; is now on scene
|-
| Pevar 'maint, un' e &quot;pop korn&quot; !
| They are four of them, one in each corner (''Breton play on words : &quot;each corner&quot; = &quot;pep korn&quot;'')
|-
| Startijenn 'zo ganto !
| They play with energy !
|-
|}
     
==== Dañsal / Dancing ====
{| border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; style=&quot;width:100%;background:transparent;color:inherit;border-collapse:collapse&quot;
|-
!style=&quot;width:50%;&quot;|Brezhoneg!!style=&quot;width:50%;&quot;|English
|-
| Dont a ri da zañsal / da goroll ?
| Will you dance ?
|-
| Pegen brav e tañsez / e korollez !
| You dance really well !
|-
| Dañsal a ra an holl / Koroll a ra an holl
| Everybody is dancing
|-
| Dañsal a ri ar salsa ganin ? Ya, laouenn ! / Chaous ganit !
| Will you dance the salsa with me ? Yes, I'd like it ! / No way !
|-
| an tango / al lamm-bada / al laride (laridenn) / kof-ha-kof (''frot-bouzelloù'')
| the tango / the lambada (''lamm'' = jump) / the laridé / belly-to-belly (''rub-bowell'')
|-
| ar bal-a-daou / an dro / ar c'has-a-barzh / an hanter-dro / an dañs plin
| the bal-for-two / the &quot;an dro&quot; / the kas-a-barzh / the &quot;hanter-dro&quot; / the &quot;plin&quot; dance
|-
| an dañs fisel / an dañs-tro (pe dañs Kernev pe c'hoazh ar gavotenn) / ar paz-doubl / ar c'hostez-'r-c'hoad
| The &quot;fisel&quot; dance / the gavotte / the paso-doble / the kost-'r-c'hoad
|-
| Aes e' da zañsal
| It's easy to dance
|-
| Pebezh dañserien vat int !
| How good are these dancers !
|-
| Plijadur 'zo amañ ! / Amañ 'zo begon !
| It's lively here !
|-
|}

=== En tavarn / In a tavern ===

==== Ostaleri / Tavern ====
{| border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; style=&quot;width:100%;background:transparent;color:inherit;border-collapse:collapse&quot;
|-
!style=&quot;width:50%;&quot;|Brezhoneg!!style=&quot;width:50%;&quot;|English
|-
| Deomp 'ta d'an ostaleri
| Let's go to the pub
|-
| Deomp 'ta ouzh ar c'hontouer
| Let's go to the bar
|-
| Sec'h eo ma c'horzailhenn !
| My throat is dry !
|-
| Evañ
| To drink
|-
| Petra 'z po da evañ ?
| What will you drink ?
|-
| Ur werennad (ur voutailhad) dour, mar plij !
| A glass (a bottle) of water, please !
|-
| gwinn / sistr / chouchenn (chufere) / bier
| wine / cider / mead / beer
|-
| Ur banne (bannac'h) chug avaloù
| Some apple juice
|-
| Sug orañjez / kafe / te / dour-pik (limez)
| Orange juice / coffee / tea / limonade
|-
| Dour-melar / Kafe tomm
| Mineral water / Hot coffee
|-
| Ha bier Breizh 'zo ?
| And there is Breton beer ?
|-
| Lak ur banne bier din
| Pour a glass of beer for me
|-
|}

==== Debriñ / Food ====
{| border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; style=&quot;width:100%;background:transparent;color:inherit;border-collapse:collapse&quot;
|-
!style=&quot;width:50%;&quot;|Brezhoneg!!style=&quot;width:50%;&quot;|English
|-
| Mat eo ar boued
| The food is good
|-
| Ur grampouezhenn 'po ?
| Do you want a pancake ?
|-
| Ur grampouezhenn gant sukr 'po ?
| Do you want a pancake with sugar ?
|-
| Gant amann ha sukr / gant chokolad / gant kaotigell
| With butter and sugar / with chocolate / with jam
|-
| Ya, ur grampouezhenn gant sukr am bo, mar plij !
| Yes, I will have a pancake with sugar, please !
|-
|}

==== Paeañ / The bill ====
{| border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; style=&quot;width:100%;background:transparent;color:inherit;border-collapse:collapse&quot;
|-
!style=&quot;width:50%;&quot;|Brezhoneg!!style=&quot;width:50%;&quot;|English
|-
| Pegement eo an taol ?
| How much are the drinks ?
|-
| Pegement eo ar banne bier ?
| How much is the beer ?
|-
| Ker eo / N'eo ket ker
| It's expensive / It's not expensive
|-
| Ur gwenneg bennak 'zo ganit ?
| Have you got some change ?
|-
| N'eus ket a voneiz ganin
| I have no change
|-
| Ha degemer a reer chekennoù en ostaleri-mañ ?
| Do you accept checks in this tavern ?
|-
| Kartennoù-bank / Chekennoù-vakansoù
| Banking cards / Holiday checks (''specific french disposition whereby enterprises grant checks to employees for holidays'')
|-
| Ha gallout a ran digeriñ ur gont ?
| And I can open an account ?
|-
| 1-Unan / 2-Daoù / 3-Tri / 4-Pevar / 5-Pemp / 6-C'hwec'h / 7-Seizh / 8-Eizh / 9-Nav / 10-Dek
| 
|-
| Un euro eo. Daou euro eo
| It's one euro . It's two euros
|-
| Hanter-kant gwenneg eo
| It's fifty cents
|-
| Daou euro hanter-kant eo
| It's two euros fifty cents
|-
|}

=== Going back home ===

==== Gouel 'zo ! / It's fun ! ====
{|width=&quot;100%&quot; border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; style=&quot;background:transparent;color:inherit;border-collapse:collapse&quot;
|-
!style=&quot;width:50%;&quot;|Brezhoneg!!style=&quot;width:50%;&quot;|English
|-
| Merc'hetañ / Paotretañ
| Looking for girls / boys
|-
| Daoust hag eñ 'zo tan ganit, mar plij ?
| Have you a match, please ?
|-
| Ya, laouenn, evel just
| Yes, with pleasure, of course
|-
| O chom e ti da dud out ?
| Do you stay by your parents ?
|-
| Brav eo da zaoulagad !
| How nice are your eyes !
|-
|}

==== O soñjal mont a-raok / Thinking to leave ====
{|width=&quot;100%&quot; border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; style=&quot;background:transparent;color:inherit;border-collapse:collapse&quot;
|-
!style=&quot;width:50%;&quot;|Brezhoneg!!style=&quot;width:50%;&quot;|English
|-
| Koazezañ a rafen a-walc'h pemp munud / Azezañ a rafen ...
| I'd like to sit for five minutes
|-
| Petra 'zo nevez ganit er bed ?
| What's new ? (Lit. &quot;What's new for you in the world ?&quot;)
|-
| Abalamour da betra c'h out en imor fall ? 
| Why are you in a bad mood ?
|-
| Petra 'zo nevez er gazetenn ?
| What's new in the newspaper ?
|-
| Serr da c'henoù, 'ta !
| Shut your mouth, then !
|-
| Eta (short : 'ta)
| Then
|-
| Sell ! Suzanna ha Mona 'zo skuizh-marv, poent eo mont d'ar gêr da gousket.
| Look ! Suzan and Mona are real tired : it's high time to go back home.
|-
| Na kaerat ur gouel !
| What a nice feast !
|-
| Dreist eo! Brutal eo ! Mat-kaer eo ! Spontus mat eo ! Kaer spontus ! ...
| It's so nice !
|-
| Dont a rin en-dro d'ar gouelioù-meur-mañ da vloaz ! a-benn bloaz !
| I will come back next year to this festival !
|-
| Ken ar wech-all ! Ken ar-c'hentañ
| Good bye !
|-
| Bevet Breizh !
| High Brittany ! Long live Brittany !
|-
| Bevet ar brezhoneg !
| Long live the Breton language !
|-
|}
     
==== Mont d'ar ger pe get ? / Do we go back home or not ? ====
{|width=&quot;100%&quot; border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; style=&quot;background:transparent;color:inherit;border-collapse:collapse&quot;
|-
!style=&quot;width:50%;&quot;|Brezhoneg!!style=&quot;width:50%;&quot;|English
|-
| Da belec'h 'c'haller mont da gousket ?
| Where can we sleep ?
|-
| Furoc'h 'vo chom da gousket er c'harr.
| It would be wiser to sleep in the car.
|-
| Deus du-mañ da gousket.
| Sleep in my home.
|-
| Daoust ha gallout a rit kas ac'hanon da Wengamp
| Could you drive me to Gwengamp ?
|-
| Ha plas 'zo e-barzh ho kwetur / karr-tan ?
| Have you room in your car ?
|-
| Ya, gant plijadur.
| Yes, with pleasure.
|-
| Nann 'vat.
| No sorry.
|-
|}

== Exercises ==

==== Ex 1 : Quiz ====
Go to the [[/Quiz|Quiz]].

==== Ex 2 : Memory training ====
Write out the Breton words, section by section.

Have 2 columns, clearly separated, and write Breton and English. Then cover up one column (eg. English) with paper and write the corresponding words on the paper.
Then try it the other way round, cover up the Breton, and write out the words using the English as cues. This will be a little bit more difficult.

Repeat all this after an interval, the more you do it the easier you will remember the words.

|}

{{Template:Page Turner
|PreviousLesson=Brezhoneg Pevar
|PreviousPage=Brezhoneg Pemp
|NextPage=Brezhoneg Pemp/Lesson 2
|LessonFirstPage=Brezhoneg Pemp
|NextLesson=Brezhoneg C'hwec'h
|FirstPage=Topic:Breton
|Division=Topic:Brythonic Celtic Languages Division
}}

[[Category: Breton]]
[[Category:Brezhoneg Pemp]]</text>
      <sha1>l4ghz8jhl1ju8wj56tobm1vmtjdidfs</sha1>
    </revision>
  </page>
  <page>
    <title>Brezhoneg C'hwec'h/Lesson 2</title>
    <ns>0</ns>
    <id>58933</id>
    <revision>
      <id>2831964</id>
      <parentid>2807933</parentid>
      <timestamp>2026-09-07T06:46:57Z</timestamp>
      <contributor>
        <username>ShakespeareFan00</username>
        <id>6645</id>
      </contributor>
      <minor />
      <comment>Attempting to solve lints - Please ignore the notification this edit generated.</comment>
      <origin>2831964</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="12705" sha1="tij73h5i9vtptfu5halqckkh09vdpo9" xml:space="preserve">{{Breton}}

{| cellpadding=&quot;10&quot; cellspacing=&quot;5&quot; style=&quot;width: 99%; background-color: inherit;color:inherit; margin-left: auto; margin-right: auto&quot;
| style=&quot;background-color: PapayaWhip;{{Text default color}}; border: 1px solid #777777; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;&quot; colspan=&quot;2&quot; |

== Irregular verbs / The Past Tense ==

=== &quot;To have&quot; / &quot;Kaout&quot; or &quot;Endevout&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Endevout / Kaout (''To have'') - Past'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Past Tense&lt;br&gt;Personal form!! Past Tense&lt;br&gt;Impersonal form!! Continuous Tense&lt;br&gt;Personal form!! Continuous Tense&lt;br&gt;Impersonal form!! English meaning
|-
|style=&quot;background:LightGreen;{{text default color}}';&quot;|am boa
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#FEC3AC;{{text default color}}';&quot;|am beze
|style=&quot;background:#FF5E4D;{{text default color}}';&quot;|
|style=&quot;background:LightBlue;{{text default color}}';&quot;|I had
|-
|style=&quot;background:LightGreen;{{text default color}}';&quot;|az poa
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#FEC3AC;{{text default color}}';&quot;|az peze
|style=&quot;background:#FF5E4D;{{text default color}}';&quot;|
|style=&quot;background:LightBlue;{{text default color}}';&quot;|You had (sg.)
|-
|style=&quot;background:LightGreen;{{text default color}}';&quot;|en doa
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#FEC3AC;{{text default color}}';&quot;|en deveze
|style=&quot;background:#FF5E4D;{{text default color}}';&quot;|
|style=&quot;background:LightBlue;{{text default color}}';&quot;|He had
|-
|style=&quot;background:LightGreen;{{text default color}}';&quot;|he doa
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#FEC3AC;{{text default color}}';&quot;|he deveze
|style=&quot;background:#FF5E4D;{{text default color}}';&quot;|
|style=&quot;background:LightBlue;{{text default color}}';&quot;|She had
|-
|style=&quot;background:LightGreen;{{text default color}}';&quot;|hor boa
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#FEC3AC;{{text default color}}';&quot;|hor beze
|style=&quot;background:#FF5E4D;{{text default color}}';&quot;|
|style=&quot;background:LightBlue;{{text default color}}';&quot;|We had
|-
|style=&quot;background:LightGreen;{{text default color}}';&quot;|ho poa
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#FEC3AC;{{text default color}}';&quot;|ho peze
|style=&quot;background:#FF5E4D;{{text default color}}';&quot;|
|style=&quot;background:LightBlue;{{text default color}}';&quot;|You had (pl.)
|-
|style=&quot;background:LightGreen;{{text default color}}';&quot;|o doa 
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#FEC3AC;{{text default color}}';&quot;|o deveze
|style=&quot;background:#FF5E4D;{{text default color}}';&quot;|
|style=&quot;background:LightBlue;{{text default color}}';&quot;|They had
|-
|style=&quot;background:White;{{text default color}}';&quot;| 
|style=&quot;background:White;{{text default color}}';&quot;| 
|style=&quot;background:White;{{text default color}}';&quot;| 
|style=&quot;background:White;{{text default color}}';&quot;| 
|style=&quot;background:White;{{text default color}}';&quot;|
|-
|style=&quot;background:LightGreen;{{text default color}}';&quot;| 
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#FEC3AC;{{text default color}}';&quot;| 
|style=&quot;background:#FF5E4D;{{text default color}}';&quot;| 
|style=&quot;background:LightBlue;{{text default color}}';&quot;|Impersonal &lt;br&gt;passive
|-
|}
{{center bottom}}

=== &quot;To know&quot; / &quot;Gouzout&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Gouzout (''To know'') - Past'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Past Tense&lt;br&gt;Personal form!! Past Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Alamaneg a ouien
|style=&quot;background:82C46C;{{text default color}}';&quot;|Me a ouie Alamaneg
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Gouzout a raen Alamaneg
|style=&quot;background:LightBlue;{{text default color}}';&quot;|I knew German
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Alamaneg a ouies
|style=&quot;background:82C46C;{{text default color}}';&quot;|Te a ouie Alamaneg
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Gouzout a raes Alamaneg
|style=&quot;background:LightBlue;{{text default color}}';&quot;|You knew German (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Alamaneg a ouie
|style=&quot;background:82C46C;{{text default color}}';&quot;|En a ouie Alamaneg
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Gouzout a rae Alamaneg
|style=&quot;background:LightBlue;{{text default color}}';&quot;|He knew German
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Alamaneg a ouie
|style=&quot;background:82C46C;{{text default color}}';&quot;|He a ouie Alamaneg
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Gouzout a rae Alamaneg
|style=&quot;background:LightBlue;{{text default color}}';&quot;|She knew German
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Alamaneg a ouiemp
|style=&quot;background:82C46C;{{text default color}}';&quot;|Ni a ouie Alamaneg
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Gouzout a raemp Alamaneg
|style=&quot;background:LightBlue;{{text default color}}';&quot;|We knew German
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Alamaneg a ouiec'h
|style=&quot;background:82C46C;{{text default color}}';&quot;|C'hwi a ouie Alamaneg
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Gouzout a raec'h Alamaneg
|style=&quot;background:LightBlue;{{text default color}}';&quot;|You knew German (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Alamaneg a ouient
|style=&quot;background:82C46C;{{text default color}}';&quot;|Int a ouie Alamaneg
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Gouzout a raent Alamaneg
|style=&quot;background:LightBlue;{{text default color}}';&quot;|They knew german
|-  
|style=&quot;background:White;{{text default color}}';&quot;| 
|style=&quot;background:White;{{text default color}}';&quot;|
|style=&quot;background:White;{{text default color}}';&quot;| 
|style=&quot;background:White;{{text default color}}';&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Alamaneg a ouied 
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Gouzout a raed Alamaneg
|style=&quot;background:LightBlue;{{text default color}}';&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

=== &quot;To go&quot; / &quot;Mont&quot; ===

[[[wikt:br:mont||Troioù lavar / Usual expressions]]]

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Mont (''To go'') - Past'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Past Tense&lt;br&gt;Personal form!! Past Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Da Gemper ez aen
|style=&quot;background:82C46C;{{text default color}}';&quot;|Me a yae da Gemper
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Mond a raen da Gemper
|style=&quot;background:LightBlue;{{text default color}}';&quot;|I went to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Da Gemper ez aes
|style=&quot;background:82C46C;{{text default color}}';&quot;|Te a yae da Gemper
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Mond a raes da Gemper
|style=&quot;background:LightBlue;{{text default color}}';&quot;|You went to Kemper (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Da Gemper ez ae
|style=&quot;background:82C46C;{{text default color}}';&quot;|En a yae da Gemper
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Mond a rae da Gemper
|style=&quot;background:LightBlue;{{text default color}}';&quot;|He went to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Da Gemper ez ae
|style=&quot;background:82C46C;{{text default color}}';&quot;|He a yae da Gemper
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Mond a rae da Gemper
|style=&quot;background:LightBlue;{{text default color}}';&quot;|She went to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Da Gemper ez aemp
|style=&quot;background:82C46C;{{text default color}}';&quot;|Ni a yae da Gemper
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Mond a raemp da Gemper
|style=&quot;background:LightBlue;{{text default color}}';&quot;|We went to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Da Gemper ez aec'h
|style=&quot;background:82C46C;{{text default color}}';&quot;|C'hwi a yae da Gemper
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Mond a raec'h da Gemper
|style=&quot;background:LightBlue;{{text default color}}';&quot;|You went to Kemper (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Da Gemper ez aent
|style=&quot;background:82C46C;{{text default color}}';&quot;|Int a yae da Gemper
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Mond a raent da Gemper
|style=&quot;background:LightBlue;{{text default color}}';&quot;|They went to Kemper
|-  
|style=&quot;background:White;{{text default color}}';&quot;| 
|style=&quot;background:White;{{text default color}}';&quot;|
|style=&quot;background:White;{{text default color}}';&quot;| 
|style=&quot;background:White;{{text default color}}';&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Da Gemper ez aed 
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| Mond a raed da Gemper
|style=&quot;background:LightBlue;{{text default color}}';&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

=== &quot;To do&quot; / &quot;Ober&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Ober (''To do'') - Past'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Past Tense&lt;br&gt;Personal form!! Past Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Trouz a raen
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| 
|style=&quot;background:LightBlue;{{text default color}}';&quot;|I made noise
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Trouz a raes
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| 
|style=&quot;background:LightBlue;{{text default color}}';&quot;|You made noise (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Trouz a rae
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| 
|style=&quot;background:LightBlue;{{text default color}}';&quot;|He made noise
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Trouz a rae
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| 
|style=&quot;background:LightBlue;{{text default color}}';&quot;|She made noise
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Trouz a raemp
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| 
|style=&quot;background:LightBlue;{{text default color}}';&quot;|We made noise
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Trouz a raec'h
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| 
|style=&quot;background:LightBlue;{{text default color}}';&quot;|You made noise (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Trouz a raent 
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| 
|style=&quot;background:LightBlue;{{text default color}}';&quot;|They made noise
|-  
|style=&quot;background:White;{{text default color}}';&quot;| 
|style=&quot;background:White;{{text default color}}';&quot;|
|style=&quot;background:White;{{text default color}}';&quot;| 
|style=&quot;background:White;{{text default color}}';&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}}';&quot;|Trouz a raed 
|style=&quot;background:82C46C;{{text default color}}';&quot;|
|style=&quot;background:#F0E36B;{{text default color}}';&quot;| 
|style=&quot;background:LightBlue;{{text default color}}';&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

== Exercises/Ober ==

=== Self training ===
Now , you have seen how it's done.

Take the verbs from this lesson and write their Past tense.

Now underneath , make some sentences up , for each verb.  Eg. ''Me a oar kembraeg'' (I know welsh).

=== Quiz ===

[[/Quiz|Go to the Quiz]]

|}

{{Template:Page Turner
|PreviousLesson=Brezhoneg Pemp
|PreviousPage=Brezhoneg C'hwec'h/Lesson 1
|NextPage=Brezhoneg C'hwec'h/Lesson 3
|LessonFirstPage=Brezhoneg C'hwec'h
|NextLesson=Brezhoneg Seizh
|FirstPage=Topic:Breton
|Division=Topic:Brythonic Celtic Languages Division
}}

[[Category:Brezhoneg C'hwec'h]]</text>
      <sha1>tij73h5i9vtptfu5halqckkh09vdpo9</sha1>
    </revision>
  </page>
  <page>
    <title>Brezhoneg C'hwec'h/Lesson 5</title>
    <ns>0</ns>
    <id>59194</id>
    <revision>
      <id>2831968</id>
      <parentid>2214602</parentid>
      <timestamp>2026-09-07T06:51:50Z</timestamp>
      <contributor>
        <username>ShakespeareFan00</username>
        <id>6645</id>
      </contributor>
      <minor />
      <comment>Attempting to solve lints - Please ignore the notification this edit generated.</comment>
      <origin>2831968</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="25684" sha1="hgwhnnzwjgmed32hp9dtbfsl0s4nqsz" xml:space="preserve">{{Breton}}

{| cellpadding=&quot;10&quot; cellspacing=&quot;5&quot; style=&quot;width: 99%; background-color: inherit;color:inherit; margin-left: auto; margin-right: auto&quot;
| style=&quot;background-color: PapayaWhip;{{Text default color}}; border: 1px solid #777777; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;&quot; colspan=&quot;2&quot; |

== Irregular verbs / The Conditional Present Tense ==

=== &quot;To have&quot; / &quot;Kaout&quot; or &quot;Endevout&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Endevout / Kaout (''To have'') - Conditional Present'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Present Tense&lt;br&gt;Personal form!! Conditional Present Tense&lt;br&gt;Impersonal form!! Continuous Tense&lt;br&gt;Personal form!! Continuous Tense&lt;br&gt;Impersonal form!! English meaning
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|am befe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would have
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|az pefe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have (sg.)
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|en defe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would have
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|he defe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would have
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|hor befe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would have
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|ho pefe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have (pl.)
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|o defe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would have
|-
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;| 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;| 
|style=&quot;background:#FF5E4D;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-
|}
{{center bottom}}

=== &quot;To know&quot; / &quot;Gouzout&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Gouzout (''To know'') - Conditional Present'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Present Tense&lt;br&gt;Personal form!! Conditional Present Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufen
|style=&quot;background:#82C46C;{{text default color}};&quot;|Me a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafen Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would know Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufes
|style=&quot;background:#82C46C;{{text default color}};&quot;|Te a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafes Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would know Breton (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufe
|style=&quot;background:#82C46C;{{text default color}};&quot;|En a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafe Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would know Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufe
|style=&quot;background:#82C46C;{{text default color}};&quot;|He a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafe Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would know Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufemp
|style=&quot;background:#82C46C;{{text default color}};&quot;|Ni a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafemp Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would know Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufec'h
|style=&quot;background:#82C46C;{{text default color}};&quot;|C'hwi a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafec'h Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would know Breton (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufent
|style=&quot;background:#82C46C;{{text default color}};&quot;|Int a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafent Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would know Breton
|-  
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufed 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafed Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

=== &quot;To go&quot; / &quot;Mont&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Mont (''To go'') - Conditional Present'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Present Tense&lt;br&gt;Personal form!! Conditional Present Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afen
|style=&quot;background:#82C46C;{{text default color}};&quot;|Me a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafen da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would go to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afes
|style=&quot;background:#82C46C;{{text default color}};&quot;|Te a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafes da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would go to Kemper (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afe
|style=&quot;background:#82C46C;{{text default color}};&quot;|En a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafe da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would go to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afe
|style=&quot;background:#82C46C;{{text default color}};&quot;|He a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafe da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would go to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afemp
|style=&quot;background:#82C46C;{{text default color}};&quot;|Ni a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafemp da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would go to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afec'h
|style=&quot;background:#82C46C;{{text default color}};&quot;|C'hwi a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafec'h da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would go to Kemper (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afent
|style=&quot;background:#82C46C;{{text default color}};&quot;|Int a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafent da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would go to Kemper
|-  
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afed 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafed da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

=== &quot;To do&quot; / &quot;Ober&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Ober (''To do'') - Conditional Present'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Present Tense&lt;br&gt;Personal form!! Conditional Present Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafen
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would make noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafes
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would make noise (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would make noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would make noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafemp
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would make noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafec'h
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would make noise (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafent 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would make noise
|-  
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafed 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

== Exercises/Ober ==

=== Self training ===
Now , you have seen how it's done.

Take the verbs from this lesson and write their Conditional Present tense.

Now underneath , make some sentences up , for each verb.  Eg. ''Me a oar kembraeg'' (I know welsh).

=== Quiz ===

[[/Quiz|Go to the Quiz]]

|}

{| cellpadding=&quot;10&quot; cellspacing=&quot;5&quot; style=&quot;width: 99%; background-color: inherit; margin-left: auto; margin-right: auto&quot;
| style=&quot;background-color: PapayaWhip;{{Text default color}}; border: 1px solid #777777; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;&quot; colspan=&quot;2&quot; |

== Irregular verbs / The Conditional Past Tense ==

=== &quot;To have had&quot; / &quot;Kaout&quot; or &quot;Endevout&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Endevout / Kaout (''To have had'') - Conditional Past'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Past Tense&lt;br&gt;Personal form!! Conditional Past Tense&lt;br&gt;Impersonal form!! Continuous Tense&lt;br&gt;Personal form!! Continuous Tense&lt;br&gt;Impersonal form!! English meaning
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|am bije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would have had
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|az pije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have had (sg.)
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|en dije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would have had
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|he dije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would have had
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|hor bije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would have had
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|ho pije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have had (pl.)
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|o dije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would have had
|-
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;| 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;| 
|style=&quot;background:#FF5E4D;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-
|}
{{center bottom}}

=== &quot;To have known&quot; / &quot;go&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb go (''To have known'') - Conditional Past'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Past Tense&lt;br&gt;Personal form!! Conditional Past Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouijen
|style=&quot;background:#82C46C;{{text default color}};&quot;|Me a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a rajen Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would have known Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouijes
|style=&quot;background:#82C46C;{{text default color}};&quot;|Te a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a rajes Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have known Breton (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouije
|style=&quot;background:#82C46C;{{text default color}};&quot;|En a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a raje Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would have known Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouije
|style=&quot;background:#82C46C;{{text default color}};&quot;|He a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a raje Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would have known Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouijemp
|style=&quot;background:#82C46C;{{text default color}};&quot;|Ni a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a rajemp Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would have known Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouijec'h
|style=&quot;background:#82C46C;{{text default color}};&quot;|C'hwi a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a rajec'h Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have known Breton (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouijent
|style=&quot;background:#82C46C;{{text default color}};&quot;|Int a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a rajent Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would have known Breton
|-  
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouijed 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a rajed Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

=== &quot;To have gone&quot; / &quot;Mont&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Mont (''To have gone'') - Conditional Past'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Past Tense&lt;br&gt;Personal form!! Conditional Past Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez ajen
|style=&quot;background:#82C46C;{{text default color}};&quot;|Me a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rajen da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would have gone to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez ajes
|style=&quot;background:#82C46C;{{text default color}};&quot;|Te a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rajes da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have gone to Kemper (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez aje
|style=&quot;background:#82C46C;{{text default color}};&quot;|En a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a raje da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would have gone to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez aje
|style=&quot;background:#82C46C;{{text default color}};&quot;|He a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a raje da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would have gone to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez ajemp
|style=&quot;background:#82C46C;{{text default color}};&quot;|Ni a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rajemp da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would have gone to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez ajec'h
|style=&quot;background:#82C46C;{{text default color}};&quot;|C'hwi a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rajec'h da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have gone to Kemper (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez ajent
|style=&quot;background:#82C46C;{{text default color}};&quot;|Int a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rajent da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would have gone to Kemper
|-  
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez ajed 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rajed da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

=== &quot;To do&quot; / &quot;Ober&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Ober (''To do'') - Conditional Past'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Past Tense&lt;br&gt;Personal form!! Conditional Past Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rajen
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would have made noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rajes
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have made noise (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a raje
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would have made noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a raje
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would have made noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rajemp
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would have made noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rajec'h
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have made noise (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rajent 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would have made noise
|-  
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rajed 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

== Exercises/Ober ==

=== Self training ===
Now , you have had seen how it's done.

Take the verbs from this lesson and write their Conditional Past tense.

Now underneath , have made some sentences up , for each verb.  Eg. ''Me a oar kembraeg'' (I have known welsh).

=== Quiz ===

[[/Quiz2|Go to the Quiz]]

|}

{{Template:Page Turner
|PreviousLesson=Brezhoneg Pemp
|PreviousPage=Brezhoneg C'hwec'h/Lesson 4
|NextPage=Brezhoneg C'hwec'h/Lesson 6
|LessonFirstPage=Brezhoneg C'hwec'h
|NextLesson=Brezhoneg Seizh
|FirstPage=Topic:Breton
|Division=Topic:Brythonic Celtic Languages Division
}}

[[Category:Brezhoneg C'hwec'h]]</text>
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    <revision>
      <id>2831971</id>
      <parentid>2831968</parentid>
      <timestamp>2026-09-07T06:52:28Z</timestamp>
      <contributor>
        <username>ShakespeareFan00</username>
        <id>6645</id>
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      <format>text/x-wiki</format>
      <text bytes="25698" sha1="80tiitslpe4klofxdcydsb96v4frnp4" xml:space="preserve">{{Breton}}

{| cellpadding=&quot;10&quot; cellspacing=&quot;5&quot; style=&quot;width: 99%; background-color: inherit;color:inherit; margin-left: auto; margin-right: auto&quot;
| style=&quot;background-color: PapayaWhip;{{Text default color}}; border: 1px solid #777777; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;&quot; colspan=&quot;2&quot; |

== Irregular verbs / The Conditional Present Tense ==

=== &quot;To have&quot; / &quot;Kaout&quot; or &quot;Endevout&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Endevout / Kaout (''To have'') - Conditional Present'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Present Tense&lt;br&gt;Personal form!! Conditional Present Tense&lt;br&gt;Impersonal form!! Continuous Tense&lt;br&gt;Personal form!! Continuous Tense&lt;br&gt;Impersonal form!! English meaning
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|am befe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would have
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|az pefe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have (sg.)
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|en defe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would have
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|he defe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would have
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|hor befe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would have
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|ho pefe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have (pl.)
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|o defe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would have
|-
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;| 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;| 
|style=&quot;background:#FF5E4D;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-
|}
{{center bottom}}

=== &quot;To know&quot; / &quot;Gouzout&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Gouzout (''To know'') - Conditional Present'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Present Tense&lt;br&gt;Personal form!! Conditional Present Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufen
|style=&quot;background:#82C46C;{{text default color}};&quot;|Me a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafen Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would know Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufes
|style=&quot;background:#82C46C;{{text default color}};&quot;|Te a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafes Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would know Breton (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufe
|style=&quot;background:#82C46C;{{text default color}};&quot;|En a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafe Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would know Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufe
|style=&quot;background:#82C46C;{{text default color}};&quot;|He a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafe Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would know Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufemp
|style=&quot;background:#82C46C;{{text default color}};&quot;|Ni a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafemp Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would know Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufec'h
|style=&quot;background:#82C46C;{{text default color}};&quot;|C'hwi a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafec'h Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would know Breton (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufent
|style=&quot;background:#82C46C;{{text default color}};&quot;|Int a oufe Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafent Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would know Breton
|-  
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a oufed 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Gouzout a rafed Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

=== &quot;To go&quot; / &quot;Mont&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Mont (''To go'') - Conditional Present'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Present Tense&lt;br&gt;Personal form!! Conditional Present Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afen
|style=&quot;background:#82C46C;{{text default color}};&quot;|Me a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafen da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would go to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afes
|style=&quot;background:#82C46C;{{text default color}};&quot;|Te a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafes da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would go to Kemper (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afe
|style=&quot;background:#82C46C;{{text default color}};&quot;|En a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafe da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would go to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afe
|style=&quot;background:#82C46C;{{text default color}};&quot;|He a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafe da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would go to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afemp
|style=&quot;background:#82C46C;{{text default color}};&quot;|Ni a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafemp da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would go to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afec'h
|style=&quot;background:#82C46C;{{text default color}};&quot;|C'hwi a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafec'h da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would go to Kemper (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afent
|style=&quot;background:#82C46C;{{text default color}};&quot;|Int a yafe da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafent da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would go to Kemper
|-  
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez afed 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rafed da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

=== &quot;To do&quot; / &quot;Ober&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Ober (''To do'') - Conditional Present'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Present Tense&lt;br&gt;Personal form!! Conditional Present Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafen
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would make noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafes
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would make noise (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would make noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafe
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would make noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafemp
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would make noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafec'h
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would make noise (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafent 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would make noise
|-  
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rafed 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

== Exercises/Ober ==

=== Self training ===
Now , you have seen how it's done.

Take the verbs from this lesson and write their Conditional Present tense.

Now underneath , make some sentences up , for each verb.  Eg. ''Me a oar kembraeg'' (I know welsh).

=== Quiz ===

[[/Quiz|Go to the Quiz]]

|}

{| cellpadding=&quot;10&quot; cellspacing=&quot;5&quot; style=&quot;width: 99%; background-color: inherit;color:inherit; margin-left: auto; margin-right: auto&quot;
| style=&quot;background-color: PapayaWhip;{{Text default color}}; border: 1px solid #777777; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;&quot; colspan=&quot;2&quot; |

== Irregular verbs / The Conditional Past Tense ==

=== &quot;To have had&quot; / &quot;Kaout&quot; or &quot;Endevout&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Endevout / Kaout (''To have had'') - Conditional Past'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Past Tense&lt;br&gt;Personal form!! Conditional Past Tense&lt;br&gt;Impersonal form!! Continuous Tense&lt;br&gt;Personal form!! Continuous Tense&lt;br&gt;Impersonal form!! English meaning
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|am bije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would have had
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|az pije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have had (sg.)
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|en dije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would have had
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|he dije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would have had
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|hor bije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would have had
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|ho pije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have had (pl.)
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;|o dije
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;|
|style=&quot;background:#FF5E4D;{{text default color}};&quot;|
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would have had
|-
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-
|style=&quot;background:LightGreen;{{text default color}};&quot;| 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#FEC3AC;{{text default color}};&quot;| 
|style=&quot;background:#FF5E4D;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-
|}
{{center bottom}}

=== &quot;To have known&quot; / &quot;go&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb go (''To have known'') - Conditional Past'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Past Tense&lt;br&gt;Personal form!! Conditional Past Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouijen
|style=&quot;background:#82C46C;{{text default color}};&quot;|Me a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a rajen Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would have known Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouijes
|style=&quot;background:#82C46C;{{text default color}};&quot;|Te a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a rajes Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have known Breton (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouije
|style=&quot;background:#82C46C;{{text default color}};&quot;|En a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a raje Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would have known Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouije
|style=&quot;background:#82C46C;{{text default color}};&quot;|He a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a raje Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would have known Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouijemp
|style=&quot;background:#82C46C;{{text default color}};&quot;|Ni a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a rajemp Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would have known Breton
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouijec'h
|style=&quot;background:#82C46C;{{text default color}};&quot;|C'hwi a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a rajec'h Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have known Breton (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouijent
|style=&quot;background:#82C46C;{{text default color}};&quot;|Int a ouije Brezhoneg
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a rajent Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would have known Breton
|-  
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Brezhoneg a ouijed 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;|Gouzout a rajed Brezhoneg
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

=== &quot;To have gone&quot; / &quot;Mont&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Mont (''To have gone'') - Conditional Past'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Past Tense&lt;br&gt;Personal form!! Conditional Past Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez ajen
|style=&quot;background:#82C46C;{{text default color}};&quot;|Me a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rajen da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would have gone to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez ajes
|style=&quot;background:#82C46C;{{text default color}};&quot;|Te a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rajes da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have gone to Kemper (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez aje
|style=&quot;background:#82C46C;{{text default color}};&quot;|En a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a raje da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would have gone to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez aje
|style=&quot;background:#82C46C;{{text default color}};&quot;|He a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a raje da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would have gone to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez ajemp
|style=&quot;background:#82C46C;{{text default color}};&quot;|Ni a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rajemp da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would have gone to Kemper
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez ajec'h
|style=&quot;background:#82C46C;{{text default color}};&quot;|C'hwi a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rajec'h da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have gone to Kemper (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez ajent
|style=&quot;background:#82C46C;{{text default color}};&quot;|Int a yaje da Gemper
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rajent da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would have gone to Kemper
|-  
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Da Gemper ez ajed 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| Mond a rajed da Gemper
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

=== &quot;To do&quot; / &quot;Ober&quot; ===

{{center top}}
{| cellpadding=&quot;10&quot; cellspacing=&quot;2&quot; style=&quot;text-align:center; font-size:100%&quot;
|+ '''Irregular Verb Ober (''To do'') - Conditional Past'''
|-style=&quot;background:LightGrey; color:Brown&quot;
! Conditional Past Tense&lt;br&gt;Personal form!! Conditional Past Tense&lt;br&gt;Impersonal form!! With auxiliary&lt;br&gt;Personal form!! English meaning 
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rajen
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|I would have made noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rajes
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have made noise (sg.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a raje
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|He would have made noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a raje
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|She would have made noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rajemp
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|We would have made noise
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rajec'h
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|You would have made noise (pl.)
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rajent 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|They would have made noise
|-  
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|style=&quot;background:#White;{{text default color}};&quot;| 
|style=&quot;background:#White;{{text default color}};&quot;|
|-  
|style=&quot;background:LightGreen;{{text default color}};&quot;|Trouz a rajed 
|style=&quot;background:#82C46C;{{text default color}};&quot;|
|style=&quot;background:#F0E36B;{{text default color}};&quot;| 
|style=&quot;background:LightBlue;{{text default color}};&quot;|Impersonal &lt;br&gt;passive
|-  
|}
{{center bottom}}

== Exercises/Ober ==

=== Self training ===
Now , you have had seen how it's done.

Take the verbs from this lesson and write their Conditional Past tense.

Now underneath , have made some sentences up , for each verb.  Eg. ''Me a oar kembraeg'' (I have known welsh).

=== Quiz ===

[[/Quiz2|Go to the Quiz]]

|}

{{Template:Page Turner
|PreviousLesson=Brezhoneg Pemp
|PreviousPage=Brezhoneg C'hwec'h/Lesson 4
|NextPage=Brezhoneg C'hwec'h/Lesson 6
|LessonFirstPage=Brezhoneg C'hwec'h
|NextLesson=Brezhoneg Seizh
|FirstPage=Topic:Breton
|Division=Topic:Brythonic Celtic Languages Division
}}

[[Category:Brezhoneg C'hwec'h]]</text>
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|- 
| style=&quot;background:#ccccff;{{Text default color}};text-align:center&quot; colspan=3| '''Topics in [[Topic:C_Sharp|C#]]'''
|- 
!style=&quot;background:#bbbbff;{{Text default color}};text-align:center&quot; | '''Beginners''' 
!style=&quot;background:#bbbbff;{{Text default color}};text-align:center&quot; | '''Intermediate''' 
!style=&quot;background:#bbbbff;{{Text default color}};text-align:center&quot; | '''Advanced'''
|-
| style=&quot;vertical-align:top;&quot; |
* [[Introduction to .NET|Lesson 1: Introduction to .NET]] and [[Introduction to Mono]]
* [[C Sharp/Compilers|Lesson 2: C# Compilers]]
* [[C Sharp/Introduction|Lesson 3: Introduction to C#]]
* [[C Sharp/First Program|Lesson 4: First Program]]
* [[C Sharp/Variables|Lesson 5: Variables and Casting]]
* [[C Sharp/Math|Lesson 6: Math and User Input]]
* [[C Sharp/Conditions|Lesson 7: Conditions]]
* [[C Sharp/Loops|Lesson 8: Loops]]
* [[C Sharp/Functions|Lesson 9: Functions]]
* [[C Sharp/Exceptions|Lesson 10: Exceptions and Exception Handling]]
| style=&quot;vertical-align:top;&quot; |
* [[C Sharp/Collections|Lesson 1: Lists, Stacks, Queues]]
* [[C Sharp/Structs|Lesson 2: Structures and Enumerations]]
* [[C Sharp/Delegates|Lesson 3: Delegates]]
* [[C Sharp/Generics|Lesson 4: Generics]]
* [[C Sharp/Classes|Lesson 5: Partial and Static Classes]]
| style=&quot;vertical-align:top;&quot; |
* [[C Sharp/Lambda|Lesson 1: Lambda Expressions]]
* [[C Sharp/Singleton|Lesson 2: Singleton Pattern]]
|-
|style=&quot;background:#aaaaff;{{Text default color}};text-align:center&quot; colspan=3 | Part of the [[:School:Computer_Science|School of Computer Science]]
|-
|}
[[Category:C Sharp]]
&lt;noinclude&gt;[[Category:Course navigation templates]]
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&lt;b&gt;To custodian:&lt;/b&gt; This team appeared to have blanked out their wiki page.  Please give them some time before deleting this page in case they need to recover anything from this page.  Thank you. 
[[User:Eml4500.f08|Eml4500.f08]] 09:28, 25 September 2008 (UTC)
&lt;/div&gt;

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      <text bytes="2079" sha1="3bp6tehql9yo24mwuh2t52c77oxddz7" xml:space="preserve">{{psychology}}
Qualitative methods in sociological research refer to distinctive types of research activities: participant observation, intensive interviewing, and focus groups. The three qualitative designs differ but also share many similar characteristics that distinguish them from quantitative methods of research.  Qualitative researchers begin their research with an exploratory research question (for many times there isn't sufficient data to formulate a structured and specific goal).  And once started they make sure to pay attention to the social context in which social phenomena occur, human subjectivity and  how they themselves can influence any situation.

== Participant observation ==
 
'''Participant observation''' is a method for gathering data that involves developing a relationship with people while they go about their daily, normal activities.  It is a means for seeing the social world as the research subjects see it, in its totality, and for understanding subjects' interpretations of that world (Wolcott, 1995:66).

For more information, see [[w:Participant observation|Participant observation]] (Wikipedia)

== Intensive Interviewing ==

is a method in which the researcher seeks in-dept information from their interviewee's feelings, experiences, and perceptions.

== Focus Groups ==

is a method in where the researcher seeks to encourage discussion among participants about a certain topic of interest.

== Discussion questions, essay ideas, and AI prompt ideas ==
{{Template:AI-generated-section}}

* Examine how researcher reactivity/reflexivity alters the dynamic between an observer and participants, particularly when the presence of an investigator inadvertently reshapes the norms of the environment under study.
* Explore whether true objectivity remains a viable objective in exploratory qualitative inquiry, or if acknowledging researcher subjectivity offers a more accurate account of social reality.

== References ==

Wolcott, Harry F. 1995. ''The Art of Fieldwork''. Walnut Creek, CA: AltaMira Press.

[[Category:Research methods]]</text>
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{{tertiary education}}
{{mathematics}}
{{launch}}

Differential equations serve as mathematical models of physical processes.  This course is intended to be an introduction to ordinary differential equations and their solutions.
A '''differential equation''' (DE) is an equation relating a function to its derivatives. If the function is of only one variable, we call the equation an '''ordinary differential equation''' (ODE). Equations relating the partial derivatives (See: [[Vector calculus]]) of a function of several variables are called '''partial differential equations''' (PDEs). Ordinary differential equations are much easier to solve than partial differential equations, so these will be our main focus.

==Syllabus==
*Introduction to ordinary differential equations.
**[[/Ordinary Differential Equations/]]
**[[/Slope Fields/]]
*First-order equations
**[[/Introduction to First Order Linear Differential Equations/]]
**[[/First-order nonlinear equations/]]
**[[/Separable differential equations/]] &lt;small&gt;50%&lt;/small&gt;[[Image:50%25.svg|20px|]]
**[[/Exact differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Homogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Integrating factors/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Change of variables/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
*Higher-order linear equations
**[[/Linear homogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Linear inhomogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Laplace transforms/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Power series solutions/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
*Introduction to nonlinear equations
**[[/Fixed point classification in 1D|Stability problems in 1D/]]
**[[/Fixed point classification in 2D|Stability problems in 2D/]]
**[[/Approximate solutions to differential equations/]]

[[Category:Differential equations| ]]
[[Category:Mathematics courses]]

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{{tertiary education}}
{{mathematics}}
{{launch}}

Differential equations serve as mathematical models of physical processes.  This course is intended to be an introduction to ordinary differential equations and their solutions.
A '''differential equation''' (DE) is an equation relating a function to its derivatives. If the function is of only one variable, we call the equation an '''ordinary differential equation''' (ODE). Equations relating the partial derivatives (See: [[Vector calculus]]) of a function of several variables are called '''partial differential equations''' (PDEs). Ordinary differential equations are much easier to solve than partial differential equations, so these will be our main focus.

==Syllabus==
*Introduction to ordinary differential equations.
**[[/Ordinary Differential Equations/]]
**[[/Slope Fields/]]
*First-order equations
**[[/Introduction to First Order Linear Differential Equations/]]
**[[/First-order nonlinear equations/]]
**[[/Separable differential equations/]] &lt;small&gt;50%&lt;/small&gt;[[Image:50%25.svg|20px|]]
**[[/Exact differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Homogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Integrating factors/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Change of variables/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
*Higher-order linear equations
**[[/Linear homogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Linear inhomogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Laplace transforms/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Power series solutions/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
*Introduction to nonlinear equations
**[[/Fixed point classification in 1D|Stability problems in 1D/]]
**[[/Fixed point classification in 2D|Stability problems in 2D/]]
**[[/Approximate solutions to differential equations/]]

=== Problems to be organized ===
First-order problems
[[Category:Differential equations| ]]
[[Category:Mathematics courses]]

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{{tertiary education}}
{{mathematics}}
{{launch}}

Differential equations serve as mathematical models of physical processes.  This course is intended to be an introduction to ordinary differential equations and their solutions.
A '''differential equation''' (DE) is an equation relating a function to its derivatives. If the function is of only one variable, we call the equation an '''ordinary differential equation''' (ODE). Equations relating the partial derivatives (See: [[Vector calculus]]) of a function of several variables are called '''partial differential equations''' (PDEs). Ordinary differential equations are much easier to solve than partial differential equations, so these will be our main focus.

==Syllabus==
*Introduction to ordinary differential equations.
**[[/Ordinary Differential Equations/]]
**[[/Slope Fields/]]
*First-order equations
**[[/Introduction to First Order Linear Differential Equations/]]
**[[/First-order nonlinear equations/]]
**[[/Separable differential equations/]] &lt;small&gt;50%&lt;/small&gt;[[Image:50%25.svg|20px|]]
**[[/Exact differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Homogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Integrating factors/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Change of variables/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
*Higher-order linear equations
**[[/Linear homogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Linear inhomogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Laplace transforms/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Power series solutions/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
*Introduction to nonlinear equations
**[[/Fixed point classification in 1D|Stability problems in 1D/]]
**[[/Fixed point classification in 2D|Stability problems in 2D/]]
**[[/Approximate solutions to differential equations/]]

=== Problems to be organized ===
**[[/First-order problems/]]
[[Category:Differential equations| ]]
[[Category:Mathematics courses]]

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{{tertiary education}}
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{{launch}}

Differential equations serve as mathematical models of physical processes.  This course is intended to be an introduction to ordinary differential equations and their solutions.
A '''differential equation''' (DE) is an equation relating a function to its derivatives. If the function is of only one variable, we call the equation an '''ordinary differential equation''' (ODE). Equations relating the partial derivatives (See: [[Vector calculus]]) of a function of several variables are called '''partial differential equations''' (PDEs). Ordinary differential equations are much easier to solve than partial differential equations, so these will be our main focus.

==Syllabus==
*Introduction to ordinary differential equations.
**[[/Ordinary Differential Equations/]]
**[[/Slope fields/]]
*First-order equations
**[[/Introduction to First Order Linear Differential Equations/]]
**[[/First-order nonlinear equations/]]
**[[/Separable differential equations/]] &lt;small&gt;50%&lt;/small&gt;[[Image:50%25.svg|20px|]]
**[[/Exact differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Homogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Integrating factors/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Change of variables/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
*Higher-order linear equations
**[[/Linear homogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Linear inhomogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Laplace transforms/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Power series solutions/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
*Introduction to nonlinear equations
**[[/Fixed point classification in 1D|Stability problems in 1D/]]
**[[/Fixed point classification in 2D|Stability problems in 2D/]]
**[[/Approximate solutions to differential equations/]]

=== Problems to be organized ===
**[[/First-order problems/]]
[[Category:Differential equations| ]]
[[Category:Mathematics courses]]

{{subpagesif}}</text>
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{{tertiary education}}
{{mathematics}}
{{launch}}

Differential equations serve as mathematical models of physical processes.  This course is intended to be an introduction to ordinary differential equations and their solutions.
A '''differential equation''' (DE) is an equation relating a function to its derivatives. If the function is of only one variable, we call the equation an '''ordinary differential equation''' (ODE). Equations relating the partial derivatives (See: [[Vector calculus]]) of a function of several variables are called '''partial differential equations''' (PDEs). Ordinary differential equations are much easier to solve than partial differential equations, so these will be our main focus.

==Syllabus==
*Introduction to ordinary differential equations.
**[[/Ordinary Differential Equations/]]
**[[/Slope fields/]]
*First-order equations
**[[/Introduction to First Order Linear Differential Equations/]]
**[[/First-order nonlinear equations/]]
**[[/Separable differential equations/]] &lt;small&gt;50%&lt;/small&gt;[[Image:50%25.svg|20px|]]
**[[/Exact differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Homogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Integrating factors/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Change of variables/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
*Higher-order linear equations
**[[/Linear homogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Linear inhomogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Laplace transforms/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Power series solutions/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
*Introduction to nonlinear equations
**[[/Fixed point classification in 1D|Stability problems in 1D/]]
**[[/Fixed point classification in 2D|Stability problems in 2D/]]
**[[/Approximate solutions to differential equations/]]

=== Problems to be organized ===
*[[First-order problems]]
[[Category:Differential equations| ]]
[[Category:Mathematics courses]]

{{subpagesif}}

== Related resources ==

* '''[[wikibooks:Ordinary_Differential_Equations|Differential equations wikibook]]'''</text>
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{{tertiary education}}
{{mathematics}}
{{launch}}

Differential equations serve as mathematical models of physical processes.  This course is intended to be an introduction to ordinary differential equations and their solutions.
A '''differential equation''' (DE) is an equation relating a function to its derivatives. If the function is of only one variable, we call the equation an '''ordinary differential equation''' (ODE). Equations relating the partial derivatives (See: [[Vector calculus]]) of a function of several variables are called '''partial differential equations''' (PDEs). Ordinary differential equations are much easier to solve than partial differential equations, so these will be our main focus.

==Syllabus==
*Introduction to ordinary differential equations.
**[[/Ordinary Differential Equations/]]
**[[/Slope fields/]]
*First-order equations
**[[/Introduction to First Order Linear Differential Equations/]]
**[[/First-order nonlinear equations/]]
**[[/Separable differential equations/]] &lt;small&gt;50%&lt;/small&gt;[[Image:50%25.svg|20px|]]
**[[/Exact differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Homogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Integrating factors/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Change of variables/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
*Higher-order linear equations
**[[/Linear homogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Linear inhomogeneous differential equations/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Laplace transforms/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
**[[/Power series solutions/]] &lt;small&gt;25%&lt;/small&gt;[[Image:25%25.svg|20px|]]
*Introduction to nonlinear equations
**[[/Fixed point classification in 1D|Stability problems in 1D/]]
**[[/Fixed point classification in 2D|Stability problems in 2D/]]
**[[/Approximate solutions to differential equations/]]

=== Problems to be organized ===
*[[/First-order problems/]]
[[Category:Differential equations| ]]
[[Category:Mathematics courses]]

{{subpagesif}}

== Related resources ==

* '''[[wikibooks:Ordinary_Differential_Equations|Differential equations wikibook]]'''</text>
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    <title>Harmful Effects and Policy</title>
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== Harmful Effects of the Coal Industry ==

Over the past few decades, the region of the Colorado Plateau has experienced a slow deterioration of its once ideal atmosphere (Grahame &amp; Sisk, 2002). Coal-burning power plants are largely responsible for this change, producing 64% of Arizona’s air pollution (Grand Canyon Trust). As the population grows and the energy demands of nearby cities, such as Las Vegas, Los Angeles, and Phoenix, increase, these power plants inflict more and more damage upon the environment and its inhabitants. Recent studies show that each year, 17 coal-burning stations on or around the Colorado Plateau dump 132 million tons of carbon dioxide, 200,000 tons of sulfur dioxide, and 270,000 tons of nitrogen oxides combined (Grand Canyon Trust). These chemicals contribute to the global warming effect and threaten to offset the balance of the delicate conditions in which the region’s rich wildlife and plant-life can survive. Of equal concern is the air quality’s threat to the health of its human inhabitants. Asthmatics, the elderly, and children are particularly susceptible to respiratory illnesses due to pollution.

Aside from harming the ecological system, coal-burning power plants strain water resources, further contributing to a human-induced change upon the environment. To facilitate transportation from mining sites, such as Black Mesa, to the power plants, coal is transformed into a slurry form (Grahame &amp; Sisk, 2002). This depletes ground water in an already arid environment, contributing to droughts, loss of native vegetation and wildlife habitats, and an increase of invasive plant species.

The coal-fired Navajo Generating Station near Page, Arizona (Grahame &amp; Sisk, 2002).

== Related Policies ==

=== Clean Air Act ===
* Requires an operating permit for commercial sources designating what type of chemical and how much can be released (EPA).
* Works with governors and local legislators to create an implementation plan where standards are not being met; also enforced through penalties and court action (EPA).
* Mohave Generating Plant violated the Clean Air Act and was shut down in 2005 through a lawsuit by the Navajo and Hopi nations, who also cut off their reservation’s water supply to the plant (EIA).

=== Executive Order 2010-06 ===
* Established the Climate Change Oversight Group under Governor Brewer to monitor the work of the Western Climate Initiative and to advise the Governor.
* Has not achieved measurable results (EPA).

== Economic Implications ==

Coal currently accounts for about half of the nation’s electrical needs. While its prices have risen moderately, prices of oil and natural gas have increased sharply over the past decade. Therefore, coal has emerged as the preferred resource. However, residents of coal-rich areas are reaping very few financial benefits. They receive royalty payments and relatively low-income jobs through mining contracts and power plant facilities while non-resident shareholders, often in larger cities, receive the most profit (ScienceDaily). Meanwhile, residents continue to be forced from their homes. Their, sometimes sacred, environments are exploited and the ecosystem is perhaps irreparably damaged (Grand Canyon Trust).

== Moral Considerations ==

Now, more than ever, renewable energy is a growing area of exploration and investment. With the resources and the technology available, it seems natural that our nation’s energy demand should be able to be met while keeping our environment intact. Delaying this process, however, is the low cost of coal, its abundance, and its ability to comply with federally regulated standards given its low sulfur content in regions such as the Colorado Plateau (ScienceDaily). Coal-burning plants have also received support from initiatives that research cleaner practices of burning coal. It is a convenient, established, and profitable method that shareholders will not easily abandon. Nevertheless, the amount of water that it demands in transportation, heating, and cooling are huge disadvantages of coal-burning plants, particularly as this contributes to drought and warming. The amount of chemicals it pours into the atmosphere also leads to more extreme temperature ranges, thus making life impossible for some species and damaging the overall ecosystem.

Proactive measures, therefore, must be seriously explored, which involves ethical considerations of the environment as central to our greater ecosystem, rather than simply profit and tradition. A former representative in the Hopi nation summarized the problem by saying, “What we have is the absence of political will” (Grand Canyon Trust). Although the government may be unsuccessful at directly legislating environmental morality, they may achieve progress toward climate stability by encouraging the development and implementation of innovations for renewable resources and by placing stricter standards on coal-burning power plants and continuing to enforce them. Furthermore, local groups have pioneered change in our ethical considerations. The Grand Canyon Trust, for instance, participates in community outreach in which it educates the public about greenhouse gas emissions and the importance of a clean environment (Grand Canyon Trust). The group also organized the first training workshop in the Southwest for global warming activists. Individual efforts can reinforce this by investing in solar panels and wind turbines when appropriate. This participation of the community is vital to expanding the energy market’s use of renewable resources. In order for a change to occur, it must not be guided by the profits of long-standing corporations, but by enterprises whose ethical considerations include the environment and our symbiotic relationship with it.

[[Category:Essays]]</text>
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      <text bytes="5828" sha1="2vtwts3uz100f9c9i65kuortgutjl29" xml:space="preserve">== Harmful Effects of the Coal Industry ==

Over the past few decades, the region of the Colorado Plateau has experienced a slow deterioration of its once ideal atmosphere (Grahame &amp; Sisk, 2002). Coal-burning power plants are largely responsible for this change, producing 64% of Arizona’s air pollution (Grand Canyon Trust). As the population grows and the energy demands of nearby cities, such as Las Vegas, Los Angeles, and Phoenix, increase, these power plants inflict more and more damage upon the environment and its inhabitants. Recent studies show that each year, 17 coal-burning stations on or around the Colorado Plateau dump 132 million tons of carbon dioxide, 200,000 tons of sulfur dioxide, and 270,000 tons of nitrogen oxides combined (Grand Canyon Trust). These chemicals contribute to the global warming effect and threaten to offset the balance of the delicate conditions in which the region’s rich wildlife and plant-life can survive. Of equal concern is the air quality’s threat to the health of its human inhabitants. Asthmatics, the elderly, and children are particularly susceptible to respiratory illnesses due to pollution.

Aside from harming the ecological system, coal-burning power plants strain water resources, further contributing to a human-induced change upon the environment. To facilitate transportation from mining sites, such as Black Mesa, to the power plants, coal is transformed into a slurry form (Grahame &amp; Sisk, 2002). This depletes ground water in an already arid environment, contributing to droughts, loss of native vegetation and wildlife habitats, and an increase of invasive plant species.

The coal-fired Navajo Generating Station near Page, Arizona (Grahame &amp; Sisk, 2002).

== Related Policies ==

=== Clean Air Act ===
* Requires an operating permit for commercial sources designating what type of chemical and how much can be released (EPA).
* Works with governors and local legislators to create an implementation plan where standards are not being met; also enforced through penalties and court action (EPA).
* Mohave Generating Plant violated the Clean Air Act and was shut down in 2005 through a lawsuit by the Navajo and Hopi nations, who also cut off their reservation’s water supply to the plant (EIA).

=== Executive Order 2010-06 ===
* Established the Climate Change Oversight Group under Governor Brewer to monitor the work of the Western Climate Initiative and to advise the Governor.
* Has not achieved measurable results (EPA).

== Economic Implications ==

Coal currently accounts for about half of the nation’s electrical needs. While its prices have risen moderately, prices of oil and natural gas have increased sharply over the past decade. Therefore, coal has emerged as the preferred resource. However, residents of coal-rich areas are reaping very few financial benefits. They receive royalty payments and relatively low-income jobs through mining contracts and power plant facilities while non-resident shareholders, often in larger cities, receive the most profit (ScienceDaily). Meanwhile, residents continue to be forced from their homes. Their, sometimes sacred, environments are exploited and the ecosystem is perhaps irreparably damaged (Grand Canyon Trust).

== Moral Considerations ==

Now, more than ever, renewable energy is a growing area of exploration and investment. With the resources and the technology available, it seems natural that our nation’s energy demand should be able to be met while keeping our environment intact. Delaying this process, however, is the low cost of coal, its abundance, and its ability to comply with federally regulated standards given its low sulfur content in regions such as the Colorado Plateau (ScienceDaily). Coal-burning plants have also received support from initiatives that research cleaner practices of burning coal. It is a convenient, established, and profitable method that shareholders will not easily abandon. Nevertheless, the amount of water that it demands in transportation, heating, and cooling are huge disadvantages of coal-burning plants, particularly as this contributes to drought and warming. The amount of chemicals it pours into the atmosphere also leads to more extreme temperature ranges, thus making life impossible for some species and damaging the overall ecosystem.

Proactive measures, therefore, must be seriously explored, which involves ethical considerations of the environment as central to our greater ecosystem, rather than simply profit and tradition. A former representative in the Hopi nation summarized the problem by saying, “What we have is the absence of political will” (Grand Canyon Trust). Although the government may be unsuccessful at directly legislating environmental morality, they may achieve progress toward climate stability by encouraging the development and implementation of innovations for renewable resources and by placing stricter standards on coal-burning power plants and continuing to enforce them. Furthermore, local groups have pioneered change in our ethical considerations. The Grand Canyon Trust, for instance, participates in community outreach in which it educates the public about greenhouse gas emissions and the importance of a clean environment (Grand Canyon Trust). The group also organized the first training workshop in the Southwest for global warming activists. Individual efforts can reinforce this by investing in solar panels and wind turbines when appropriate. This participation of the community is vital to expanding the energy market’s use of renewable resources. In order for a change to occur, it must not be guided by the profits of long-standing corporations, but by enterprises whose ethical considerations include the environment and our symbiotic relationship with it.

[[Category:Essays]]</text>
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      <text bytes="5524" sha1="gq0bukutub3l2ssawnaweo50bfuturk" xml:space="preserve">Michael Ten is a pen name of mine. 
&lt;!-- If you believe overcoming pro-aging mindsets is important please [http://patreon.com/defeataging support me on Patreon]. --&gt;
Please help me to help people to overcome pro-aging mindsets. 
* [http://michaelten.net Ideas]
__NOTOC__
What if we utilize [[vertical farming]] to convert farmland back into forests? What if we use [[electric cars]] and [[green energy]] to drastically reduce pollution in cities and all over? Some universities study ideas like [[basic income]] that [https://basicincome.stanford.edu/about/what-is-ubi/ may help] to eliminate poverty. [[Automation]] is increasingly changing economic dynamics on Earth. 
* [https://wikipedialibrary.wmflabs.org/users/my_library/ Library]
==Miscellaneous==
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* [https://en.wikiversity.org/wiki/Special:RecentChanges?hidebots=1&amp;hidecategorization=1&amp;hideWikibase=1&amp;namespace=0&amp;limit=1000&amp;days=15&amp;enhanced=1&amp;urlversion=2 Resources]
* [[Strategies for Engineered Negligible Senescence]]
* [[Overcoming pro-aging mindsets]]
* [[Android programming]]
* [[Renewable energy]]
* [[Ologies]]
* [[Pro se legal representation]]
* [[Business/Employee-owned companies|Employee-owned companies]]
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* [[Online social entrepreneurship]]
* [[Large language models]]
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* [[Reddit for learning]]
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* [[Cryonics]]
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hmm

* [[w:Morihei_Ueshiba#Works|The Art of Peace]] by [[q:Morihei Ueshiba|Morihei Ueshiba]]

==== Study and research interests ====
*How might large language models affect learning and research. Will LLM's eventually seen like calculators are in math and sciences now? But for everything (all subjects/topics, including math, physics, ethics, biology, psychology, chemistry, engineering, art)?

==== Ideas to possibly explore ====
* constructive feedback
:: potential search to start &quot;constructive feedback site:.edu&quot; (without quotes)
* Can this Solar System potentially support a prosperous human population of over 500 billion humans who can all live lives of abundance and post-scarcity?
* The integration between large language models and robotics.
* Are there any open source large language models that are able to continually integrate new information as a form of training or fine tuning?

== Discussion questions, essay ideas, and educational/research related AI prompt ideas ==

== Discussion questions, essay topics, and AI prompt ideas ==

== Discussion questions, essay topics, and educational AI prompt ideas ==

== Discussion questions, essay ideas, and learning related AI prompt ideas ==
what could we add to this wiki page? how could it be useful ?</text>
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      <text bytes="5587" sha1="5xql1t5bmh6rp0l2cdtijrndk62th9k" xml:space="preserve">Michael Ten is a pen name of mine. 
&lt;!-- If you believe overcoming pro-aging mindsets is important please [http://patreon.com/defeataging support me on Patreon]. --&gt;
Please help me to help people to overcome pro-aging mindsets. 
* [http://michaelten.net Ideas]
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What if we utilize [[vertical farming]] to convert farmland back into forests? What if we use [[electric cars]] and [[green energy]] to drastically reduce pollution in cities and all over? Some universities study ideas like [[basic income]] that [https://basicincome.stanford.edu/about/what-is-ubi/ may help] to eliminate poverty. [[Automation]] is increasingly changing economic dynamics on Earth. 
* [https://wikipedialibrary.wmflabs.org/users/my_library/ Library]
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hmm

* [[w:Morihei_Ueshiba#Works|The Art of Peace]] by [[q:Morihei Ueshiba|Morihei Ueshiba]]

==== Study and research interests ====
*How might large language models affect learning and research. Will LLM's eventually seen like calculators are in math and sciences now? But for everything (all subjects/topics, including math, physics, ethics, biology, psychology, chemistry, engineering, art)?

==== Ideas to possibly explore ====
* constructive feedback
:: potential search to start &quot;constructive feedback site:.edu&quot; (without quotes)
* Can this Solar System potentially support a prosperous human population of over 500 billion humans who can all live lives of abundance and post-scarcity?
* The integration between large language models and robotics.
* Are there any open source large language models that are able to continually integrate new information as a form of training or fine tuning?

== Discussion questions, essay ideas, and educational/research related AI prompt ideas ==

== Discussion questions, essay topics, and AI prompt ideas ==

== Discussion questions, essay topics, and educational AI prompt ideas ==

== Discussion questions, essay ideas, and learning related AI prompt ideas ==
what could we add to this wiki page? how could it be useful ?</text>
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      <text bytes="25746" sha1="pefz2ukkcihrvovj2rezu078oqucjoe" xml:space="preserve">{{center|[[/How to contribute to this resource/]]}}
==Introduction==
[[File:Walton(reconstitution).png|thumb|right|250px|Do you believe in alien abductions? Why or why not?]]
{{TOC right | limit|limit=1}}
How do you decide what to [[w:en:belief|believe]]? How do you distinguish between fact and opinion? When you hear a claim, how do you assess the reliability of the sources? What do you consider to be a reliable rather than an unreliable information source? How do you gather and assess evidence for or against some proposition? If some trusted authority supports a particular belief and direct evidence you see disputes that belief, how do you resolve this discrepancy? Are your beliefs well-founded and consistent? What would cause you to change a belief?
{{100%done}}
How do you separate the [[w:Signal-to-noise_ratio|clear signal from all the noise]]? {{By|lbeaumont}}
This course will help you explore these questions and develop your own well-considered rules for deciding what to believe. These rules are called your ''theory of knowledge'', and when you have developed your own theory of knowledge you will finally ''know how you know''. 

The objectives of this course are:
*Examine how you decide what you believe,
*Explore the range of more reliable and less reliable information sources,
*Explore the [[Knowing How You Know/Tyranny of Evidence|tyranny of evidence]],
*Survey example theories of knowledge,
*Develop your own Theory of Knowledge,
*Test and refine your Theory of Knowledge,
*Apply your Theory of Knowledge to improve the accuracy and consistency of your beliefs, and
*Align your beliefs with reality.

There are no specific prerequisites to this course; all students are welcome. Students may benefit from completing the course [[Facing Facts]] before beginning this course.

Use this [[/Daily Practice Checklist: “Knowing How You Know”/|daily practice checklist]] to make knowing how you know a habit. 

This course is part of the [[Wisdom/Curriculum|Applied Wisdom curriculum]].
[[File:Knowing How You Know Audio Dialogue.wav|thumb|Knowing How You Know Audio Dialogue]]

If you wish to contact the instructor, please [[Special:Emailuser/Lbeaumont | click here to send me an email]].

==Deciding what to Believe==
How do you decide what to believe? Many people believe whatever they want to as they select information that seems to [[w:Confirmation_bias|confirm what is convenient]] for them to believe and dismiss contrary or conflicting information. Other people listen to what their friends have to say, or follow the opinions of various celebrities. It might be that the group that shouts the loudest or most often or most cleverly gets your attention. Perhaps you are influenced by people in power, listening to what parents and teachers said when you were young, rebelling against them as an adolescent, and then choosing other authority figures to follow as an adult. People are often captivated by attractive, charming, glib, or charismatic people. Mystical language seems to seduce and entrance others. Many of us are members of some tribe which supports its own belief system. This might be a political party, an advocacy group, a professional society or industry group, a club, religious or cultural traditions, or proponents of some ideology.
[[File:Ripples of influence.jpg|thumb|left|300px |We are influenced by many factors that ripple through our minds as our beliefs form, evolve, and may eventually change.]]
None of these approaches can accurately distinguish reliable information from rumor, myth, gossip, advertisement, propaganda, or other forms of unreliable, outdated, misleading, untrue, or deceptive misinformation. Also, because we are most comfortable when we are most certain, regardless of the validity of our beliefs, we naturally avoid or resist exposure to information that threatens our own tenuous certainty.&lt;ref&gt;
{{cite book |last=Burton |first=Robert |authorlink=w:Robert_A._Burton |title=On Being Certain: Believing You Are Right Even When You're Not |year=2008 |publisher=St. Martin's Press |isbn=978-0312359201  |pages=272}}&lt;/ref&gt;

In the USA, the Supreme Court broadly upholds the first amendment protection of free speech. Hate speech, misleading information, and deliberate lies are all constitutionally protected forms of expression.&lt;ref&gt;see, for example: [[w:R.A.V._v._City_of_St._Paul|R.A.V. v. City of St. Paul]] and [[w:United_States_v._Alvarez|United States v. Alvarez]]&lt;/ref&gt; The Internet welcomes all contributors and as a result support for almost any belief, regardless of its truth, is easily found. This constant influx of unverified information makes it essential that we take personal responsibility to decide for ourselves what is reliable and what is not.

“You're entitled to your own opinions”, Senator Daniel Patrick Moynihan declares, “but you're not entitled to your own facts.” This succinctly captures the extent and boundaries of [[Virtues/Tolerance|tolerance]].  While tolerance is essential in the realm of opinion, it has no place in the realm of fact. Of course you need to be able to distinguish fact from opinion to be tolerant.

Facts correspond to reality. Because we all live on the same earth, we all share the same reality, observed through our unique points of view.  This is our [[Facing Facts/Reality is our common ground|common ground]], we need to dig deeply to find that common ground and stand together on the bedrock of reality.
Facts establish the middle ground. We can each choose to move toward the political left or the right, but we each must start from the facts while we constantly stay connected to the facts.

Taking responsibility for your own beliefs is not easy, but it is immensely rewarding.  When you know how you know, you can be confident in what you know. You can then strive to purify the knowledge stream you accumulate and assimilate.  When you know how you know you can easily identify the fools, fakers, and frauds among us, and confidently dispute, correct, dismiss, or avoid them.

Knowing how you know is a big step you can take now to reduce the influence of money and special interests in politics. Because you are less susceptible to misleading, manipulative, deceptive, and unhelpful influences, money spent by special interests on propaganda designed to support only their cause becomes less effective. You know how to make up your own mind based on a careful, accurate, nuanced, and balanced assessment of reliable information.  Facts are stubborn. When you are justifiably confident in knowing what is true, what is false, and what you are unsure of you know when to stand firm, when to yield, and when to change your beliefs.

===Assignment:===
Your beliefs are what you accept as being true. This assignment begins to examine your beliefs.

'''Part 1:'''
#Write down a few of your own beliefs. Choose a range of more widely accepted and less widely accepted beliefs.
#For each of these beliefs, write down how you decided it is true.
#Optionally read this essay on [[Forming beliefs]].
#Optionally read this Wikipedia article on [[w:belief|beliefs]].

[[File:Café wall.svg|thumb|right|300px|Do you believe the horizontal lines in this figure are parallel or tilted?]]
'''Part 2:'''
# Look at the checkered diagram on the right.
# Do you believe the horizontal lines are straight and parallel or do you believe they are tilted to the right or the left?
# Now look at the array from the side or use a straight edge or ruler to examine and measure the horizontal lines. It may be helpful to double click on the figure to examine a larger rendering of the image. You may find it best to print out the image and examine the hard copy rendering of it. Focus on the image one square at a time. Can you see the horizontal lines bend at any point? Do the horizontal lines seem parallel or tilted when you analyze them objectively?
# Based on what you learned in #3 above, look again at the figure. Do you now believe them to be parallel or tilted?
# Do you have more confidence in your ''conception'' of the figure or your ''perception'' of it?

'''Part 3:'''

# View the video: [http://www.ted.com/talks/julia_galef_why_you_think_you_re_right_even_if_you_re_wrong? Why you think you're right — even if you're wrong], Julia Galef, TED Talk, February 2016
# As you go through your daily activities, notice if you are behaving as a ''soldier'' and defending your current beliefs, or if you are acting as a ''scout'' and exploring, expanding your experiences, and challenging your beliefs.  What mindset is serving you best in each instance?

==What is a Theory of Knowledge?==
[[File:Knowing how you Know.jpg|thumb|right|300px|Each of us uses some ''theory of knowledge'' to assess the cacophony of raw stimulus we are constantly exposed to and decide what it is we believe.]]
Our world is full of various stimuli that contend for our attention and masquerade as the truth. Unfortunately much of the information we are exposed to is unreliable and misleading. The diagram on the right illustrates our need to filter the raw stimuli we are exposed to in the world to arrive at our own beliefs. Our ''theory of knowledge'' is the process we use to analyze and integrate raw information sources into our beliefs about what is true, what is false, what we are unsure of, and what we are unaware of.

Your ''theory of knowledge'' is the set of rules you follow to decide what to believe. Since you have chosen your beliefs, you must have some theory of knowledge in some form, however it is unlikely you have given it much thought, written it down, tested it, refined it, or applied it conscientiously to evaluating your own beliefs.
=== Extracting knowledge from information ===
Relationships between data, information, knowledge, and wisdom can be represented by the [[w:DIKW_pyramid|DIKW pyramid]]. Your theory of knowledge is an essential tool for extracting [[w:Knowledge|knowledge]] from a collection of [[w:Information|information]]. 
===Assignment===
*Select 3 information sources from the following list to study.

::News, opinions, analysis, commentary, satire, testimonials, endorsements, threats, conversations, dialogue, rumors, gossip, folk lore, traditions, rules, superstitions, taboos, censorship, speculation, predictions, fear mongering, forecasts, propaganda, advertisement, sales pitches, advocacy, political talking points, religious dogma, scriptures, prophesies, ideology, text books, school lessons, numbers, data, statistics,  lobbying efforts, reports, street lore, peer pressure, web pages, Facebook, twitter, hearsay, disinformation, stories, anecdotes,  legends, fables, myths, allegories, intuition, feelings, premonitions, origin stories, archetypes, suppositions, fallacies, red herrings, authorities, experts, celebrities, councilors, mystics, clairvoyants, charlatans, fools, fakers, and frauds all contend for our attention and opportunities to exert their influence.

*For each of the sources chosen, identify why they may be influential, why they are memorable, why they seem credible, and why they may be misleading or untrue.
*optionally identify each as a source of 1) data, 2) information, 3) knowledge, or 4) wisdom. 
*Identify some belief you have accepted as true based on each of the sources studied above.
*Why (on what basis) do you accept that belief as a true belief?

==Matters of Fact==
Distinguishing among: 1) matters of fact, 2) matters of preference, or 3) matters of controversy is an essential skill in knowing how you know.
Statements can be classified as one of the following three types:&lt;ref&gt;{{cite book |last1=Paul |first1=Richard |last2=Elder |first2=Linda |date=December 5, 2014 |title=Thinker's Guide to the Art of Socratic Questioning (Thinker's Guide Library),  |publisher=Foundation for Critical Thinking |pages=134 |isbn=978-0944583319}} Three Kinds of Questions.&lt;/ref&gt;
#'''Matters of fact.''' These statements can be assessed and verified through the correct use of evidence gathering, and reasoning. A correct statement can be made with conviction. These statements declare “what is” and careful researchers agree on the answer. Examples include: The boiling point of water is 100° Centigrade,  gold is denser than lead, and the movie ''Spotlight'' won Best Picture in 2016. Notice the use of “is” to convey certainty in these statements. These matters of fact are the targets of your theory of knowledge. A reliable theory of knowledge will describe how to effectively research factual claims, how to identify and use reliable sources, and how to resolve disputed or contradictory factual claims. The principle of [[w:Consilience|consilience]] will ensure that reliably researched facts will converge toward the actual reality. 
#'''Matters of taste, preference, or opinion.''' Any claim is acceptable here, because the statement depends only on the preferences of the person making it. Examples include: I feel that purple is the most beautiful color, I prefer chocolate ice-cream to vanilla ice-cream, and I believe that Rembrandt was a better artist than Picasso. Notice the use of “prefer”, “feel”, and “believe” to convey a personal preference. These matters of preference fall outside your theory of knowledge. Just enjoy them.
#'''Matters of controversy.''' Although these are not opinions, sincere experts often disagree on the best answer or the best course of action. These statements propose “what ought to be” or they ask about a topic that is not yet fully and carefully explored or researched. Examples include: I believe the most pressing problem facing the world today is the lack of clean safe drinking water for all people, I think the best approach to reducing gun violence is to require comprehensive background checks for all gun purchases, and I believe incarceration rates are too high in the US. Notice the use of “believe” and “think” to convey personal positions here. Although it is instructive to learn more about matters of controversy by exploring them with [[Practicing Dialogue|dialogue]] and [[Socratic Methods]], they lie outside of your theory of knowledge. 
===Assignment===
#Read this essay on the [[/Height of the Eiffel Tower/]].
#Read over this list of [[Socratic Methods/questions to classify|questions to classify]]. 
#Identify at least five of these questions in each of the following classifications: 1) matters of fact, 2) matters of preference, or 3) matters of controversy.
#Consider the role the principle of [[w:Consilience|consilience]] will play in your own theory of knowledge.

==The Unity of Knowledge==
Because we all live on the same earth, in the same universe, reliable knowledge about our world must converge toward a consistent description of that world. Each phenomenon we observe must fit into a single coherent and integrated description of our universe.  Because we all live in the same universe, as we continue to examine our universe more and more closely, we can agree on a larger set of facts about our universe. Reliable epistemologies—ways of knowing—increase our shared common knowledge.  
===Assignment===
#Browse this [https://archive.org/details/PrintEmergence emergence diagram].
#Read this essay on our [[Knowing How You Know/One World|one world]].
#Please consider your position regarding the [[w:Consilience|unity of knowledge]]. 
##Do you believe that although each person has their own unique life experiences and unique point of view, we are all experiencing the same world, and there are facts that describe our world that we can all agree on? In other words, referring to the allegory of the [[w:Blind_men_and_an_elephant|blind men and an elephant]], each of us is experiencing some aspects of the ''same'' elephant. Furthermore, the [[Knowing How You Know/Height of the Eiffel Tower|Eiffel tower does have a particular height]]. 
##Or do you believe that each of us experiences our own world, their is a different world for each of us and there are not facts that are common among that multiplicity of worlds? Each of us is experiencing a ''different'' elephant. Furthermore, the [[Knowing How You Know/Height of the Eiffel Tower|height of the Eiffel tower]] depends on who is asked about it, and how they are feeling at the moment.
#Consider how your theory of knowledge will address the unity of knowledge. When new information comes to your attention that is inconsistent with a coherent description of the universe, will you: 1) dismiss that new information, 2) modify your present description of the universe to accommodate that new information, or 3) tolerate inconsistencies?
== Examining Ideologies ==
Please complete the module on [[/Examining Ideologies/]] along with the associated assignments.
== Beware of Friendly Persuasion ==
We evolved to trust what friends tell us. Today we have many communications with people who are acquaintances we hardly know. It is wise to verify hearsay by checking facts with reliable sources.
=== Assignment: ===
#[[w:Fact_checking|Fact check]] rumors before repeating them, or assimilating them into your knowledge base.
#Read the essay on [[/Friendly Persuasion/]].
#Complete the Wikiversity Course on [[Evaluating Evidence]].
#Complete the Wikiversity Course on [[Thinking Scientifically]].
#Check facts using [[w:Wikipedia:Identifying_reliable_sources|reliable sources]].

==A Gallery of Example Theories of Knowledge==
It will be helpful to study example Theories of Knowledge to prepare yourself to write your own.
===Assignment:===
#Read the essay [[/Divided by epistemology/]]. 
#Survey this [[Knowing_How_You_Know/gallery|gallery of example Theories of Knowledge]] to understand better how one might be designed and written down. If any of these appeals to you, feel free to adopt it. If you disagree with these, or believe you can improve on these, then please write your own, using the instructions given in the next section.

==Developing your own Theory of Knowledge==
I hope the background provided in this course so far motives you to create your own theory of knowledge.  In this section you will examine how you decide what to believe and write it down; this is your own theory of knowledge. Let’s get started.
===Assignment:===
#Study the materials suggested in this [[Knowing_How_You_Know/annotated|annotated version of the template]] to expand your thinking about how best to decide what to believe. 
#Answer the questions in this [[Knowing_How_You_Know/template|template]] to focus your thinking on this topic. Use the template to get started, and begin knowing how you know.
#Using your answers to the questions in the template as source material, write your theory of knowledge as a series of steps or decision rules.
==Testing your Theory of Knowledge==
Your theory of knowledge will get refined as you use it to decide what to believe. The next assignment provides some questions to use to gain experience using and testing your Theory of Knowledge.
===Assignment===
#Choose 5 questions from this list of [[/general knowledge questions/]] to research.
#Research answers to these questions using any sources deemed reliable by your own Theory of Knowledge.
#Refine your written Theory of Knowledge if you find it difficult to use, or if it gives surprising, conflicting, or unreliable results.
# Continue to align your beliefs with reality.

==Applying your Theory of Knowledge==
Use your theory of Knowledge every day to decide what to believe, and to refine and purify your knowledge stream.
===Assignment===
'''Part 1:'''
#Pay attention to new information as it reaches you. This information may arrive from a news report, social media, books, conversation, podcast, text message, email, phone conversation, gossip, rumors, or other sources.
#Notice if you are inclined to believe this new information or if you are inclined to doubt it.
#Analyze why and how you decided to believe or disbelieve this new information.
#Scrutinize this new information by applying each of the steps of your newly-developed Theory of knowledge.
#Notice if applying your newly-developed Theory of knowledge changes your mind about the new information. 

'''Part 2:'''
#Scan your own beliefs to identify some that may not be well justified.
#Subject beliefs you have held for some time to your newly-developed Theory of knowledge.
#Note if: 1) They are confirmed by your theory of knowledge, 2) your new theory of knowledge causes you to modify, doubt, or change your beliefs, or 3) you refine your theory of knowledge to better reflect your concept of truth.

==Further Reading==
Students interested in learning more about developing and applying a Theory of Knowledge may be interested in the following materials:
*{{cite book |last=Weston |first=Anthony |authorlink=w:Anthony_Weston |title=A Rulebook for Arguments |year=2000 |publisher=Hackett Pub Co Inc |isbn=978-0872205529  |pages=90}}
*{{cite book |last=Copi |first=Irving M. |authorlink=w:Irving_Copi |title=Introduction to Logic |year=2001 |publisher=Prentice Hall |isbn=978-0130337351  |pages=647}}
*{{cite book |last=Cialdini |first=Robert B. |authorlink=w:Robert_Cialdini |title=Influence: The Psychology of Persuasion  |year=1993 |publisher=Collins|isbn=978-0688128166  |pages=336}}
*{{cite book |last=Sewell |first=Keith |authorlink= |title=Leaving Truth |year=2012 |publisher=eBookIt.com |pages=70}}
* {{cite book |last=Haidt |first=Jonathan |authorlink=w:Jonathan_Haidt |title=The Righteous Mind: Why Good People Are Divided by Politics and Religion |year= 2012 |publisher=Pantheon |isbn=978-0307377906  |pages=448}}
* {{cite book |last=de Bono |first=Edward |authorlink=w:Edward_de_Bono |title=Six Thinking Hats |year=1999 |publisher=Back Bay Books |isbn=978-0316178310 |pages=192}}
* {{cite book |last=Silver |first=Nate |authorlink=w:Nate_Silver |title=The Signal and the Noise: Why So Many Predictions Fail — but Some Don't  |year=2012 |publisher=Penguin Press |isbn=978-1594204111 |pages=544}}
* {{cite book |last=Gore |first=Al |authorlink=w:Al_Gore |title=The Assault on Reason |year=2008 |publisher=Penguin Books  |isbn=978-0143113621  |pages=308}}
*{{cite book |last=Ariely |first=Dan |author-link=w:Dan_Ariely |date=September 17, 2024 |title=Misbelief: What Makes Rational People Believe Irrational Things |publisher=Harper Perennial  |pages=320 |isbn=978-0063280434}}
*{{cite book |last=Burton |first=Robert |authorlink=w:Robert_A._Burton |date=March 2008 |title=On Being Certain: Believing You Are Right Even When You're Not |publisher=St. Martin's Griffin |isbn=978-0312541521}}
*{{cite book |last1=Tavris |first1=Carol |last2=Aronson |first2=Elliot |authorlink1=w:Carol_Tavris |authorlink2=w:Elliot_Aronson|date=March 2008 |title=[[w:Mistakes_Were_Made_(But_Not_by_Me)|Mistakes Were Made (But Not by Me)]]: Why We Justify Foolish Beliefs, Bad Decisions, and Hurtful Acts  |publisher=Mariner Books |isbn= 978-0156033909}}
*{{cite book |last=Wolpert |first=Lewis|date=July 2008 |title=Six Impossible Things Before Breakfast: The Evolutionary Origins of Belief   |publisher=W. W. Norton &amp; Company |pages=256 |isbn=978-0393332032 }}
*{{cite book |last=Galef |first=Julia |author-link=w:Julia_Galef|date=April 13, 2021 |title=The Scout Mindset: Why Some People See Things Clearly and Others Don't |publisherPortfolio  |pages=288 |isbn=978-0735217553}}
*{{cite book |last=Pinker |first= Steven |author-link=w:Steven_Pinker|date= September 28, 2021  |title=[[w:Rationality_(book)| Rationality: What It Is, Why It Seems Scarce, Why It Matters]]| publisher= Viking |pages=432 |isbn= 978-0525561996 }}
* {{cite video |people=Robert Kenner |date=July 7, 2015|title=Merchants of Doubt |medium=DVD |language=English  |publisher=Sony Pictures Home Entertainment }}
*{{cite book |last=Gelwick |first=Richard |date=May 12, 2004 |title=The Way of Discovery, an introduction to the thought of Michael Polanyi |publisher=Wipf &amp; Stock |pages=200 |isbn= 978-1592446872}}
*{{cite book |last=Shermer |first=Michael |author-link=w:Michael_Shermer |date=August 7, 2012 |title=The Believing Brain: From Ghosts and Gods to Politics and Conspiracies---How We Construct Beliefs and Reinforce Them as Truths |publisher=St. Martin's Griffin |pages=385 |isbn=978-1250008800}}
*{{cite book |last=Gray |first=Dave |author-link= |date=September 14, 2016 |title=Liminal Thinking: Create the Change You Want by Changing the Way You Think  |publisher=Two Waves Books |pages=184 |isbn=978-1933820460}}
*{{cite book |last=Schulz |first=Kathryn |author-link=w:Kathryn_Schulz |date=June 8, 2010 |title=Being Wrong: Adventures in the Margin of Error |publisher=Ecco |pages=416 |isbn=0061176044}}
* [http://archive.constantcontact.com/fs121/1110472547640/archive/1115496395992.html#LETTER.BLOCK10 Noise to Wisdom]—an appreciative inquiry about wisdom, Essay by Anne Adams November 2013, 
* [http://www.criticalthinkeracademy.com/ Critical Thinker Academy] — Learn how to think, not what to think.
* [http://www.ted.com/talks/naomi_oreskes_why_we_should_believe_in_science Why we should trust scientists], TED Talk, May 2014, Naomi Oreskes

I have not yet read the following books, but they seem interesting and relevant. They are listed here to invite further research.

* ''In the Mind's Eye: Truth Versus Perception: ELA Lessons for Gifted and Advanced Learners in Grades 6'' by Emily Mofield
* ''The Confidence Game'', by Maria Konnikova
* ''The Misinformation Age: How False Beliefs Spread'', by Cailin O'Connor and James Owen Weatherall

==References==
&lt;references/&gt;
{{subpagesif}}
{{CourseCat}} 
[[Category:Life skills]]
[[Category:Applied Wisdom]]
[[Category:Philosophy]]
[[Category:Epistemology]]
[[Category:Knowing How You Know]]
[[Category:Clear Thinking]]
[[Category:Courses]]
{{Clear Thinking}}</text>
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  <page>
    <title>United States Law</title>
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| style=&quot;width:100px&quot; | [[File:Constitution of the United States - DPLA - 9ca804144bd5965e992ae3528bc3c6a3 (page 1).jpg|100px|frameless]]
|
&lt;div style=&quot;font-size:200%;border:none;margin: 0;padding:.1em;color:#000&quot;&gt;'''United States Law Learning Project'''&lt;/div&gt;
&lt;div style=&quot;top:0.2em;font-size:150%&quot;&gt;part of the [[School:Law|'''School of Law''']]&lt;/div&gt;
| style=&quot;width:100px&quot; | [[File:Scale of justice 2.svg|75px|frameless]]
|
|}

&lt;div style=&quot;display:block;border:1px solid #aaaaaa;vertical-align: top;width:99%; background-color:#f9f9ff;{{Text default color}};margin-bottom:10px;margin-top:5px;padding-left:5px;padding-right:4px;&quot;&gt;
&lt;h2 style=&quot;padding:3px; background:#aaccff;{{Text default color}}; color:#000; text-align:center; font-weight:bold; font-size:100%; margin-bottom:5px;margin-top:0;margin-left:-5px;margin-right:-4px;&quot;&gt;Welcome&lt;/h2 &gt;
A very warm welcome to the {{w|United States Law}} Learning Project! The legal system of the United States of America is a complex one with two major levels, namely the federal and state levels. The training of lawyers is controlled by the {{w|American Bar Association}} (ABA). Lawyers advise their clients on legal matters including writing contracts, interpreting the law, and representing them in court.

Another aspect of US law is that it also split into civil and criminal law. Both may involve courts, but the rules are different. In a court trial, criminal cases are more likely to involve juries than civil cases. There are two basic differences between civil and criminal cases:  
# Civil cases are decided on the weight of the evidence. Criminal cases require proof beyond {{w|reasonable doubt}}.  
# Civil cases involving a jury require a majority. Criminal cases require a unanimous decision.  

An example of the difference between the two is the civil suit brought against the {{w|Federal Bureau of Investigation}} (FBI) for their role in the assassination of {{w|Martin Luther King, Jr.}}:  the family succeeded because a majority of the jurors concluded that the weight of the evidence favored the family. A criminal procedure did not come to trial, presumably because the prosecutors felt that the evidence was not sufficient to obtain a unanimous judgment beyond reasonable doubt that certain FBI agents were complicit.&lt;ref&gt;{{cite book |author={{w|William Francis Pepper|Pepper, William F.}} | year=1995 | title=Orders to Kill: The truth behind the murder of Martin Luther King, Jr. |publisher=Warner Books |isbn=0-446-67394-3}}&lt;/ref&gt;

Any questions about following the US Constitution can be presented to the {{w|Supreme Court}} whose nine judges can deem a law or action unconstitutional. If deemed such it is impossible to reinstated unless the Supreme Court revokes its judgement or it is overturned by a subsequent constitutional amendment.

This Project focusses on US Law and covers topics at a college level but it is not a formal qualification. The Project is designed to provide an informal learning experience, which may provide knowledge and skills that can be used elsewhere.

The Project comprises a number of units, each of which covers a separate area of US Law. As tempting as it might be to compare this with the structure of a formal law degree, Wikiversity does not allocate &quot;credits&quot; or &quot;points&quot; to any of the units. Each unit contains a number of smaller subunits and is designed to be studied alongside a relevant textbook from Wikibooks, one of the partner websites of Wikiversity. The links for the textbooks can be found at the start of each unit. Each unit outline will also list additional recommended texts, articles and other materials, which are not compulsory but intended for deeper independent study. Throughout each unit there will be opportunities in the form of quizzes and short essays to enable you to reflect on the material and see how much you understand. There is a larger quiz at the end of the unit, which you can repeat as any times as you wish until you are confident of your understanding of the material. Additionally, there are a number of case studies and suggested essays to complement your studies as well as recommendations for further reading.
&lt;/div&gt;

&lt;div style=&quot;display:block;border:1px solid #aaaaaa;vertical-align: top;width:100%; background-color:#f9f9ff;{{Text default color}};margin-bottom:10px;padding-bottom:5px;padding-left:5px;padding-right:4px;&quot;&gt;
&lt;h2 style=&quot;padding:3px; background:#aaccff;{{Text default color}}; color:#000; text-align:center; font-weight:bold; font-size:100%; margin-bottom:5px;margin-top:0;margin-left:-5px;margin-right:-4px;&quot;&gt;Project summary&lt;/h2 &gt;
* '''Project code:''' United States Law
* '''Prerequisites:''' None
* '''Time investment:''' 1 calendar year
* '''Assessment suggestions:''' 
** A series of quizzes in lieu of examinations on various aspects of United States Law including relevant case law: '''40%'''&lt;!--estimated guess--&gt;
** A series of detailed essays written as journal articles for peer-reviewing: '''40%'''&lt;!--estimated guess--&gt;
** A multi-part personal development portfolio: '''20%'''&lt;!--estimated guess--&gt;
* '''[[WV:Major portals|Portal]]:''' [[Portal:Humanities|Humanities]]
* '''[[WV:Schools|School]]:''' [[School:Law|Law]]
* '''Level:''' Introductory—Advanced
&lt;/div&gt;

&lt;div style=&quot;display:block;border:1px solid #aaaaaa;vertical-align: top;width:100%; background-color:#f9f9ff;{{Text default color}};margin-bottom:10px;padding-bottom:5px;padding-left:5px;padding-right:4px;&quot;&gt;
&lt;h2 style=&quot;padding:3px; background:#aaccff;{{Text default color}}; color:#000; text-align:center; font-weight:bold; font-size:100%; margin-bottom:5px;margin-top:0;margin-left:-5px;margin-right:-4px;&quot;&gt;Content summary&lt;/h2 &gt;
* In this Learning Project, participants will learn about the history and development of United States Law from the 18th century to the modern era, with a particular focus on areas that are usually part of law degrees.

* One of the goals of this project is to utilise free materials, so the learner does not have to pay expensive subscriptions. This will be achieved by the use of a series of free textbooks (from Wikibooks), original source material for statutes and cases, a series of [[Wikiversity Law Reports]], the development of a [[Wikiversity Law Review]], quizzes and other freely available resources.

* It will be noted that purely academic study is insufficient in preparing for legal practice and thus there will be suggested tools to enable some of these aspects. The limitations of online courses like this inhibit more active participation such as the classical skill of {{w|moot court}} but there will be recommendations for overcoming these obstacles.
&lt;/div&gt;

&lt;div style=&quot;display:block;border:1px solid #aaaaaa;vertical-align: top;width:100%; background-color:#f9f9ff;{{Text default color}};margin-bottom:10px;padding-bottom:5px;padding-left:5px;padding-right:4px;&quot;&gt;
&lt;h2 style=&quot;padding:3px; background:#aaccff;{{Text default color}}; color:#000; text-align:center; font-weight:bold; font-size:100%; margin-bottom:5px;margin-top:0;margin-left:-5px;margin-right:-4px;&quot;&gt;Goals&lt;/h2 &gt;
* Study and understand the origins of United States Law;
* Examine the current state of United States Law;
* Suggest tools and methods for participants to improve their practical skills.
&lt;/div&gt;

&lt;div style=&quot;display:block;border:1px solid #aaaaaa;vertical-align: top;width:100%; background-color:#f9f9ff;{{Text default color}};margin-bottom:10px;padding-bottom:5px;padding-left:5px;padding-right:4px;&quot;&gt;
&lt;h2 style=&quot;padding:3px; background:#aaccff;{{Text default color}}; color:#000; text-align:center; font-weight:bold; font-size:100%; margin-bottom:5px;margin-top:0;margin-left:-5px;margin-right:-4px;&quot;&gt;Resources&lt;/h2&gt;
{{center|'''&lt;big&gt;[[/Introduction/]]&lt;/big&gt;'''&lt;br&gt;[[/History/]]&amp;nbsp;&amp;#9642;&amp;nbsp;[[/Reform/]]&amp;nbsp;&amp;#9642;&amp;nbsp;[[/System/]]&amp;nbsp;&amp;#9642;&amp;nbsp;[[/Legal Writing/]]&amp;nbsp;&amp;#9642;&amp;nbsp;[[/First Year Guide/]]}}
{{col-begin}}
{{col-break}}
* [[Comparative law and justice/United States]]
* [[/Civil Procedure/]] ([[:b:US Civil Procedure|Wikibook]])
* [[/Constitutional/]]
* [[/Contract/]] ([[:b:US Contract Law|Wikibook]])
* [[/Copyright/]] ([[:b:US Copyright Law|Wikibook]])
* [[/Corporate/]] ([[:b:US Corporate Law|Wikibook]])
* [[/Criminal/]] ([[:b:US Criminal Law|Wikibook]])
* [[/Education/]]
* [[/Evidence/]] ([[:b:Federal Rules of Evidence|Wikibook]])
* [[/Patents/]] ([[:b:US Patent Law|Wikibook]])
* [[/Property/]] ([[:b:US Property Law|Wikibook]])
* [[/Tort/]] ([[:b:US Tort Law|Wikibook]])
* [[/Trusts and Estates/]] ([[:b:US Trusts and Estates Law|Wikibook]])
* [[Pro se legal representation]]
{{col-break}}
;Supplementary
* [[/Ethics/]]
* [[/Bibliography/]]
** [[/Bibliography/Authors|Authors]]
* [[Wikiversity Law Reports]]
** [[/Case List/]]
* [[/Statute List/]]
* [[Wikiversity Law Review]]
{{col-end}}
&lt;/div&gt;

&lt;div style=&quot;display:block;border:1px solid #aaaaaa;vertical-align: top;width:100%; background-color:#f9f9ff;{{Text default color}};margin-bottom:10px;padding-bottom:5px;padding-left:5px;padding-right:4px;&quot;&gt;
&lt;h2 style=&quot;padding:3px; background:#aaccff;{{Text default color}}; color:#000; text-align:center; font-weight:bold; font-size:100%; margin-bottom:5px;margin-top:0;margin-left:-5px;margin-right:-4px;&quot;&gt;[[Portal:Learning Projects#Learning Groups|Active participants]]&lt;/h2 &gt;
* {{u|Green Giant}}
* {{u|Jadecoppieters}}
* &lt;!--Add your signature here using {{u|Username}}--&gt;
&lt;/div&gt;

&lt;div style=&quot;display:block;border:1px solid #aaaaaa;vertical-align: top;width:100%; background-color:#f9f9ff;{{Text default color}};margin-bottom:10px;padding-bottom:5px;padding-left:5px;padding-right:4px;&quot;&gt;
&lt;h2 style=&quot;padding:3px; background:#aaccff;{{Text default color}}; color:#000; text-align:center; font-weight:bold; font-size:100%; margin-bottom:5px;margin-top:0;margin-left:-5px;margin-right:-4px;&quot;&gt;Notes&lt;/h2 &gt;
{{Reflist}}
&lt;/div&gt;

== External links==
* [https://romeoandjulietlaw.us/ close age consumption law ]

[[Category:United States Law| ]]
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    <title>Coordinate systems/Derivation of formulas/Original Copy from Wikipedia</title>
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      <text bytes="34133" sha1="hpibf37e1eampxtje707cyf9q2bve0k" xml:space="preserve">==Table from Wikipedia==
* from https://en.wikipedia.org/w/index.php?title=Del_in_cylindrical_and_spherical_coordinates&amp;oldid=612099218
* This is the backup copy.  PLEASE DO NOT EDIT (Instead copy and paste onto another page)
{| class=&quot;wikitable&quot; style=&quot;background: white; {{Text default color}}&quot;
|+ Table with the [[del]] operator in cylindrical, spherical and parabolic cylindrical coordinates
&lt;!-- Header --&gt;
|-
! style=&quot;background: white; {{Text default color}}&quot; | Operation
! style=&quot;background: white; {{Text default color}}&quot; | [[Cartesian coordinates]] (''x'', ''y'', ''z'')
! style=&quot;background: white; {{Text default color}}&quot; | [[Cylindrical coordinates]] (''ρ'', ''ϕ'', ''z'')
! style=&quot;background: white; {{Text default color}}&quot; | [[Spherical coordinates]] (''r'', ''θ'', ''ϕ'')
! style=&quot;background: white; {{Text default color}}&quot; | [[Parabolic cylindrical coordinates]] (''σ'', ''τ'', ''z'')

&lt;!-- Definition of coordinates --&gt;
|- style=&quot;text-align:center&quot;
! rowspan=&quot;2&quot; style=&quot;background: white;{{Text default color}};&quot; | Definition&lt;br&gt;of&lt;br&gt;coordinates
| &lt;math&gt;\begin{align}
\rho &amp;= \sqrt{x^2+y^2} \\
\phi &amp;= \arctan(y/x) \\
z    &amp;= z \end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
x &amp;= \rho\cos\phi \\
y &amp;= \rho\sin\phi \\
z &amp;= z \end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
x &amp;= r\sin\theta\cos\phi \\
y &amp;= r\sin\theta\sin\phi \\
z &amp;= r\cos\theta \end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
x &amp;= \sigma \tau\\
y &amp;= \tfrac{1}{2} \left( \tau^{2} - \sigma^{2} \right) \\
z &amp;= z \end{align}&lt;/math&gt;
|- style=&quot;text-align:center&quot;
| &lt;math&gt;\begin{align}
r      &amp;= \sqrt{x^2+y^2+z^2} \\
\theta &amp;= \arccos(z/r)\\
\phi   &amp;= \arctan(y/x) \end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
r      &amp;= \sqrt{\rho^2 + z^2} \\
\theta &amp;= \arctan{(\rho/z)}\\
\phi   &amp;= \phi \end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\rho &amp;= r\sin\theta \\
\phi &amp;= \phi\\
z    &amp;= r\cos\theta \end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\rho\cos\phi &amp;= \sigma \tau\\
\rho\sin\phi &amp;= \tfrac{1}{2} \left( \tau^{2} - \sigma^{2} \right) \\
z &amp;= z \end{align}&lt;/math&gt;

&lt;!-- Definition of unit vectors --&gt;
|- style=&quot;text-align:center&quot;
! rowspan=&quot;2&quot; style=&quot;background: white;{{Text default color}};&quot; | Definition&lt;br&gt;of&lt;br&gt;unit&lt;br&gt;vectors
| &lt;math&gt;\begin{align}
\hat{\boldsymbol\rho} &amp;= \frac{  x \hat{\mathbf x} + y \hat{\mathbf y}}{\sqrt{x^2+y^2}} \\
\hat{\boldsymbol\phi} &amp;= \frac{- y \hat{\mathbf x} + x \hat{\mathbf y}}{\sqrt{x^2+y^2}} \\
\hat{\mathbf z}       &amp;= \hat{\mathbf z}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\hat{\mathbf x} &amp;= \cos\phi\hat{\boldsymbol\rho} - \sin\phi\hat{\boldsymbol\phi} \\
\hat{\mathbf y} &amp;= \sin\phi\hat{\boldsymbol\rho} + \cos\phi\hat{\boldsymbol\phi} \\
\hat{\mathbf z} &amp;= \hat{\mathbf z}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\hat{\mathbf x} &amp;= \sin\theta\cos\phi\hat{\boldsymbol r} + \cos\theta\cos\phi\hat{\boldsymbol\theta}-\sin\phi\hat{\boldsymbol\phi} \\
\hat{\mathbf y} &amp;= \sin\theta\sin\phi\hat{\boldsymbol r} + \cos\theta\sin\phi\hat{\boldsymbol\theta}+\cos\phi\hat{\boldsymbol\phi} \\
\hat{\mathbf z} &amp;= \cos\theta        \hat{\boldsymbol r} - \sin\theta        \hat{\boldsymbol\theta}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\hat{\boldsymbol\sigma} &amp;= \frac{\tau \hat{\mathbf x} - \sigma \hat{\mathbf y}}{\sqrt{\tau^2+\sigma^2}} \\
\hat{\boldsymbol\tau}   &amp;= \frac{\sigma \hat{\mathbf x} + \tau \hat{\mathbf y}}{\sqrt{\tau^2+\sigma^2}} \\
\hat{\mathbf z}         &amp;= \hat{\mathbf z}
\end{align}&lt;/math&gt;
|- style=&quot;text-align:center&quot;
| &lt;math&gt;\begin{align}
\hat{\mathbf r}         &amp;= \frac{x \hat{\mathbf x} + y \hat{\mathbf y} + z \hat{\mathbf z}}{\sqrt{x^2+y^2+z^2}} \\
\hat{\boldsymbol\theta} &amp;= \frac{x z \hat{\mathbf x} + y z \hat{\mathbf y} - \left(x^2 + y^2\right) \hat{\mathbf z}}{\sqrt{x^2+y^2} \sqrt{x^2+y^2+z^2}} \\
\hat{\boldsymbol\phi}   &amp;= \frac{- y \hat{\mathbf x} + x \hat{\mathbf y}}{\sqrt{x^2+y^2}}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\hat{\mathbf r}         &amp;= \frac{\rho \hat{\boldsymbol\rho} +    z \hat{\mathbf z}}{\sqrt{\rho^2 +z^2}} \\
\hat{\boldsymbol\theta} &amp;= \frac{   z \hat{\boldsymbol\rho} - \rho \hat{\mathbf z}}{\sqrt{\rho^2 +z^2}} \\
\hat{\boldsymbol\phi}   &amp;= \hat{\boldsymbol\phi}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\hat{\boldsymbol\rho} &amp;= \sin\theta \hat{\mathbf r} + \cos\theta \hat{\boldsymbol\theta} \\
\hat{\boldsymbol\phi} &amp;= \hat{\boldsymbol\phi} \\
\hat{\mathbf z}       &amp;= \cos\theta \hat{\mathbf r} - \sin\theta \hat{\boldsymbol\theta}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{matrix}
\end{matrix}&lt;/math&gt;

&lt;!-- Definition of A --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white; {{Text default color}}&quot; | A [[vector field]] &lt;math&gt;\mathbf A&lt;/math&gt;
| &lt;math&gt;A_x      \hat{\mathbf x}         + A_y      \hat{\mathbf y}         + A_z    \hat{\mathbf z}&lt;/math&gt;
| &lt;math&gt;A_\rho   \hat{\boldsymbol\rho}   + A_\phi   \hat{\boldsymbol\phi}   + A_z    \hat{\mathbf z}&lt;/math&gt;
| &lt;math&gt;A_r      \hat{\boldsymbol r}     + A_\theta \hat{\boldsymbol\theta} + A_\phi \hat{\boldsymbol\phi}&lt;/math&gt;
| &lt;math&gt;A_\sigma \hat{\boldsymbol\sigma} + A_\tau   \hat{\boldsymbol\tau}   + A_\phi \hat{\mathbf z}&lt;/math&gt;

&lt;!-- grad f --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white; {{Text default color}}&quot; | [[Gradient]] &lt;math&gt;\nabla f&lt;/math&gt;
| &lt;math&gt;{\partial f \over \partial x}\hat{\mathbf x} + {\partial f \over \partial y}\hat{\mathbf y}
+ {\partial f \over \partial z}\hat{\mathbf z}&lt;/math&gt;
| &lt;math&gt;{\partial f \over \partial \rho}\hat{\boldsymbol \rho}
+ {1 \over \rho}{\partial f \over \partial \phi}\hat{\boldsymbol \phi}
+ {\partial f \over \partial z}\hat{\mathbf z}&lt;/math&gt;
| &lt;math&gt;{\partial f \over \partial r}\hat{\boldsymbol r}
+ {1 \over r}{\partial f \over \partial \theta}\hat{\boldsymbol \theta}
+ {1 \over r\sin\theta}{\partial f \over \partial \phi}\hat{\boldsymbol \phi}&lt;/math&gt;
| &lt;math&gt; \frac{1}{\sqrt{\sigma^{2} + \tau^{2}}} {\partial f \over \partial \sigma}\hat{\boldsymbol \sigma} + \frac{1}{\sqrt{\sigma^{2} + \tau^{2}}} {\partial f \over \partial \tau}\hat{\boldsymbol \tau} + {\partial f \over \partial z}\hat{\mathbf z}&lt;/math&gt;

&lt;!-- div A --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white; {{Text default color}}&quot; | [[Divergence]] &lt;math&gt;\nabla \cdot \mathbf{A}&lt;/math&gt;
| &lt;math&gt;{\partial A_x \over \partial x} + {\partial A_y \over \partial y} + {\partial A_z \over \partial z}&lt;/math&gt;
| &lt;math&gt;{1 \over \rho}{\partial \left( \rho A_\rho  \right) \over \partial \rho}
+ {1 \over \rho}{\partial A_\phi \over \partial \phi}
+ {\partial A_z \over \partial z}&lt;/math&gt;
| &lt;math&gt;{1 \over r^2}{\partial \left( r^2 A_r \right) \over \partial r}
+ {1 \over r\sin\theta}{\partial \over \partial \theta} \left(  A_\theta\sin\theta \right)
+ {1 \over r\sin\theta}{\partial A_\phi \over \partial \phi}&lt;/math&gt;
| &lt;math&gt; \frac{1}{\sigma^{2} + \tau^{2}}\left({\partial (\sqrt{\sigma^2+\tau^2} A_\sigma) \over \partial \sigma} + {\partial (\sqrt{\sigma^2+\tau^2} A_\tau) \over \partial \tau}\right) + {\partial A_z \over \partial z}&lt;/math&gt;

&lt;!-- curl A --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white;{{Text default color}};&quot; | [[Curl (mathematics)|Curl]] &lt;math&gt;\nabla \times \mathbf{A}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  \left(\frac{\partial A_z}{\partial y} - \frac{\partial A_y}{\partial z}\right) &amp;\hat{\mathbf x} + \\
+ \left(\frac{\partial A_x}{\partial z} - \frac{\partial A_z}{\partial x}\right) &amp;\hat{\mathbf y} + \\
+ \left(\frac{\partial A_y}{\partial x} - \frac{\partial A_x}{\partial y}\right) &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  \left(
    \frac{1}{\rho} \frac{\partial A_z}{\partial \phi}
  - \frac{\partial A_\phi}{\partial z}
  \right) &amp;\hat{\boldsymbol \rho} \\
+ \left(
    \frac{\partial A_\rho}{\partial z}
  - \frac{\partial A_z}{\partial \rho}
  \right) &amp;\hat{\boldsymbol \phi} \\
+ \frac{1}{\rho} \left(
    \frac{\partial \left(\rho A_\phi\right)}{\partial \rho}
  - \frac{\partial A_\rho}{\partial \phi}
  \right) &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  \frac{1}{r\sin\theta} \left(
    \frac{\partial}{\partial \theta} \left(A_\phi\sin\theta \right)
  - \frac{\partial A_\theta}{\partial \phi}
  \right) &amp;\hat{\boldsymbol r} \\
+ \frac{1}{r} \left(
    \frac{1}{\sin\theta} \frac{\partial A_r}{\partial \phi}
  - \frac{\partial}{\partial r} \left( r A_\phi \right)
  \right) &amp;\hat{\boldsymbol \theta}  \\
+ \frac{1}{r} \left(
    \frac{\partial}{\partial r} \left( r A_\theta \right)
  - \frac{\partial A_r}{\partial \theta}
  \right) &amp;\hat{\boldsymbol \phi}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  \left(
    \frac{1}{\sqrt{\sigma^2 + \tau^2}} \frac{\partial A_z}{\partial \tau}
  - \frac{\partial A_\tau}{\partial z}
  \right) &amp;\hat{\boldsymbol \sigma} \\
- \left(
    \frac{1}{\sqrt{\sigma^2 + \tau^2}} \frac{\partial A_z}{\partial \sigma}
  - \frac{\partial A_\sigma}{\partial z}
  \right) &amp;\hat{\boldsymbol \tau} \\
+ \frac{1}{\sqrt{\sigma^2 + \tau^2}} \left(
    \frac{\partial \left(\sqrt{\sigma^2 + \tau^2} A_\sigma \right)}{\partial \tau}
  - \frac{\partial \left(\sqrt{\sigma^2 + \tau^2} A_\tau \right)}{\partial \sigma}
  \right) &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;

&lt;!-- Laplacian f --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white; {{Text default color}}&quot; | [[Laplace operator]] &lt;math&gt;\Delta f \equiv \nabla^2 f&lt;/math&gt;
| &lt;math&gt;{\partial^2 f \over \partial x^2} + {\partial^2 f \over \partial y^2} + {\partial^2 f \over \partial z^2}&lt;/math&gt;
| &lt;math&gt;{1 \over \rho}{\partial \over \partial \rho}\left(\rho {\partial f \over \partial \rho}\right)
+ {1 \over \rho^2}{\partial^2 f \over \partial \phi^2}
+ {\partial^2 f \over \partial z^2}&lt;/math&gt;
| &lt;math&gt;{1 \over r^2}{\partial \over \partial r}\!\left(r^2 {\partial f \over \partial r}\right)
\!+\!{1 \over r^2\!\sin\theta}{\partial \over \partial \theta}\!\left(\sin\theta {\partial f \over \partial \theta}\right)
\!+\!{1 \over r^2\!\sin^2\theta}{\partial^2 f \over \partial \phi^2}&lt;/math&gt;
| &lt;math&gt; \frac{1}{\sigma^{2} + \tau^{2}}
\left(  \frac{\partial^{2} f}{\partial \sigma^{2}} +
\frac{\partial^{2} f}{\partial \tau^{2}} \right) +
\frac{\partial^{2} f}{\partial z^{2}}
&lt;/math&gt;

&lt;!-- vector Laplacian A --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white; {{Text default color}}&quot; | [[Vector Laplacian]] &lt;math&gt;\Delta \mathbf{A} \equiv \nabla^2 \mathbf{A}&lt;/math&gt;
| &lt;math&gt;\Delta A_x \hat{\mathbf x} + \Delta A_y \hat{\mathbf y} + \Delta A_z \hat{\mathbf z} &lt;/math&gt;
| {{hidden begin|title = click to view or hide}}
&lt;math&gt;\begin{align}
  \mathopen{}\left(\Delta A_\rho - \frac{A_\rho}{\rho^2} - \frac{2}{\rho^2} \frac{\partial A_\phi}{\partial \phi}\right)\mathclose{} &amp;\hat{\boldsymbol\rho} \\
+ \mathopen{}\left(\Delta A_\phi - \frac{A_\phi}{\rho^2} + \frac{2}{\rho^2} \frac{\partial A_\rho}{\partial \phi}\right)\mathclose{} &amp;\hat{\boldsymbol\phi} \\
+ \Delta A_z &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;
{{hidden end}}
| style=&quot;text-align:center&quot; | {{hidden begin|title = click to view or hide}}
&lt;math&gt;\begin{align}
  \left(\Delta A_r - \frac{2 A_r}{r^2}
  - \frac{2}{r^2\sin\theta} \frac{\partial \left(A_\theta \sin\theta\right)}{\partial\theta}
  - \frac{2}{r^2\sin\theta}{\frac{\partial A_\phi}{\partial \phi}}\right) &amp;\hat{\boldsymbol r} \\
+ \left(\Delta A_\theta - \frac{A_\theta}{r^2\sin^2\theta}
  + \frac{2}{r^2} \frac{\partial A_r}{\partial \theta}
  - \frac{2 \cos\theta}{r^2\sin^2\theta} \frac{\partial A_\phi}{\partial \phi}\right) &amp;\hat{\boldsymbol\theta} \\
+ \left(\Delta A_\phi - \frac{A_\phi}{r^2\sin^2\theta}
  + \frac{2}{r^2\sin\theta} \frac{\partial A_r}{\partial \phi}
  + \frac{2 \cos\theta}{r^2\sin^2\theta} \frac{\partial A_\theta}{\partial \phi}\right) &amp;\hat{\boldsymbol\phi}
\end{align}&lt;/math&gt;
{{hidden end}}

&lt;!-- Material derivative (A dot del)B --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white; {{Text default color}}&quot; | [[Material derivative]]&lt;ref name=&quot;Mathworld&quot;&gt;{{cite web |url=http://mathworld.wolfram.com/ConvectiveOperator.html|title=Convective Operator |author=Weisstein, Eric W. |date= |work=Mathworld |publisher= |accessdate=23 March 2011}}&lt;/ref&gt;
&lt;math&gt;(\mathbf{A} \cdot \nabla) \mathbf{B}&lt;/math&gt;
&lt;!--         Cartesian --&gt;
| {{hidden begin|title = click to view or hide}}
&lt;math&gt;\begin{align}
  \left(A_x \frac{\partial B_x}{\partial x} + A_y \frac{\partial B_x}{\partial y} + A_z \frac{\partial B_x}{\partial z}\right) &amp;\hat{\mathbf{x}} \\
+ \left(A_x \frac{\partial B_y}{\partial x} + A_y \frac{\partial B_y}{\partial y} + A_z \frac{\partial B_y}{\partial z}\right) &amp;\hat{\mathbf{y}} \\
+ \left(A_x \frac{\partial B_z}{\partial x} + A_y \frac{\partial B_z}{\partial y} + A_z \frac{\partial B_z}{\partial z}\right) &amp;\hat{\mathbf{z}}
\end{align}&lt;/math&gt;
{{hidden end}}
&lt;!--         Cylindrical \frac{\partial B_}{\partial } --&gt;
| {{hidden begin|title = click to view or hide}}
&lt;math&gt;\begin{align}
  \left(A_\rho \frac{\partial B_\rho}{\partial \rho}+\frac{A_\phi}{\rho}\frac{\partial B_\rho}{\partial \phi}+A_z\frac{\partial B_\rho}{\partial z}-\frac{A_\phi B_\phi}{\rho}\right)
  &amp;\hat{\boldsymbol\rho} \\
+ \left(A_\rho \frac{\partial B_\phi}{\partial \rho} + \frac{A_\phi}{\rho}\frac{\partial B_\phi}{\partial \phi} + A_z\frac{\partial B_\phi}{\partial z} + \frac{A_\phi B_\rho}{\rho}\right)
  &amp;\hat{\boldsymbol\phi}\\
+ \left(A_\rho \frac{\partial B_z}{\partial \rho}+\frac{A_\phi}{\rho}\frac{\partial B_z}{\partial \phi}+A_z\frac{\partial B_z}{\partial z}\right)
  &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;
{{hidden end}}
&lt;!--         Sp --&gt;
| style=&quot;text-align:center&quot; | {{hidden begin|title = click to view or hide}}
&lt;math&gt;\begin{align}
  \left(
    A_r \frac{\partial B_r}{\partial r}
  + \frac{A_\theta}{r} \frac{\partial B_r}{\partial \theta}
  + \frac{A_\phi}{r\sin\theta} \frac{\partial B_r}{\partial \phi}
  - \frac{A_\theta B_\theta + A_\phi B_\phi}{r}
  \right) &amp;\hat{\boldsymbol r} \\
+ \left(
    A_r \frac{\partial B_\theta}{\partial r}
  + \frac{A_\theta}{r} \frac{\partial B_\theta}{\partial \theta}
  + \frac{A_\phi}{r\sin\theta} \frac{\partial B_\theta}{\partial \phi}
  + \frac{A_\theta B_r}{r} - \frac{A_\phi B_\phi\cot\theta}{r}
  \right) &amp;\hat{\boldsymbol\theta} \\
+ \left(
    A_r \frac{\partial B_\phi}{\partial r}
  + \frac{A_\theta}{r} \frac{\partial B_\phi}{\partial \theta}
  + \frac{A_\phi}{r\sin\theta} \frac{\partial B_\phi}{\partial \phi}
  + \frac{A_\phi B_r}{r}
  + \frac{A_\phi B_\theta \cot\theta}{r}
  \right) &amp;\hat{\boldsymbol\phi}
\end{align}&lt;/math&gt;
{{hidden end}}

&lt;!-- Differentials displacement --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white; {{Text default color}}&quot; | Differential displacement
| &lt;math&gt;d\mathbf{l} = dx \, \hat{\mathbf x} + dy \, \hat{\mathbf y} + dz \, \hat{\mathbf z}&lt;/math&gt;
| &lt;math&gt;d\mathbf{l} = d\rho \, \hat{\boldsymbol \rho} + \rho \, d\phi \, \hat{\boldsymbol \phi} + dz \, \hat{\mathbf z}&lt;/math&gt;
| &lt;math&gt;d\mathbf{l} = dr \, \hat{\mathbf r} + r \, d\theta \, \hat{\boldsymbol \theta} + r \, \sin\theta \, d\phi \, \hat{\boldsymbol \phi}&lt;/math&gt;
| &lt;math&gt;d\mathbf{l} = \sqrt{\sigma^2 + \tau^2} \,  d\sigma \, \hat{\boldsymbol \sigma} + \sqrt{\sigma^2 + \tau^2} \, d\tau \, \hat{\boldsymbol \tau} + dz \, \hat{\mathbf z}&lt;/math&gt;

&lt;!-- Differentials normal area --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white; {{Text default color}}&quot; | Differential normal area &lt;math&gt;d \mathbf S&lt;/math&gt;
| &lt;math&gt;\begin{align}
  dy \, dz &amp;\hat{\mathbf x} \\
+ dx \, dz &amp;\hat{\mathbf y} \\
+ dx \, dy &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  \rho \, d\phi \, dz    &amp;\hat{\boldsymbol\rho} \\
+         d\rho \, dz    &amp;\hat{\boldsymbol\phi} \\
+ \rho \, d\rho \, d\phi &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  r^2 \sin\theta \, d\theta \, d\phi   &amp;\hat{\mathbf r} \\
+ r   \sin\theta \, dr      \, d\phi   &amp;\hat{\boldsymbol\theta} \\
+ r              \, dr      \, d\theta &amp;\hat{\boldsymbol\phi}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  \sqrt{\sigma^2 + \tau^2}       \, d\tau   \, dz    &amp;\hat{\boldsymbol\sigma} \\
+ \sqrt{\sigma^2 + \tau^2}       \, d\sigma \, dz    &amp;\hat{\boldsymbol\tau} \\
+ \left(\sigma^2 + \tau^2\right) \, d\sigma \, d\tau &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;

&lt;!-- Differentials volume --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white;{{Text default color}};&quot; | Differential volume &lt;math&gt;dV&lt;/math&gt;
| &lt;math&gt;dx \, dy \, dz&lt;/math&gt;
| &lt;math&gt;\rho \, d\rho \, d\phi \, dz&lt;/math&gt;
| &lt;math&gt;r^2 \sin\theta \, dr \, d\theta \, d\phi&lt;/math&gt;
| &lt;math&gt;\left(\sigma^2 + \tau^2\right) d\sigma \, d\tau \, dz&lt;/math&gt;

&lt;!-- nabla's on nabla's --&gt;
|-
| colspan=5 | &lt;strong&gt;Non-trivial calculation rules:&lt;/strong&gt;
#  &lt;math&gt;\operatorname{div}  \, \operatorname{grad} f          \equiv \nabla \cdot  \nabla f = \nabla^2 f \equiv \Delta f&lt;/math&gt;
#  &lt;math&gt;\operatorname{curl} \, \operatorname{grad} f          \equiv \nabla \times \nabla f = \mathbf 0&lt;/math&gt;
#  &lt;math&gt;\operatorname{div}  \, \operatorname{curl} \mathbf{A} \equiv \nabla \cdot  (\nabla \times \mathbf{A}) = 0&lt;/math&gt;
#  &lt;math&gt;\operatorname{curl} \, \operatorname{curl} \mathbf{A} \equiv \nabla \times (\nabla \times \mathbf{A}) = \nabla (\nabla \cdot \mathbf{A}) - \nabla^2 \mathbf{A}&lt;/math&gt; ([[Triple_product#Vector_triple_product|Lagrange's formula]] for del)
#  &lt;math&gt;\Delta (f g) = f \Delta g + 2 \nabla f \cdot \nabla g + g \Delta f&lt;/math&gt;
|}

==Original Wikipedia Table==
{{hidden begin|title= hidden because it uses the Wikiversity-dysfunctional collapsable template}}
* from https://en.wikipedia.org/w/index.php?title=Del_in_cylindrical_and_spherical_coordinates&amp;oldid=612099218
* Please do not edit or modify this table without very good reason
{| class=&quot;wikitable&quot; style=&quot;background: white;{{Text default color}};&quot;
|+ Table with the [[del]] operator in cylindrical, spherical and parabolic cylindrical coordinates
&lt;!-- Header --&gt;
|-
! style=&quot;background: white;{{Text default color}};&quot; | Operation
! style=&quot;background: white;{{Text default color}};&quot; | [[Cartesian coordinates]] (''x'', ''y'', ''z'')
! style=&quot;background: white;{{Text default color}};&quot; | [[Cylindrical coordinates]] (''ρ'', ''ϕ'', ''z'')
! style=&quot;background: white;{{Text default color}};&quot; | [[Spherical coordinates]] (''r'', ''θ'', ''ϕ'')
! style=&quot;background: white;{{Text default color}};&quot; | [[Parabolic cylindrical coordinates]] (''σ'', ''τ'', ''z'')

&lt;!-- Definition of coordinates --&gt;
|- style=&quot;text-align:center&quot;
! rowspan=&quot;2&quot; style=&quot;background: white;{{Text default color}};&quot; | Definition&lt;br&gt;of&lt;br&gt;coordinates
| &lt;math&gt;\begin{align}
\rho &amp;= \sqrt{x^2+y^2} \\
\phi &amp;= \arctan(y/x) \\
z    &amp;= z \end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
x &amp;= \rho\cos\phi \\
y &amp;= \rho\sin\phi \\
z &amp;= z \end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
x &amp;= r\sin\theta\cos\phi \\
y &amp;= r\sin\theta\sin\phi \\
z &amp;= r\cos\theta \end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
x &amp;= \sigma \tau\\
y &amp;= \tfrac{1}{2} \left( \tau^{2} - \sigma^{2} \right) \\
z &amp;= z \end{align}&lt;/math&gt;
|- style=&quot;text-align:center&quot;
| &lt;math&gt;\begin{align}
r      &amp;= \sqrt{x^2+y^2+z^2} \\
\theta &amp;= \arccos(z/r)\\
\phi   &amp;= \arctan(y/x) \end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
r      &amp;= \sqrt{\rho^2 + z^2} \\
\theta &amp;= \arctan{(\rho/z)}\\
\phi   &amp;= \phi \end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\rho &amp;= r\sin\theta \\
\phi &amp;= \phi\\
z    &amp;= r\cos\theta \end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\rho\cos\phi &amp;= \sigma \tau\\
\rho\sin\phi &amp;= \tfrac{1}{2} \left( \tau^{2} - \sigma^{2} \right) \\
z &amp;= z \end{align}&lt;/math&gt;

&lt;!-- Definition of unit vectors --&gt;
|- style=&quot;text-align:center&quot;
! rowspan=&quot;2&quot; style=&quot;background: white;{{Text default color}};&quot; | Definition&lt;br&gt;of&lt;br&gt;unit&lt;br&gt;vectors
| &lt;math&gt;\begin{align}
\hat{\boldsymbol\rho} &amp;= \frac{  x \hat{\mathbf x} + y \hat{\mathbf y}}{\sqrt{x^2+y^2}} \\
\hat{\boldsymbol\phi} &amp;= \frac{- y \hat{\mathbf x} + x \hat{\mathbf y}}{\sqrt{x^2+y^2}} \\
\hat{\mathbf z}       &amp;= \hat{\mathbf z}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\hat{\mathbf x} &amp;= \cos\phi\hat{\boldsymbol\rho} - \sin\phi\hat{\boldsymbol\phi} \\
\hat{\mathbf y} &amp;= \sin\phi\hat{\boldsymbol\rho} + \cos\phi\hat{\boldsymbol\phi} \\
\hat{\mathbf z} &amp;= \hat{\mathbf z}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\hat{\mathbf x} &amp;= \sin\theta\cos\phi\hat{\boldsymbol r} + \cos\theta\cos\phi\hat{\boldsymbol\theta}-\sin\phi\hat{\boldsymbol\phi} \\
\hat{\mathbf y} &amp;= \sin\theta\sin\phi\hat{\boldsymbol r} + \cos\theta\sin\phi\hat{\boldsymbol\theta}+\cos\phi\hat{\boldsymbol\phi} \\
\hat{\mathbf z} &amp;= \cos\theta        \hat{\boldsymbol r} - \sin\theta        \hat{\boldsymbol\theta}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\hat{\boldsymbol\sigma} &amp;= \frac{\tau \hat{\mathbf x} - \sigma \hat{\mathbf y}}{\sqrt{\tau^2+\sigma^2}} \\
\hat{\boldsymbol\tau}   &amp;= \frac{\sigma \hat{\mathbf x} + \tau \hat{\mathbf y}}{\sqrt{\tau^2+\sigma^2}} \\
\hat{\mathbf z}         &amp;= \hat{\mathbf z}
\end{align}&lt;/math&gt;
|- style=&quot;text-align:center&quot;
| &lt;math&gt;\begin{align}
\hat{\mathbf r}         &amp;= \frac{x \hat{\mathbf x} + y \hat{\mathbf y} + z \hat{\mathbf z}}{\sqrt{x^2+y^2+z^2}} \\
\hat{\boldsymbol\theta} &amp;= \frac{x z \hat{\mathbf x} + y z \hat{\mathbf y} - \left(x^2 + y^2\right) \hat{\mathbf z}}{\sqrt{x^2+y^2} \sqrt{x^2+y^2+z^2}} \\
\hat{\boldsymbol\phi}   &amp;= \frac{- y \hat{\mathbf x} + x \hat{\mathbf y}}{\sqrt{x^2+y^2}}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\hat{\mathbf r}         &amp;= \frac{\rho \hat{\boldsymbol\rho} +    z \hat{\mathbf z}}{\sqrt{\rho^2 +z^2}} \\
\hat{\boldsymbol\theta} &amp;= \frac{   z \hat{\boldsymbol\rho} - \rho \hat{\mathbf z}}{\sqrt{\rho^2 +z^2}} \\
\hat{\boldsymbol\phi}   &amp;= \hat{\boldsymbol\phi}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
\hat{\boldsymbol\rho} &amp;= \sin\theta \hat{\mathbf r} + \cos\theta \hat{\boldsymbol\theta} \\
\hat{\boldsymbol\phi} &amp;= \hat{\boldsymbol\phi} \\
\hat{\mathbf z}       &amp;= \cos\theta \hat{\mathbf r} - \sin\theta \hat{\boldsymbol\theta}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{matrix}
\end{matrix}&lt;/math&gt;

&lt;!-- Definition of A --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white; {{Text default color}}&quot; | A [[vector field]] &lt;math&gt;\mathbf A&lt;/math&gt;
| &lt;math&gt;A_x      \hat{\mathbf x}         + A_y      \hat{\mathbf y}         + A_z    \hat{\mathbf z}&lt;/math&gt;
| &lt;math&gt;A_\rho   \hat{\boldsymbol\rho}   + A_\phi   \hat{\boldsymbol\phi}   + A_z    \hat{\mathbf z}&lt;/math&gt;
| &lt;math&gt;A_r      \hat{\boldsymbol r}     + A_\theta \hat{\boldsymbol\theta} + A_\phi \hat{\boldsymbol\phi}&lt;/math&gt;
| &lt;math&gt;A_\sigma \hat{\boldsymbol\sigma} + A_\tau   \hat{\boldsymbol\tau}   + A_\phi \hat{\mathbf z}&lt;/math&gt;

&lt;!-- grad f --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white;{{Text default color}};&quot; | [[Gradient]] &lt;math&gt;\nabla f&lt;/math&gt;
| &lt;math&gt;{\partial f \over \partial x}\hat{\mathbf x} + {\partial f \over \partial y}\hat{\mathbf y}
+ {\partial f \over \partial z}\hat{\mathbf z}&lt;/math&gt;
| &lt;math&gt;{\partial f \over \partial \rho}\hat{\boldsymbol \rho}
+ {1 \over \rho}{\partial f \over \partial \phi}\hat{\boldsymbol \phi}
+ {\partial f \over \partial z}\hat{\mathbf z}&lt;/math&gt;
| &lt;math&gt;{\partial f \over \partial r}\hat{\boldsymbol r}
+ {1 \over r}{\partial f \over \partial \theta}\hat{\boldsymbol \theta}
+ {1 \over r\sin\theta}{\partial f \over \partial \phi}\hat{\boldsymbol \phi}&lt;/math&gt;
| &lt;math&gt; \frac{1}{\sqrt{\sigma^{2} + \tau^{2}}} {\partial f \over \partial \sigma}\hat{\boldsymbol \sigma} + \frac{1}{\sqrt{\sigma^{2} + \tau^{2}}} {\partial f \over \partial \tau}\hat{\boldsymbol \tau} + {\partial f \over \partial z}\hat{\mathbf z}&lt;/math&gt;

&lt;!-- div A --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white;{{Text default color}};&quot; | [[Divergence]] &lt;math&gt;\nabla \cdot \mathbf{A}&lt;/math&gt;
| &lt;math&gt;{\partial A_x \over \partial x} + {\partial A_y \over \partial y} + {\partial A_z \over \partial z}&lt;/math&gt;
| &lt;math&gt;{1 \over \rho}{\partial \left( \rho A_\rho  \right) \over \partial \rho}
+ {1 \over \rho}{\partial A_\phi \over \partial \phi}
+ {\partial A_z \over \partial z}&lt;/math&gt;
| &lt;math&gt;{1 \over r^2}{\partial \left( r^2 A_r \right) \over \partial r}
+ {1 \over r\sin\theta}{\partial \over \partial \theta} \left(  A_\theta\sin\theta \right)
+ {1 \over r\sin\theta}{\partial A_\phi \over \partial \phi}&lt;/math&gt;
| &lt;math&gt; \frac{1}{\sigma^{2} + \tau^{2}}\left({\partial (\sqrt{\sigma^2+\tau^2} A_\sigma) \over \partial \sigma} + {\partial (\sqrt{\sigma^2+\tau^2} A_\tau) \over \partial \tau}\right) + {\partial A_z \over \partial z}&lt;/math&gt;

&lt;!-- curl A --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white;{{Text default color}};&quot; | [[Curl (mathematics)|Curl]] &lt;math&gt;\nabla \times \mathbf{A}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  \left(\frac{\partial A_z}{\partial y} - \frac{\partial A_y}{\partial z}\right) &amp;\hat{\mathbf x} + \\
+ \left(\frac{\partial A_x}{\partial z} - \frac{\partial A_z}{\partial x}\right) &amp;\hat{\mathbf y} + \\
+ \left(\frac{\partial A_y}{\partial x} - \frac{\partial A_x}{\partial y}\right) &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  \left(
    \frac{1}{\rho} \frac{\partial A_z}{\partial \phi}
  - \frac{\partial A_\phi}{\partial z}
  \right) &amp;\hat{\boldsymbol \rho} \\
+ \left(
    \frac{\partial A_\rho}{\partial z}
  - \frac{\partial A_z}{\partial \rho}
  \right) &amp;\hat{\boldsymbol \phi} \\
+ \frac{1}{\rho} \left(
    \frac{\partial \left(\rho A_\phi\right)}{\partial \rho}
  - \frac{\partial A_\rho}{\partial \phi}
  \right) &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  \frac{1}{r\sin\theta} \left(
    \frac{\partial}{\partial \theta} \left(A_\phi\sin\theta \right)
  - \frac{\partial A_\theta}{\partial \phi}
  \right) &amp;\hat{\boldsymbol r} \\
+ \frac{1}{r} \left(
    \frac{1}{\sin\theta} \frac{\partial A_r}{\partial \phi}
  - \frac{\partial}{\partial r} \left( r A_\phi \right)
  \right) &amp;\hat{\boldsymbol \theta}  \\
+ \frac{1}{r} \left(
    \frac{\partial}{\partial r} \left( r A_\theta \right)
  - \frac{\partial A_r}{\partial \theta}
  \right) &amp;\hat{\boldsymbol \phi}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  \left(
    \frac{1}{\sqrt{\sigma^2 + \tau^2}} \frac{\partial A_z}{\partial \tau}
  - \frac{\partial A_\tau}{\partial z}
  \right) &amp;\hat{\boldsymbol \sigma} \\
- \left(
    \frac{1}{\sqrt{\sigma^2 + \tau^2}} \frac{\partial A_z}{\partial \sigma}
  - \frac{\partial A_\sigma}{\partial z}
  \right) &amp;\hat{\boldsymbol \tau} \\
+ \frac{1}{\sqrt{\sigma^2 + \tau^2}} \left(
    \frac{\partial \left(\sqrt{\sigma^2 + \tau^2} A_\sigma \right)}{\partial \tau}
  - \frac{\partial \left(\sqrt{\sigma^2 + \tau^2} A_\tau \right)}{\partial \sigma}
  \right) &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;

&lt;!-- Laplacian f --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white;{{Text default color}};&quot; | [[Laplace operator]] &lt;math&gt;\Delta f \equiv \nabla^2 f&lt;/math&gt;
| &lt;math&gt;{\partial^2 f \over \partial x^2} + {\partial^2 f \over \partial y^2} + {\partial^2 f \over \partial z^2}&lt;/math&gt;
| &lt;math&gt;{1 \over \rho}{\partial \over \partial \rho}\left(\rho {\partial f \over \partial \rho}\right)
+ {1 \over \rho^2}{\partial^2 f \over \partial \phi^2}
+ {\partial^2 f \over \partial z^2}&lt;/math&gt;
| &lt;math&gt;{1 \over r^2}{\partial \over \partial r}\!\left(r^2 {\partial f \over \partial r}\right)
\!+\!{1 \over r^2\!\sin\theta}{\partial \over \partial \theta}\!\left(\sin\theta {\partial f \over \partial \theta}\right)
\!+\!{1 \over r^2\!\sin^2\theta}{\partial^2 f \over \partial \phi^2}&lt;/math&gt;
| &lt;math&gt; \frac{1}{\sigma^{2} + \tau^{2}}
\left(  \frac{\partial^{2} f}{\partial \sigma^{2}} +
\frac{\partial^{2} f}{\partial \tau^{2}} \right) +
\frac{\partial^{2} f}{\partial z^{2}}
&lt;/math&gt;

&lt;!-- vector Laplacian A --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white;{{Text default color}};&quot; | [[Vector Laplacian]] &lt;math&gt;\Delta \mathbf{A} \equiv \nabla^2 \mathbf{A}&lt;/math&gt;
| &lt;math&gt;\Delta A_x \hat{\mathbf x} + \Delta A_y \hat{\mathbf y} + \Delta A_z \hat{\mathbf z} &lt;/math&gt;
| {{Collapsible section |content =
&lt;math&gt;\begin{align}
  \mathopen{}\left(\Delta A_\rho - \frac{A_\rho}{\rho^2} - \frac{2}{\rho^2} \frac{\partial A_\phi}{\partial \phi}\right)\mathclose{} &amp;\hat{\boldsymbol\rho} \\
+ \mathopen{}\left(\Delta A_\phi - \frac{A_\phi}{\rho^2} + \frac{2}{\rho^2} \frac{\partial A_\rho}{\partial \phi}\right)\mathclose{} &amp;\hat{\boldsymbol\phi} \\
+ \Delta A_z &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;
}}
| style=&quot;text-align:center&quot; | {{Collapsible section |content =
&lt;math&gt;\begin{align}
  \left(\Delta A_r - \frac{2 A_r}{r^2}
  - \frac{2}{r^2\sin\theta} \frac{\partial \left(A_\theta \sin\theta\right)}{\partial\theta}
  - \frac{2}{r^2\sin\theta}{\frac{\partial A_\phi}{\partial \phi}}\right) &amp;\hat{\boldsymbol r} \\
+ \left(\Delta A_\theta - \frac{A_\theta}{r^2\sin^2\theta}
  + \frac{2}{r^2} \frac{\partial A_r}{\partial \theta}
  - \frac{2 \cos\theta}{r^2\sin^2\theta} \frac{\partial A_\phi}{\partial \phi}\right) &amp;\hat{\boldsymbol\theta} \\
+ \left(\Delta A_\phi - \frac{A_\phi}{r^2\sin^2\theta}
  + \frac{2}{r^2\sin\theta} \frac{\partial A_r}{\partial \phi}
  + \frac{2 \cos\theta}{r^2\sin^2\theta} \frac{\partial A_\theta}{\partial \phi}\right) &amp;\hat{\boldsymbol\phi}
\end{align}&lt;/math&gt;
}}

&lt;!-- Material derivative (A dot del)B --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white;{{Text default color}};&quot; | [[Material derivative]]&lt;ref name=&quot;Mathworld&quot;&gt;{{cite web |url=http://mathworld.wolfram.com/ConvectiveOperator.html|title=Convective Operator |author=Weisstein, Eric W. |date= |work=Mathworld |publisher= |accessdate=23 March 2011}}&lt;/ref&gt;
&lt;math&gt;(\mathbf{A} \cdot \nabla) \mathbf{B}&lt;/math&gt;
&lt;!--         Cartesian --&gt;
| {{Collapsible section |content =
&lt;math&gt;\begin{align}
  \left(A_x \frac{\partial B_x}{\partial x} + A_y \frac{\partial B_x}{\partial y} + A_z \frac{\partial B_x}{\partial z}\right) &amp;\hat{\mathbf{x}} \\
+ \left(A_x \frac{\partial B_y}{\partial x} + A_y \frac{\partial B_y}{\partial y} + A_z \frac{\partial B_y}{\partial z}\right) &amp;\hat{\mathbf{y}} \\
+ \left(A_x \frac{\partial B_z}{\partial x} + A_y \frac{\partial B_z}{\partial y} + A_z \frac{\partial B_z}{\partial z}\right) &amp;\hat{\mathbf{z}}
\end{align}&lt;/math&gt;
}}
&lt;!--         Cylindrical \frac{\partial B_}{\partial } --&gt;
| {{Collapsible section |content =
&lt;math&gt;\begin{align}
  \left(A_\rho \frac{\partial B_\rho}{\partial \rho}+\frac{A_\phi}{\rho}\frac{\partial B_\rho}{\partial \phi}+A_z\frac{\partial B_\rho}{\partial z}-\frac{A_\phi B_\phi}{\rho}\right)
  &amp;\hat{\boldsymbol\rho} \\
+ \left(A_\rho \frac{\partial B_\phi}{\partial \rho} + \frac{A_\phi}{\rho}\frac{\partial B_\phi}{\partial \phi} + A_z\frac{\partial B_\phi}{\partial z} + \frac{A_\phi B_\rho}{\rho}\right)
  &amp;\hat{\boldsymbol\phi}\\
+ \left(A_\rho \frac{\partial B_z}{\partial \rho}+\frac{A_\phi}{\rho}\frac{\partial B_z}{\partial \phi}+A_z\frac{\partial B_z}{\partial z}\right)
  &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;
}}
&lt;!--         Sp --&gt;
| style=&quot;text-align:center&quot; | {{Collapsible section |content =
&lt;math&gt;\begin{align}
  \left(
    A_r \frac{\partial B_r}{\partial r}
  + \frac{A_\theta}{r} \frac{\partial B_r}{\partial \theta}
  + \frac{A_\phi}{r\sin\theta} \frac{\partial B_r}{\partial \phi}
  - \frac{A_\theta B_\theta + A_\phi B_\phi}{r}
  \right) &amp;\hat{\boldsymbol r} \\
+ \left(
    A_r \frac{\partial B_\theta}{\partial r}
  + \frac{A_\theta}{r} \frac{\partial B_\theta}{\partial \theta}
  + \frac{A_\phi}{r\sin\theta} \frac{\partial B_\theta}{\partial \phi}
  + \frac{A_\theta B_r}{r} - \frac{A_\phi B_\phi\cot\theta}{r}
  \right) &amp;\hat{\boldsymbol\theta} \\
+ \left(
    A_r \frac{\partial B_\phi}{\partial r}
  + \frac{A_\theta}{r} \frac{\partial B_\phi}{\partial \theta}
  + \frac{A_\phi}{r\sin\theta} \frac{\partial B_\phi}{\partial \phi}
  + \frac{A_\phi B_r}{r}
  + \frac{A_\phi B_\theta \cot\theta}{r}
  \right) &amp;\hat{\boldsymbol\phi}
\end{align}&lt;/math&gt;
}}

&lt;!-- Differentials displacement --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white;{{Text default color}};&quot; | Differential displacement
| &lt;math&gt;d\mathbf{l} = dx \, \hat{\mathbf x} + dy \, \hat{\mathbf y} + dz \, \hat{\mathbf z}&lt;/math&gt;
| &lt;math&gt;d\mathbf{l} = d\rho \, \hat{\boldsymbol \rho} + \rho \, d\phi \, \hat{\boldsymbol \phi} + dz \, \hat{\mathbf z}&lt;/math&gt;
| &lt;math&gt;d\mathbf{l} = dr \, \hat{\mathbf r} + r \, d\theta \, \hat{\boldsymbol \theta} + r \, \sin\theta \, d\phi \, \hat{\boldsymbol \phi}&lt;/math&gt;
| &lt;math&gt;d\mathbf{l} = \sqrt{\sigma^2 + \tau^2} \,  d\sigma \, \hat{\boldsymbol \sigma} + \sqrt{\sigma^2 + \tau^2} \, d\tau \, \hat{\boldsymbol \tau} + dz \, \hat{\mathbf z}&lt;/math&gt;

&lt;!-- Differentials normal area --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white;{{Text default color}};&quot; | Differential normal area &lt;math&gt;d \mathbf S&lt;/math&gt;
| &lt;math&gt;\begin{align}
  dy \, dz &amp;\hat{\mathbf x} \\
+ dx \, dz &amp;\hat{\mathbf y} \\
+ dx \, dy &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  \rho \, d\phi \, dz    &amp;\hat{\boldsymbol\rho} \\
+         d\rho \, dz    &amp;\hat{\boldsymbol\phi} \\
+ \rho \, d\rho \, d\phi &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  r^2 \sin\theta \, d\theta \, d\phi   &amp;\hat{\mathbf r} \\
+ r   \sin\theta \, dr      \, d\phi   &amp;\hat{\boldsymbol\theta} \\
+ r              \, dr      \, d\theta &amp;\hat{\boldsymbol\phi}
\end{align}&lt;/math&gt;
| &lt;math&gt;\begin{align}
  \sqrt{\sigma^2 + \tau^2}       \, d\tau   \, dz    &amp;\hat{\boldsymbol\sigma} \\
+ \sqrt{\sigma^2 + \tau^2}       \, d\sigma \, dz    &amp;\hat{\boldsymbol\tau} \\
+ \left(\sigma^2 + \tau^2\right) \, d\sigma \, d\tau &amp;\hat{\mathbf z}
\end{align}&lt;/math&gt;

&lt;!-- Differentials volume --&gt;
|- style=&quot;text-align:center&quot;
! style=&quot;background: white;{{Text default color}};&quot; | Differential volume &lt;math&gt;dV&lt;/math&gt;
| &lt;math&gt;dx \, dy \, dz&lt;/math&gt;
| &lt;math&gt;\rho \, d\rho \, d\phi \, dz&lt;/math&gt;
| &lt;math&gt;r^2 \sin\theta \, dr \, d\theta \, d\phi&lt;/math&gt;
| &lt;math&gt;\left(\sigma^2 + \tau^2\right) d\sigma \, d\tau \, dz&lt;/math&gt;

&lt;!-- nabla's on nabla's --&gt;
|-
| colspan=5 | &lt;strong&gt;Non-trivial calculation rules:&lt;/strong&gt;
#  &lt;math&gt;\operatorname{div}  \, \operatorname{grad} f          \equiv \nabla \cdot  \nabla f = \nabla^2 f \equiv \Delta f&lt;/math&gt;
#  &lt;math&gt;\operatorname{curl} \, \operatorname{grad} f          \equiv \nabla \times \nabla f = \mathbf 0&lt;/math&gt;
#  &lt;math&gt;\operatorname{div}  \, \operatorname{curl} \mathbf{A} \equiv \nabla \cdot  (\nabla \times \mathbf{A}) = 0&lt;/math&gt;
#  &lt;math&gt;\operatorname{curl} \, \operatorname{curl} \mathbf{A} \equiv \nabla \times (\nabla \times \mathbf{A}) = \nabla (\nabla \cdot \mathbf{A}) - \nabla^2 \mathbf{A}&lt;/math&gt; ([[Triple_product#Vector_triple_product|Lagrange's formula]] for del)
#  &lt;math&gt;\Delta (f g) = f \Delta g + 2 \nabla f \cdot \nabla g + g \Delta f&lt;/math&gt;
|}
{{hidden end}}

{{CourseCat}}</text>
      <sha1>hpibf37e1eampxtje707cyf9q2bve0k</sha1>
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  </page>
  <page>
    <title>Universal Bibliography</title>
    <ns>0</ns>
    <id>171301</id>
    <revision>
      <id>2831837</id>
      <parentid>2831645</parentid>
      <timestamp>2026-09-06T18:38:00Z</timestamp>
      <contributor>
        <username>James500</username>
        <id>297601</id>
      </contributor>
      <comment>/* Japan and Korea */ Add</comment>
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      <text bytes="44565" sha1="95h2zw9zotjx8xuz8ukcqkt71aykl7a" xml:space="preserve">{{Center top}}{{Resize|3em|'''Bibliotheca Universalis'''}}{{Center bottom}}
{{Bibliography}}
{{research}}

If this resource is ever completed, it will be a universal bibliography.&lt;ref&gt;See [[w:Bibliography]].&lt;/ref&gt; Until then, it will be an approximation of a universal bibliography.

This bibliography is arranged as an index of topics.

==Index==
*[[Universal Bibliography/Bibliography|Bibliography]]
*[[Universal Bibliography/Libraries|Libraries]]
*[[Universal Bibliography/Literature|Literature]]
*[[Universal Bibliography/Languages|Languages]]
*[[Universal Bibliography/SF|SF]]
*[[Universal Bibliography/Music|Music]]
*[[Universal Bibliography/Cinema|Cinema]]
*[[Universal Bibliography/Television|Television]]
*[[Universal Bibliography/Culture|Culture]]
*[[Universal Bibliography/Publishers and imprints|Publishers and imprints]]
*[[Universal Bibliography/Printing|Printing]]
*[[Universal Bibliography/Printers|Printers]]
*[[Universal Bibliography/Microform|Microform]]
*[[Universal Bibliography/Periodicals|Periodicals]]
*[[Universal Bibliography/Reference|Reference]]
*[[Universal Bibliography/Gazetteers|Gazetteers]]
*[[Universal Bibliography/Humanities|Humanities]]
*[[Universal Bibliography/Law|Law]]
*[[Universal Bibliography/History|History]]
*[[Universal Bibliography/Archaeology|Archaeology]]
*[[Universal Bibliography/Geography|Geography]]
*[[Universal Bibliography/Countries|Countries]]
*[[Universal Bibliography/Architecture|Architecture]]
*[[Universal Bibliography/Mathematics|Mathematics]]
*[[Universal Bibliography/Computers|Computers]]
*[[Universal Bibliography/Kites|Kites]]
*[[Universal Bibliography/Nostalgia|Nostalgia]]
*[[Universal Bibliography/Children's non-fiction|Children's non-fiction]]

===About===
*[[Universal Bibliography/About|About]]

==Online libraries==
Swedish:
*[[w:Swedish Literature Bank|Litteraturbanken]] (Swedish Literature Bank)
*[[w:Project Runeberg|Projekt Runeberg]] (Project Runeberg)

French
*[[w:Persée (web portal)|Persée]] (persee.fr)

Japanese
*[[w:Aozora Bunko|Aozora Bunko]] (aozora.gr.jp)

==Biographical dictionaries etc==
See [[w:Bibliography of encyclopedias: general biographies]] and [[w:List of biographical dictionaries]]

*Fox. 'True Biographies of Nations?': The Cultural Journeys of Dictionaries of National Biography. ANU Press. 2019 [https://books.google.co.uk/books?id=siSbDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Arthur, &quot;Biographical Dictionaries in the Digital Era&quot;. Advancing Digital Humanities: Research, Methods, Theories. 2014. Chapter 6. [https://books.google.co.uk/books?id=z7MaBgAAQBAJ&amp;pg=PA83#v=onepage&amp;q&amp;f=false Page 83] et seq.

Bibliographies, indexes, etc:
*Wynar. ARBA Guide to Biographical Dictionaries. Libraries Unlimited. 1986 [https://books.google.co.uk/books?id=5FfgAAAAMAAJ]
*Slocum, Robert B (ed). Biographical Dictionaries and Related Works. Gale Research Company. 2nd Ed: 1986 [https://books.google.co.uk/books?id=5uMpAQAAMAAJ]
*Biographical Dictionaries Master Index. (Gale Biographical Index Series). [https://books.google.co.uk/books?id=ZEshAQAAMAAJ] [https://books.google.co.uk/books?id=pPAzAQAAIAAJ] see also [https://books.google.co.uk/books?id=o_gPAQAAMAAJ]
*Children's Authors and Illustrators: An Index to Biographical Dictionaries. (Gale Biographical Index Series). 2nd Ed: 1978,  3rd Ed: 1981, 4th Ed: 1987 [https://books.google.co.uk/books?id=VIsWAQAAMAAJ] [https://books.google.co.uk/books?id=DFtGAQAAIAAJ] [https://books.google.co.uk/books?id=01wjAQAAIAAJ]
*Index to the Wilson Authors Series [https://books.google.co.uk/books?id=oNZkAAAAMAAJ]
*Auchterlonie. Arabic Biographical Dictionaries: A Summary Guide and Bibliography. 1987 [https://books.google.co.uk/books?id=rW59QgAACAAJ]
*Black Biographical Dictionaries, 1790-1950 [https://books.google.co.uk/books?id=laIUAQAAMAAJ]

Particular works:

*Oxford Dictionary of National Biography; [[w:Dictionary of National Biography|Dictionary of National Biography]]
*Boase. Modern English Biography. ([http://www.google.com/search?q=editions%3Auzt3-qMuFcMC&amp;btnG=Search+Books&amp;bksoutput=html_text&amp;tbm=bks&amp;tbo=1 editions:uzt3-qMuFcMC])
*A &amp; C Black's Who's Who
*Who Was Who
*The Academic Who's Who. A &amp; C Black. 1st Ed: 1973 [https://books.google.co.uk/books?id=dnUWAQAAMAAJ] [https://books.google.co.uk/books?id=fXJmAAAAMAAJ]. 2nd Ed: 1975. Commentary: [https://books.google.co.uk/books?id=7VyOANl2qxoC&amp;pg=PA208&amp;output=html_text]. GBooks: editions:INAP7GGD2gYC editions:tA0FkHC75FIC
*Dictionary of Edwardian Biography (Pike's New Century Series)

Works that comprise largely of biographies:
*The Penguin Companion to Literature

Theatres
*A Biographical Dictionary of Actors, Actresses, Musicians, Dancers, Managers &amp; Other Stage Personnel in London, 1660-1800. [https://books.google.co.uk/books?id=TGgS9VxWJ0oC vol 15]

==Dictionaries of dates==
[https://archive.org/search.php?query=%22dictionary%20of%20dates%22 Archive.org]
*Baxter Dictionary of Dates and Events. 1st Ed: 1963: Napier, M (ed). 2nd Ed: 1971: Sanders and Laffin. Commentary: 92 Library Journal 1819 [https://books.google.co.uk/books?id=CExVAAAAYAAJ]
*Beeching, Cyril Leslie. A Dictionary of Dates. OUP. 1st Ed: 1993. 2nd Ed: 1997. [https://www.google.co.uk/search?hl=en&amp;tbm=bks&amp;q=editions:UGGp0EexZdcC editions:UGGp0EexZdcC]
*Bolton, John. Bolton's Dictionary of Dates, arranged in alphabetical order. Foulsham. 1958. Review: [https://books.google.co.uk/books?id=awJPAAAAIAAJ 172] The Publisher 880
*[[w:William Darling (politician)|William Young Darling]]. A Book of Days: A Dictionary of Dates, a Chronology of Circumstance, the Face of Time. Richards Press. 1951. [https://books.google.co.uk/books?id=PLkfAAAAMAAJ]
*Everyman's Dictionary of Dates. 1st Ed: 1911. 6th Ed: 1971. Review: (1971) 11 RQ 164 [http://www.jstor.org/stable/25824440]
*Platt, Charles. Foulsham's Dictionary of Dates and General Information. 1930.
*[[w:Haydn's Dictionary of Dates|Haydn's Dictionary of Dates]]
*Hamlyn Dictionary of Dates and Anniversaries. Newnes Dictionary of Dates.
*Williams, Henry Llewellyn. Hurst's Dictionary of Dates. 1891. [https://archive.org/details/hurstsdictionary00will]
*Keller, Helen Rex. The Dictionary of Dates. Macmillan. 1934. Commentary: [https://books.google.co.uk/books?id=Utcb32E7rsMC&amp;pg=PA93&amp;output=html_text] [https://books.google.co.uk/books?id=sAHfY6QbOEwC&amp;pg=PA351&amp;output=html_text]
*Nelson's Dictionary of Dates. A Dictionary of Dates. (Nelson's Encyclopaedic Library). 1912 [https://books.google.co.uk/books?id=Mp9lvwEACAAJ]. Reviews: (June 1912) Journal of Education, vol 34 (New Series), vol 44 (Old Series), p 392 [https://books.google.co.uk/books?id=QIRFAQAAMAAJ]; (1912) [https://books.google.co.uk/books?id=9i4_AQAAIAAJ 108] The Spectator [http://archive.spectator.co.uk/article/18th-may-1912/25/a-dictionary-of-dates-vol-i-and-english-idioms-nel 805] (18 May)
*Pulman, George Palmer. The World's Progress: A Dictionary of Dates. New York. 1861. [https://books.google.co.uk/books?printsec=frontcover&amp;id=k3dJAAAAYAAJ&amp;output=html]
*Urdang, Laurence. The World Almanac Dictionary of Dates. Longman. 1982. [https://books.google.co.uk/books?id=I4IRAQAAMAAJ] Review: (1982) 22 RQ 101 [http://www.jstor.org/stable/25826880]

Australia

*John Henniker Heaton. Australian Dictionary of Dates and Men of the Time. 1879. [https://archive.org/details/australiandicti00heatgoog]
*John James Knight. In the Early Days; History and Incident of Pioneer Queensland, with Dictionary of Dates in Chronological Order. Sapsford &amp; Co. Brisbane. 1895.

America

*Damon, Charles Ripley. The American Dictionary of Dates, 458-1920. R G Badger. 1921.

==Commodity dictionaries==
*Statistical Classification of Domestic and Foreign Commodities Exported from the United States. Commentary: [https://books.google.co.uk/books?id=91GLhsJSBj8C&amp;pg=PR22#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=RPwhAQAAMAAJ&amp;pg=RA15-PA7#v=onepage&amp;q&amp;f=false]
*Tovarnyi slovar'. (Commodity Dictionary). Reviews and commentary: Petrov, &quot;Commodity Dictionary&quot;, Ekonomicheskaya Gazeta, No 13, 30 October 1961, p 45; CDSP , 13 December 1961, p 46; (1962) [https://books.google.co.uk/books?id=2vMRAAAAIAAJ 13] Current Digest of the Soviet Press 47; (1958) 15 Quarterly Journal of Current Acquisitions 210 [https://books.google.co.uk/books?id=ZcvozpZAfpEC] [https://books.google.co.uk/books?id=S47qEIfyCr0C]; Fitzpatrick, Stalinism: New Directions, [https://books.google.co.uk/books?id=rD5FzoKnTE0C&amp;pg=PA182#v=onepage&amp;q&amp;f=false p 182] &amp; 183
*Szilágyi. Commodity Dictionary in Five Languages. Budapest. Közgazdasági és Jogi Könyvkiadó (Publishing House for Economics and Law). 1963 or 1964. Commentary: Books from Hungary, vols 4-6, pp 26 &amp; 40 [https://books.google.co.uk/books?id=6kMiAQAAMAAJ]
*Dictionnaire des produits: appellations et caractéristiques des produits francais de consommation courante, 1960. Commentary: Walford (ed), Guide to Reference Material Supplement, 1963, p 106 [https://books.google.co.uk/books?id=ej-9pHGR67oC]
*Chūgoku Shōhin Jiten. (Chinese commodity dictionary). Tokyo. 1960. [https://books.google.co.uk/books?id=Wc61lS0xj6AC&amp;pg=PA78#v=onepage&amp;q&amp;f=false]

==Encyclopedias==
See [[s:Category:Encyclopedias]], [[w:Bibliography of encyclopedias]] and [[w:Lists of encyclopedias]]

*[[w:en:Encyclopædia Britannica Eleventh Edition|Encyclopædia Britannica Eleventh Edition]]
*Paton, John (ed). Knowledge Encyclopedia: 1979, 1981, 1988. New Discovery Encyclopedia: 1990.
*The Dorling Kindersley Illustrated Family Encyclopedia

==Almanacs==
See [[s:Category:Almanacs]], [[s:Portal:Almanacs]], [[w:List of almanacs]], [[w:Category:Almanacs]].
*Year Book and Almanac of Newfoundland. 
**For 1896. 1895. [https://archive.org/details/yearbooknfld189600newfuoft]
*Whiteley. On This Date: A Day-by-Day Listing of Holidays, Birthday and Historic Events, and Special Days, Weeks and Months. 2002. [https://books.google.co.uk/books?id=sKCfomKSa74C]

==Censuses==
*Census of New Zealand and Labrador
**1901 Census. Tables 2 and 3. 1903. [https://archive.org/details/censusnewfoundl00bondgoog]
**1911 Census. Table 1. 1914. [https://archive.org/details/1911981911fnfldv11914eng]
**1921 Census. Tables 4 and 5. 1923. [https://archive.org/details/1921981921fnfldv451923eng]

==Pilot guides==
*[[w:United States Coast Pilot|United States Coast Pilot]]
*American Coast Pilot [https://books.google.co.uk/books?id=8GoDAAAAYAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]

*Sailing Directions: Newfoundland. Canadian Hydrographic Service. [https://books.google.co.uk/books?id=A77fAAAAMAAJ]
*Newfoundland Pilot. Canadian Hydrographic Service. [https://books.google.co.uk/books?id=z7zfAAAAMAAJ]
*Maxwell. The Newfoundland Pilot. Hydrographic Office, Admiralty. London. 1878. [https://books.google.co.uk/books?id=vS4BAAAAQAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]
*Newfoundland Pilot. HO No 73. Hydrographic Office. Governement Printing Office, Washington. 4th Ed: 1919: [https://books.google.co.uk/books?id=YGoDAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]. Sailing Directions for Newfoundland. 5th Ed: 1931: [https://books.google.co.uk/books?id=cMUiGo3JK9QC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]

==Books of facts==
*The Reader's Digest Book of Facts. 1st Ed: 1985. Reprinted with amendments: 1987: [https://books.google.co.uk/books?id=B8PmM_5Zm1MC]. (Review: Library Journal, [https://books.google.co.uk/books?id=EPDgAAAAMAAJ v 9], p 102, 1 Dec 1987, [http://www.bookverdict.com/details.xqy?uri=Product-94667328910921.xml Book Verdict].) 3rd Revised Ed: 1995: [https://books.google.co.uk/books?id=E5YhAQAAIAAJ]. GBooks: editions:nnJlLybWxbIC
*Chambers Book of Facts
*Crystal, David (ed). Penguin Book of Facts. [https://books.google.co.uk/books?id=k0sZAQAAIAAJ 2004]. 2nd Ed: 2008
*Handy Book of Facts: Things Everyone Should Know. C.S. Hammond &amp; Company. 1914. [https://books.google.co.uk/books?id=h5wRAAAAIAAJ]

==Series of books==
See [[w:Category:Series of books]] and [[w:Category:Monographic series]]
*George M Sinkankas, &quot;Series&quot; in Kent, Lancour and Daily (eds).  Encyclopedia of Library and Information Science. Volume 27. Marcel Dekker. 1979. Pages [https://books.google.co.uk/books?id=jU3fwyjqS5UC&amp;pg=PA250#v=onepage&amp;q&amp;f=false 250] to 273.
*&quot;Publishing in Series, 1896-1916&quot; in Eliot, Simon (ed). History of Oxford University Press. Louis,  Wm Roger (ed). Volume 3: 1896-1970. Oxford University Press. 2013. [https://books.google.co.uk/books?id=YbcJAgAAQBAJ&amp;pg=PA539#v=onepage&amp;q&amp;f=false Page 539] et seq.
*Spiers, John. The Culture of the Publisher’s Series. Palgrave Macmillan. 2011. [https://books.google.co.uk/books?id=ASaHDAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 1]. [https://books.google.co.uk/books?id=XCl-DAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 2].
*Spiers, John. Serious about Series: American 'Cheap' Libraries, British 'Railway' Libraries and Some Literary Series of the 1890's. 2007. [https://books.google.co.uk/books?id=1hRXAAAAYAAJ] [https://books.google.co.uk/books?id=AS4yQwAACAAJ]
*Rooney, Paul Raphael. Railway Reading and Late-Victorian Literary Series. Routledge. 2018. [https://books.google.co.uk/books?id=uX5aDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Khan. &quot;Monographs in series&quot;. The Principles and Practice of Library Science. 1996. Pages [https://books.google.co.uk/books?id=sAHfY6QbOEwC&amp;pg=PA208#v=onepage&amp;q&amp;f=false 207] to 209.
*Friskney. New Canadian Library: The Ross-McClelland Years, 1952-1978. Pages [https://books.google.co.uk/books?id=jHIjCCXBX9kC&amp;pg=PA6#v=onepage&amp;q&amp;f=false 6] and 7.

*Books in Series. R R Bowker Company. Commentary: [https://books.google.co.uk/books?id=uQe04OSlA7YC&amp;pg=PA11#v=onepage&amp;q&amp;f=false]
**Books in Series in the United States, 1966-1975. R R Bowker. 1977. Review: (1977) 14 Choice [https://books.google.co.uk/books?id=_e08AQAAIAAJ&amp;pg=PA1190#v=onepage&amp;q&amp;f=false 1190] (No 8, November). Commentary: [https://books.google.co.uk/books?id=LYAhAAAAQBAJ&amp;pg=PA53#v=onepage&amp;q&amp;f=false]
***Books in Series Supplement: A Supplement to Books in Series in the United States, 1966-1975. 1978. [https://books.google.co.uk/books?id=hOAaAQAAMAAJ]
**Books in Series. 3rd Ed. 1980. [https://books.google.co.uk/books?id=d_kaAQAAMAAJ]
**Books in Series, 1876-1949. R R Bowker Company. 1982. [https://books.google.co.uk/books?id=TngvAQAAIAAJ] [https://books.google.co.uk/books?id=iVIyAQAAMAAJ] [https://books.google.co.uk/books?id=R2AjAQAAIAAJ]
**Books in Series, 1985-89. [https://books.google.co.uk/books?id=yEkxAQAAIAAJ]
*Baer, Eleanora Agnes. Titles in Series: A Handbook for Librarians and Students. Scarecrow Press. Vol 1 (Books Published Prior to January 1953). 1953: [https://books.google.co.uk/books?id=GgAYAAAAMAAJ]. Vol 2 (Books Published Prior to January 1957). 1957: [https://books.google.co.uk/books?id=oqsXAAAAMAAJ]
**2nd Ed: 1964. [https://books.google.co.uk/books?id=gWlAAAAAIAAJ Vol 1]. [https://books.google.co.uk/books?id=tWpAAAAAIAAJ Vol 2]. Supplement to the Second Edition. 1967: [https://books.google.co.uk/books?id=zGARAQAAMAAJ]. Second Supplement to the Second Edition. 1971: [https://books.google.co.uk/books?id=WwXhAAAAMAAJ]
**3rd Ed: 1978. Commentary: [https://books.google.co.uk/books?id=h_wfYKnMfOkC&amp;pg=PA63#v=onepage&amp;q&amp;f=false]
*Ocran, Emmanuel Benjamin. Scientific &amp; Technical Series: A Select Bibliography. 1973: [https://books.google.co.uk/books?id=oy0EAAAAMAAJ] Review: [https://books.google.co.uk/books?id=fTCw_DQH6zkC&amp;pg=PA949#v=onepage&amp;q&amp;f=false]

*Rosenberg and Nichols. Young People's Books in Series: Fiction and Non-fiction, 1975-1991. Libraries Unlimited. 1992. [https://books.google.co.uk/books?id=REHhAAAAMAAJ]
*Young People's Literature in Series

*Catalog of Reprints in Series. (sometimes called &quot;Catalogue of Reprints in Series&quot;). 1940 onwards. [https://books.google.co.uk/books?id=MSI4AAAAIAAJ] [https://books.google.co.uk/books?id=6n1EAAAAMAAJ] Commentary: [https://books.google.co.uk/books?id=h_wfYKnMfOkC&amp;pg=PA73#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=1RxuAAAAMAAJ]

*Kuitert, Lisa. Het ene boek in vele delen. De Uitgave van Literaire Series in Nederland 1850-1900. Uitgeverij de Buitenkant. Amsterdam. 1993. Commentary: [https://books.google.co.uk/books?id=jSDnRo7YrWwC&amp;pg=PA656#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=szBcAAAAMAAJ] [https://books.google.co.uk/books?id=SVcVAQAAIAAJ] [https://books.google.co.uk/books?id=R8Pfs146nUAC&amp;pg=PA367#v=onepage&amp;q&amp;f=false]

==Series of classics==
*Penguin Classics (Penguin Modern Classics, Penguin English Library)
*Oxford World Classics
*Everyman's Library
*Wordsworth Classics
*Macmillan Collectors Library
*Bantam Classics
*Minster Classics
*The Literary Heritage Collection (Heron Books, London. William Collins Sons &amp; Co, Glasgow)
*Chandos Classics
*Temple Classics
*Longmans Heritage of Literature Series

Russian
*Greatest Masterpieces of Russian Literature (Heron Books, London)

SF
*Corgi SF Collectors Library

Children's and shorter classics etc 
*Shorter Classics. Ginn and Company.
*Ladybird Children's Classics.
*Mini Classics. Parragon Books.
*Bonny Books. Peter Haddock Ltd.
*A series published by Dean &amp; Son Ltd

==Non-fiction general series==
*[[w:Oxford Companions|Oxford Companions]]
*[[w:Cambridge Companions|Cambridge Companions]]
*Princeton Companions
*Blackwell Companions. Wiley Blackwell Companions
*Routledge Companions. Routledge Research Companions
*Ashgate Companions. Ashgate Research Companions
*Brill's Companions
*Facts on File Companions
*Guides to Information Sources. Bowker-Saur
*Butterworths Guides to Information Sources.
*Columbia Guides
*Blackwell Guides
*Edinburgh Critical Guides
*Collins Reference Dictionaries
*New Horizons. Thames and Hudson. ([[w:Découvertes Gallimard|Découvertes Gallimard]])
*Collins Gem (see [[w:List of Collins GEM books]])
*Concise Encyclopedias. Collins.
*Time Life Books (see [[w:Time Life#Book series]])
*[[w:Teach Yourself|Teach Yourself Books]]. English Universities Press. 
*[[w:Teach Yourself|Teach Yourself Books]]. Hodder and Stoughton.
*Made Simple Books. W H Allen.
*Palgrave Master Series
*Harrap's Mini Series
*Shire Albums. Shire Publications.
*Fax Pax: Knowledge in a Nutshell. Fax Pax Ltd.
*The Wonderful World Books. Macdonald and Company
*Harper's ABC series. Includes A-B-C of Housekeeping, A-B-C of Electricity, A-B-C of Gardening and A-B-C of Manners.
*Hamlyn Pocket Guides
*Oxford Monograph Series
*Study Outline Series. H W Wilson. [[s:Page:Russian Literature - A Study Outline.djvu/61|(wikisource)]]
*Helpmate Handbooks. Willow Books

University
*University Paperbacks. Meuthen &amp; Co
*World Student Series. Addison Wesley
*Unibooks. Hodder and Stoughton
*International Student Editions. Van Nostrand Reinhold
*Hutchinson University Library

Imprints
*Pelican Books

Pictorials
*Salmon Cameracolour series
*Pitkin Pictorials 

United Kingdom
*Aspects of Britain. HMSO.

Places
*The Little Guides. Meuthen [[s:Page:Cornwall (Salmon).djvu/336|(wikisource)]]
*G.W.R. Series of Travel Books [[s:Page:The Cornwall coast.djvu/391|(wikisource)]]

Art
*Movements in World Art. Meuthen.
*Movements in Modern Art. Meuthen.
*How to Draw and Paint. New Burlington.

Film
*BFI Companions

Popular science
*Contemporary Science Paperbacks. Oliver and Boyd.
*Pan Piper Science Series

Science and mathematics
*Simon and Schuster Tech Outlines
*Schaum's Outline Series

Military
*Illustrated Military Guides. Illustrated Guides. &quot;An Illustrated Guide to ...&quot;. Salamander Books.
*Combat Arms. Arco Military Books. Salamander Books. Prentice Hall Press.
*Osprey Men-at-Arms
*Jane's Pocket Books

Communication
*The Library of Communication Techniques. Focal Press.
*John Fiske (ed). Studies in Culture and Communication. Routledge.
*The Media. Wayland.

Cookery
*ABC series. Peter Pauper Press.

Gardening
*Pan Piper Small Gardens Series.

Mythology
*Series on mythology published by Southwater (imprint of Anness)

==History and Geography==
See also [[Universal Bibliography/History|History]] and [[Universal Bibliography/Geography|Geography]].
*Baker. Geography and History: Bridging the Divide. 2003. [https://books.google.co.uk/books?id=e8yf5JcefpAC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Darby. Relations of History and Geography: Studies in England, France and the United States. 2002. [https://books.google.co.uk/books?id=Vl4ZfpnP7NwC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

General series
*Cambridge Studies in Historical Geography

Atlases
*The Times Atlas of World History
*Philip's Atlas of World History

History of geography:
*Dunbar, Gary S. The History of Modern Geography: An Annotated Bibliography of Selected Works. Garland. 1985. [https://books.google.co.uk/books?id=FX4WAQAAIAAJ]

==Chronology==
See also [[Universal Bibliography/History#Millennia, centuries and decades]]

General
*Chronology of World History.
**Neville Williams. Chronology of the Modern World: 1763 to the present time. 1st Ed: 1966. (1763 to 1992). 2nd Ed: 1994.
**Neville Williams. Chronology of the Expanding World 1492 to 1762. 1969. Reissued 1994.
**Storey. Chronology of the Medieval World 800 to 1491. 1973. Reissued 1994.
**Mellersh. Chronology of the Ancient World 10,000 BC to AD 799. Barrie and Jenkins. 1976. Helicon. Simon &amp; Schuster. Reissued 1994.

Centuries
*Chronology of the 20th Century. Helicon. 1995. [https://books.google.com/books?id=pjsOAQAAMAAJ]
*Brownstone and Franck. Timelines of the 20th Century. [https://books.google.com/books?id=IZ6SQgAACAAJ]
*Beal. 20th Century Timeline. 1985. [https://books.google.com/books?id=cFrG7LBObGoC]
*20th Century Day by Day [https://books.google.com/books?id=kyxaAAAAYAAJ] [https://books.google.com/books?id=WiOAAAAACAAJ]
*Chronicle of the 20th Century [https://books.google.co.uk/books?id=pt3DYbnZO8sC] [https://books.google.co.uk/books?id=Gd1WPQAACAAJ]
*Boyle. The Chronology of the Eighteenth and Nineteenth Centuries. 1826. [https://books.google.co.uk/books?id=wDENAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]

Decades
*Series:
**Day by Day. Facts on File. [https://books.google.com/books?id=WfClvwEACAAJ] [https://books.google.com/books?id=CWNvQgAACAAJ]

Years
*Brown, D Kinnear. History of the Year. (1884 to 1885). [https://books.google.co.uk/books?id=DmRWAAAAYAAJ&amp;pg=PA113#v=onepage&amp;q&amp;f=false Catalogue].
*The History of the Year: A Narrative of the Chief Events and Topics of Interest. [https://books.google.co.uk/books?id=ljgIAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false 1881 to 1882]. [https://books.google.co.uk/books?id=1DgIAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false 1882 to 1883].
*James Mason. The History of the Year 1876. [https://books.google.co.uk/books?id=6DoIAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*[[w:The Annual Register|The Annual Register]]. [A View of the History Politics and Literature of the Year YYYY.] [https://books.google.co.uk/books?id=SrJNAAAAcAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false 1821].
*Giusto Traina. 428AD: An Ordinary Year at the End of the Roman Empire. [https://books.google.co.uk/books?id=gLumDwAAQBAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

Ancient
*Bickerman. Chronology of the Ancient World. 1968.
*Smithsonian Timelines of the Ancient World: A Visual Chronology from the Origins of Life. Dorling Kindersley. 1st American Ed: 1993.

==Anniversaries==
*Sian Facer (ed). On this Day: The History of the World in 366 Days. Octopus Illustrated Publishing, London. Crescent Books, New York and Avenel. 1992: [https://books.google.com/books?id=SYGQgwHTuE0C]. Other: [https://books.google.co.uk/books?id=W687MAEACAAJ] [https://books.google.co.uk/books?id=7ujArQEACAAJ]
*On this Day: A History of the World in 366 Days. DK. 2021. [https://books.google.co.uk/books?id=x4I5EAAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]

==Egyptology==
*Annual Egyptological Bibliography [https://books.google.co.uk/books?id=8MoUAAAAIAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=-eUUAAAAIAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

==Battlefields==
*[[w:War Walks|War Walks]]. BBC2. 1996 to 1997. [Television series]
*&quot;The Times Guide to Battlefields of Britain&quot;. Day 1: The Times, 1 August 1994, p 8. Day 2: The Times, 2 August 1994, p 8. Day 3: The Times, 3 August 1994, p 6. Day 4: The Times, 4 August 1994, p 9. Day 5: The Times, 5 August 1994, p 9. Day 6: The Times, 6 August 1994, p 6. There was also a colour wall chart.

==Armed forces==
Periodicals:
*[[w:NATO Review|NATO Review]]

Military
*The Journal of Military History

*Journal of the Royal United Service Institution [Google editions:lMJAgUvBWAEC editions:dcFNqS8JFjoC]

*The Monthly Army List [Google editions:I0t2L4ElznEC]
*The Army Quarterly and Defence Journal [Google editions:c7UjQ-q7SbUC]

*Journal of the Society for Army Historical Research [Google editions:9HZkbMTl6mcC]

*The Royal Armoured Corps Journal [https://www.google.com/search?tbm=bks&amp;q=editions:dEauCcI7kssC&amp;biw=534&amp;bih=736&amp;dpr=1.5#sbfbu=1]
*The Royal Tank Corps Journal
*The Tank [https://www.google.com/search?sa=N&amp;cs=0&amp;tbm=bks&amp;q=editions:Dv-RbpoM7acC&amp;biw=534&amp;bih=736&amp;dpr=1.5#ip=1] Editorial office at the Royal Tank Regiment
*The Cavalry Journal [https://www.google.com/search?sa=N&amp;cs=0&amp;tbm=bks&amp;q=editions:cVQlfkRl6KUC&amp;biw=534&amp;bih=688&amp;dpr=1.5#sbfbu=1]
*The Journal of the Royal Artillery [https://www.google.com/search?tbm=bks&amp;q=editions:liFy4uc0ggYC&amp;biw=534&amp;bih=736&amp;dpr=1.5]
*Minutes of Proceedings of the Royal Artillery Institution [Google editions:wdjZ588FbtMC]
*The Royal Engineers Journal [https://www.google.com/search?tbm=bks&amp;q=editions:8XobinXLbD0C&amp;biw=534&amp;bih=736&amp;dpr=1.5]
*Journal of the Royal Electrical and Mechanical Engineers [https://books.google.com/books?id=dz0cmA1jnv4C]
*Journal of the Royal Army Medical Corps [Google editions:FyUJx2dEWcQC]

United States
*Military Review
*The Coast Artillery Journal [Google editions:nMCogSJ_rlkC]
*Infantry Journal [Google editions:ULqoLmbUR5cC]
*The Reserve Officer [Google editions:JQDRDrnD1QQC]

Naval
*[[w:Navy News|Navy News]]

==Armour==
Armoured warfare; tank warfare
*Harris and Toase. Armoured Warfare. 1990. [https://books.google.com/books?id=KYPfAAAAMAAJ]
*Carver. The Apostles of Mobility: The Theory and Practice of Armoured Warfare. 1979. [https://books.google.com/books?id=8qcgAAAAMAAJ]
*Fuller. Armoured Warfare: An Annotated Edition of Fifteen Lectures on Operations between Mechanized Forces. 1943. [https://books.google.co.uk/books?id=2E4tAQAAMAAJ]
*Black. Tank Warfare. 2020. [https://books.google.co.uk/books?id=oFP5DwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Jorgensen and Mann. Tank Warfare. 2001. [https://books.google.co.uk/books?id=0AghAQAAIAAJ]
*Searle. Armoured Warfare: A Military, Political and Global History. 2017. [https://books.google.co.uk/books?id=HN4CDgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Willey. Tanks: The History of Armoured Warfare. 2018. [https://books.google.com/books?id=AXTltAEACAAJ]
*Perrett. Iron Fist: Classic Armoured Warfare Case Studies. [https://books.google.co.uk/books?id=pKGyeWqJcCEC]. Iron Fist: Classic Armoured Warfare. [https://books.google.co.uk/books?id=KKcKI4dG0VUC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Tom Clancy. Armoured Warfare: Guided Tour of an Armoured Cavalry Regiment. [https://books.google.co.uk/books?id=UxhONAAACAAJ]

Atlas
*Stephen Hart (ed). Atlas of Armored Warfare: From 1916 to the Present Day. Metro Books. 2012. [https://search.worldcat.org/title/1391166759]. Atlas of Tank Warfare. [https://books.google.com/books?id=KWqppwAACAAJ]

Armored forces
*Ogorkiewicz. Armoured Forces: A History of Armoured Forces and Their Vehicles. 1970. [https://books.google.co.uk/books?id=qIHfAAAAMAAJ]

==Mesoamerica==
*James. Aztecs &amp; Maya: The Ancient Peoples of Middle America. Tempus. 2001. 2005. History Press. [https://books.google.co.uk/books?id=XOXNhTY6TCYC 2009]. Reviews: &quot;Books Received&quot; (2003) [https://books.google.co.uk/books?id=3dozAQAAIAAJ 14] Minerva 57 (No 1); and &quot;Overviews for the general reader&quot; (2002) [https://books.google.co.uk/books?id=qShmAAAAMAAJ 76] Antiquity 252.
*Weaver. The Aztecs, Maya, and Their Predecessors. 1972. 2nd Ed: 1981: [https://books.google.co.uk/books?id=0mQkAQAAIAAJ] [https://books.google.com/books?id=OWQkAQAAIAAJ]

==Accounting==
See [[s:Category:Accounting]]

Periodicals
*[[s:The Accountant|The Accountant]] (1874 onwards)
*Accountant's Magazine (1897 onwards) Aberdeen

==Arts==
*Murray (ed).The Hutchinson Dictionary of the Arts. Helicon Publishing. 1994. Paperback Ed: 1995. Reprinted 1997.

==Biography==
*Parke. Biography: Writing Lives. 2002 [https://books.google.co.uk/books?id=6bAz2K98MeYC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Caine. Biography and History. (Theory and History). 1st Ed: 2010, 2nd Ed: 2019 [https://books.google.co.uk/books?id=h3dvDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Periodicals
*Biography. Biography: An Interdisciplinary Quarterly. 1978 onwards. Published by the University Press of Hawaii for the Biographical Research Center. [https://books.google.co.uk/books?id=s84ZAAAAYAAJ]
*Biography News. 1974 to 1975. Gale Research Company. [https://books.google.co.uk/books?id=RRsXAQAAIAAJ]

Yearbooks
*Current Biography Yearbook [https://books.google.com/books?id=Zcml63jalMIC]
*Dictionary of Literary Biography Yearbook [https://books.google.com/books?id=gNNlAAAAMAAJ]

==Information technology==
*Haynes, David (ed). Information Sources in Information Technology. (Guides to Information Sources). Bowker Saur. 1990. [https://books.google.co.uk/books?id=0hYjAAAAQBAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]

==Economics==
General series:
*Dryden Press Series in Economics
*Hurl, Bryan (ed). Studies in the UK Economy. Heinemann Educational
*Nuffield Economics &amp; Business. Nuffield Foundation. Longman.

Other:
*Bannock, Baxter and Davis. The Penguin Dictionary of Economics. Penguin Books. 4th Ed: 1987. Bannock, Baxter and Rees. 1972. 2nd Ed: 1978. 3rd Ed: 1984.

*Begg, Fischer and Dornbusch. Economics. McGraw Hill. 1984. 2nd Ed: 1987. 3rd Ed: 1991.
*Anderton, Alain. Economics. Causeway Press. 1991.
*Maile, Roger. Economics. (Core Business Studies). Mitchell Beazly. 1983.
*Maunder, Myers, Wall and Miller. Economics Explained. Collins Educational. 1987. 2nd Ed: 1991.
*Tibbitt, Andrew. A guide to A Level Economics. Thomas Nelson and Sons. 1986.

*Lipsey, Richard G. An Introduction to Positive Economics. Weidenfeld and Nicolson. 1963. 2nd Ed: 1966. 3rd Ed: 1971. 4th Ed: 1975. 5th Ed: 1979. 6th Ed: 1983. 7th Ed: 1989.

*Nicolson, Walter. Microeconomic Theory: Basic Principles and Extensions. (Dryden Press Series in Economics). Dryden Press, Holt-Saunders. 3rd Ed: 1985. 

*Caves and Jones. World Trade and Payments: An Introduction. Little, Brown and Company. 1973. 1977. 3rd Ed: 1981.

*National Institute of Economic and Social Research. The UK economy. (Studies in the UK Economy). Heinemann Educational. 1990.
*Smith, Charles. UK trade and sterling. (Studies in the UK Economy). Heinemann Educational. 1992.

==Games==
Chess
*Hooper and Whyld. The Oxford Companion to Chess. Oxford University Press. 1984. Paperback: 1987.
*Golombek, Harry. The Game of Chess. 1954. 2nd Ed: 1963. 3rd Ed: 1980.
*Pritchard, D. Brine. The Right Way to Play Chess. 1950. 8th Ed: 1971. 10th Ed: 1974. 11th Ed: 1977.
*Horowitz, Al. From Morphy to Fischer: A history of the World Chess Championship. B T Batsford. 1973. The World Chess Championship: A History. Macmillan. 1973. 

General series
*Batsford Chess Books
**Discovering Chess Series. B T Batsford.

Periodicals

See [[Universal Bibliography/Periodicals#Chess|Periodicals, Chess]]
*British Chess Magazine

Othello
*Goro Hasegawa with Maxine Brady. How to Win at Othello. (A Harvest/HBJ book). Jove Publications. 1977. ISBN 0-15-642215-8. [https://books.google.co.uk/books?id=mTdhlwVeyCcC]

Wargames
*Battleground. Tyne Tees. (ITV). 1978. [Television]. 6 episodes, with Edward Woodward.
**Laurie Taylor. &quot;Attila the Hun invades Tyne Tees&quot;. TV Times. 1978. pp 28 &amp; 29.
**Terry Wise. &quot;Battleground&quot;. Battle for Wargamers. June 1978. pp 261 &amp; 262.
*[[w:Game of War|Game of War]]. Channel 4. 1997. [Television].

==Toys==
Periodicals
*Games &amp; Toys: The Leading Trade Journal for Home &amp; Export. (H Richard Simmons Limited). [https://books.google.co.uk/books?id=pMmbZ_JTnXYC] Google: editions:UO8GID_4Ck0C
*Toys and Novelties. (Sporting Goods Pub Co). [https://books.google.co.uk/books?id=zKdAAQAAMAAJ] [https://archive.org/details/toys-and-novelties-volume-9-1913/page/n53/mode/1up] (Toys and Novelties Publishing Company) [https://archive.org/details/toys-and-novelties-volume-19-issue-no.-1-6-january-june-1922/page/n173/mode/1up]. Cf. &quot;Harcourt To Buy Journals From Haire Publishing Co&quot; [https://books.google.co.uk/books?id=J7hEAQAAIAAJ 194] Publishers Weekly 29
*[[w:Playthings (magazine)|Playthings: The National Magazine of the Toy Trade]]. (McCready Publishing Co) [https://books.google.co.uk/books?id=eCQHzuYWDY4C] [https://books.google.co.uk/books?id=mnRO5WFXDfEC]. (Geyer-McAllister Publications). Cf. &quot;Playthings bought by Geyer-McAllister&quot; [https://books.google.co.uk/books?id=itAaAQAAMAAJ 52] Industrial Marketing

==Cricket==
See [[w:Bibliography of cricket]]

*Peter Arnold and Peter Wynne-Thomas. The Complete Encyclopedia of Cricket. 2006. 4th Ed: 2011: [https://books.google.co.uk/books?id=2R_pXwAACAAJ].
**Peter Arnold. The Illustrated Encyclopedia of World Cricket.
*Morgan. The Encyclopedia of World Cricket. 2007. [https://books.google.co.uk/books?id=gFCbkgEACAAJ]

Scores and biographies
*Marylebone Club Cricket Scores and Biographies. [https://books.google.co.uk/books?id=dl8IAAAAQAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
**See [[w:Arthur Haygarth]] and [[w:Fred Lillywhite]]

Periodicals
*[[w:Cricket: A Weekly Record of the Game|Cricket: A Weekly Record of the Game]]. [https://books.google.co.uk/books?id=eX9QAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false].

Australia
*Malcolm Andrews. The Encyclopaedia of Australian Cricket. 1980. [https://catalogue.nla.gov.au/Record/1531463]
*The Oxford Companion to Australian Cricket

India 
*The Encyclopaedia of Indian Cricket, 1965. [https://books.google.com/books?id=CE4Joad6iwAC] [Includes biographies]

Annuals
*[[w:Indian Cricket (annual)|Indian Cricket]].  [https://books.google.co.uk/books?id=ioRLAAAAYAAJ 1966].

===Cricketers===
Cricketers, including biographical dictionaries and collections of biographies
*[[w:ESPNcricinfo|ESPNcricinfo]]
*[[w:CricketArchive|CricketArchive]]

*John Arlott's Book of Cricketers. 1979. [https://books.google.co.uk/books?id=8-WBAAAAMAAJ]

*World Cricketers: A Biographical Dictionary [https://books.google.com/books?id=IpBLAAAAYAAJ]
*Carr's Dictionary of Extraordinary Cricketers. 1977. Aurum Press. 2005. [https://books.google.com/books?id=CfwsAAAACAAJ]

*Sproat. Debrett's Cricketers' Who's Who. 1980.
*S Canynge Caple. The Cricketer's Who's Who. Williams. Lincoln. 1934.
*Cricket Who's Who: The Cricket Blue Book. 1909. [https://catalogue.nla.gov.au/Record/119715]. 1912. Bibliography: [https://books.google.co.uk/books?id=IjQyAQAAMAAJ]

*Who's Who in Test Cricket: A Biographical Dictionary of Test Cricketers [https://books.google.com/books?id=5uF5PQAACAAJ]

*Frindall. England Test Cricketers: The Complete Record from 1877. 1989. [https://books.google.com/books?id=2zHYLIW7h9UC]
*Brooke. The Collins Who's Who of English First-Class Cricket, 1945-1984. 1985. [https://books.google.com/books?id=NGSPAAAACAAJ]. Review: [https://books.google.co.uk/books?id=iHMsAAAAYAAJ]. Commentary: [https://books.google.co.uk/books?id=wPg5AQAAIAAJ]

Gloucestershire
*Gloucestershire Cricketers, 1870-1979. (ACS Cricketers Series [https://archive.acscricket.com/cricketers_series/index.html]). The Association of Cricket Statisticians. Cleethorpes. 1979. [https://archive.acscricket.com/cricketers_series/gloucestershire_cricketers_1870-1979/index.html]
*Rex Pogson. Gloucestershire Cricket and Cricketers, 1919-1939. Lytham St Annes. 1944. Catalogues: [https://catalogue.nla.gov.au/Record/850643] [https://books.google.co.uk/books?id=CS83vXlB1ZIC] [https://www.worldcat.org/title/504354999]. Also printed as microfilm: [https://books.google.co.uk/books?id=iqXeDTKUEl4C].
*Dean Hayes. Gloucestershire Cricketing Greats: 46 of the Best Cricketers for Gloucestershire. Tunbridge Wells. 1990. Catalogues: [https://books.google.co.uk/books?id=OmsqAQAAIAAJ] [https://www.worldcat.org/title/25202795]

Australia
*The A-Z of Australian Cricketers [https://books.google.com/books?id=w-0zAAAACAAJ]
*Piesse. Encyclopedia of Australian Cricket Players. 2012. [https://books.google.com/books?id=Jsh4MAEACAAJ]
*C P Moody. Australian Cricket and Cricketers 1856-1893-4. Melbourne. 1894.
*Jack Pollard. Australian Cricket: The Game and the Players. Hodder and Stoughton. ABC Books. Sydney. Lane Cove, New South Wales. 1982. Angus &amp; Robertson. London. North Ryde, New South Wales. Sydney. Revised Ed: 1988. Commentary: [https://books.google.co.uk/books?id=WotYAAAAYAAJ]. Review: [https://books.google.co.uk/books?id=KzNYAAAAMAAJ].

==Geology==
*Read and Watson. Introduction to Geology. Macmillan Education. 1962. 2nd Ed: 1968. Volume 1: Principles. Volume 2: Earth History.

==Mineralogy==
*Bibliography of Mineralogy for 1886. Annual Report of the Board of Regents of the Smithsonian Institution. Year Ending 30 June 1887. 1889. Pages [https://books.google.co.uk/books?id=wDcWAAAAYAAJ&amp;pg=PA473#v=onepage&amp;q&amp;f=false 473] to 476.

*Battey, Maurice Hugh. Mineralogy for students. Oliver &amp; Boyd. 1972. 2nd Ed. Longman. 1981.

==Paper==
See [[s:Category:Paper]]

*Surface. Bibliography of the Pulp and Paper Industries. Forest Service. Bulletin 123. 1913. [https://archive.org/details/bibliographyofpu12surf]
*West. Reading List on Papermaking Materials. 1920 to 1921. [https://archive.org/details/readinglistonpa00westgoog] [https://archive.org/details/readinglistonpa01westgoog]

==Books==
*British Book News [https://books.google.co.uk/books?id=2oFTAAAAIAAJ]
*Australasian Book News and Literary Journal. Australasian Book News and Library Journal. [https://books.google.co.uk/books?id=QVQPAQAAIAAJ]

*Book News. 1882 to 1918. (John Wanamaker). Called &quot;Book News Monthly&quot; from 1906. [https://books.google.co.uk/books?id=KtwRAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Stechert-Hafner Book News [https://books.google.co.uk/books?id=BmDqAAAAMAAJ]
*U.S.A. Book News [https://books.google.co.uk/books?id=36gVAQAAIAAJ]
*Branch Library Book News. [https://books.google.co.uk/books?id=NM8aAAAAMAAJ]

*Hungarian Book Review [https://books.google.co.uk/books?id=6U85AQAAIAAJ]
*Soviet Book News. (Earl Browder). 1947 [https://books.google.co.uk/books?id=QrXQ6LYSOF4C]

*Miniature Book News. [https://books.google.co.uk/books?id=MascAQAAMAAJ]

Rare
*Berger. Rare Books and Special Collections. American Library Association. 2014. [https://books.google.co.uk/books?id=IFUangEACAAJ]

Printed
*Annual Bibliography of the History of the Printed Book and Libraries. [https://books.google.co.uk/books?id=GLigoebhrd8C&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 30] [https://books.google.co.uk/books?id=UBN-IUZlF4gC&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 31]

==Paperback and Paperbound==
*Swados, &quot;Paper Books: What do they Promise?&quot; (1953) [https://books.google.co.uk/books?id=TwaJtQzwj1gC 173] The Nation 114
*Wagman, &quot;The Paperbound Book Business&quot; (1957) 9 Michigan Business Review [https://books.google.co.uk/books?id=9pA8uolQjnkC&amp;pg=RA4-PA9#v=onepage&amp;q&amp;f=false 9] (No 5, November)

==Science==
*Lafferty and Rowe. The Hutchinson Dictionary of Science. Helicon Publishing. 1993. 2nd Ed: 1998.

==Entertainment==
*The Directory (The Times, 1996 onwards) Commentary: [https://www.marketingweek.com/as-times-starts-listings-supplement/]

==Comedy and tragedy==
*E H Mikhail. Comedy and Tragedy: A Bibliography of Critical Studies. 1972. [https://books.google.co.uk/books?id=5bgEAAAAMAAJ]

===Comedy===
*James E Evans. Comedy: An Annotated Bibliography of Theory and Criticism. 1987. [https://books.google.co.uk/books?id=s9ZgthAs1t8C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Meghan Duffy (ed). Daniel Gerould (senior ed). Comedy: A Bibliography of Critical Studies in English on the Theory and Practice of Comedy in Drama, Theatre, and Performance. New York. 2006. [https://books.google.co.uk/books?id=fI0jAQAAIAAJ]
*David Humphrey. The Time of Laughter: Comedy and the Media Cultures of Japan. University of Michigan Press. 2023. [https://books.google.co.uk/books?id=CkTLEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

==Radio and television==
*William E McCavitt. Radio and Television: A Selected Annotated Bibliography. Scarecrow Press. 1978. [https://books.google.com/books?id=DAQVAQAAIAAJ]
*Gertrude G Broderick. Radio and Television Bibliography. Bulletin 1948 No 17. [https://books.google.co.uk/books?id=yIPP1dsmNtAC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
*Patricia Beall Hamill. Radio and Television: A Selected Bibliography. Bulletin 1960 No 25. [https://books.google.co.uk/books?id=AJhGAQAAMAAJ&amp;pg=PP3#v=onepage&amp;q&amp;f=false]

==Film and television==
*Jean Mitry. Bibliographie internationale du cinéma et de la télévision. 1966 onwards. [https://books.google.co.uk/books?id=SC3gAAAAMAAJ] Commentary: A Reference Guide for English Studies, [https://books.google.co.uk/books?id=h_wfYKnMfOkC&amp;pg=PA439#v=onepage&amp;q&amp;f=false p 439].

==Animation==
*John Halas and Roger Manvell. The Technique of Film Animation. 4th Ed: 1976. Focal Press. ISBN 0240509005.
*Clements and McCarthy. The Anime Encyclopedia. 3rd Rev Ed: [https://books.google.co.uk/books?id=E03KBgAAQBAJ&amp;pg=PA1958#v=onepage&amp;q&amp;f=false].

==Colours==
*Eiseman and Recker. Pantone: The 20th Century in Color. [https://books.google.co.uk/books?id=j3H7nSVS3UMC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. Reviews: [https://www.theguardian.com/books/2011/nov/13/pantone-20th-century-color-review][https://www.theatlantic.com/entertainment/archive/2011/11/pantone-100-years-of-color/249016/][https://eu.vvdailypress.com/story/lifestyle/health-fitness/2012/01/16/color-reel-20th-century-s/37119883007/]

==Bilateral==
Britain and Japan
*Pearse. Companion to Japanese Britain and Ireland. In Print. 1991. [https://books.google.co.uk/books?id=KtAxAAAAIAAJ]

==Prehistoric life==
Prehistoric animals
*[[w:Michael Benton|Michael Benton]]. Prehistoric Animals: An A-Z Guide. Kingfisher Books. 1989. Derrydale Books, New York. 1989. [Illustrations: Jim Channell and Kevin Maddison.]
*Ellis Owen. Prehistoric Animals: The Extraordinary Story of Life before Man. Octopus Books Limited. London. 1975. [Sculptures: Arthur Hayward.] Review: [https://books.google.co.uk/books?id=II-B8R-8Ov8C 17] Wildlife 422. Commentary: [https://books.google.co.uk/books?id=aUbYAAAAQBAJ&amp;pg=PA269#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=jFNBAAAAIBAJ&amp;pg=PA5#v=onepage&amp;q&amp;f=false].
**Prehistorische dieren: de geschiedenis van het leven vóór de mens. Translated by JJ Hoedeman. In den Toren, Baarn. Westland, Schoten. 1977.  Commentary: [https://books.google.co.uk/books?id=ToVMAQAAIAAJ]
**Les Animaux préhistoriques: l'extraordinaire histoire de la vie avant l'homme.

Dinosaurs
*Michael Benton. Dinosaurs: An A-Z Guide. Kingfisher Books. 1988. Derrydale Books, New York. 1988. [Illustrations: Jim Channell and Kevin Maddison.]

==Continents==
===Asia===
====Far East====
Bibliography
*Kuniyoshi. Far East. (PACAF Basic Bibliographies). 1957. [https://books.google.co.uk/books?id=Q5TLdCbP2HcC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]

====Japan and Korea====
Bibliography
*Bernard S Silberman. Japan and Korea: A Critical Bibliography. University of Arizona Press. 1962. [https://books.google.co.uk/books?id=y6UIAAAAIAAJ]
*Frank J Shulman. Japan and Korea: An Annotated Bibliography of Doctoral Dissertations in Western Languages 1877-1969. American Library Association. 1970. Routledge. 2013. [https://books.google.co.uk/books?id=xs62AQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

====South Asia====
*South Asian Bibliography: A Handbook and Guide. Harvester Press. [https://books.google.co.uk/books?id=aqwNAQAAIAAJ]
*The Bibliography of South Asian Periodicals: A Union-list of Periodicals in South Asian Languages. Harvester Press. [https://books.google.co.uk/books?id=COV0nIUK0bgC]

==Culture and society==
*Victoria Lyon Bestor, Theodore C Bestor and Akiko Yamagata (eds). Routledge Handbook of Japanese Culture and Society. 2011. [https://books.google.co.uk/books?id=0cBYffHp5L4C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Josef Kreiner and Hans-Dieter Ölschleger (eds). Japanese Culture and Society: Models of Interpretation. 1996. [https://books.google.co.uk/books?id=6skwAQAAIAAJ]
*Dolores P Martinez. Modern Japanese Culture and Society. 2007. [https://books.google.co.uk/books?id=l6kMAQAAMAAJ vol 1]
*C Andrew Gerstle. 18th Century Japan: Culture and Society. 1989. [https://books.google.co.uk/books?id=ViglDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Periodicals
*Review of Japanese Culture and Society [https://books.google.co.uk/books?id=W_o-AQAAIAAJ]

==See also==
*[[Bibliography]]

==Notes==
{{Reflist}}
{{subpagesif}}
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{{Bibliography}}
{{research}}

If this resource is ever completed, it will be a universal bibliography.&lt;ref&gt;See [[w:Bibliography]].&lt;/ref&gt; Until then, it will be an approximation of a universal bibliography.

This bibliography is arranged as an index of topics.

==Index==
*[[Universal Bibliography/Bibliography|Bibliography]]
*[[Universal Bibliography/Libraries|Libraries]]
*[[Universal Bibliography/Literature|Literature]]
*[[Universal Bibliography/Languages|Languages]]
*[[Universal Bibliography/SF|SF]]
*[[Universal Bibliography/Music|Music]]
*[[Universal Bibliography/Cinema|Cinema]]
*[[Universal Bibliography/Television|Television]]
*[[Universal Bibliography/Culture|Culture]]
*[[Universal Bibliography/Publishers and imprints|Publishers and imprints]]
*[[Universal Bibliography/Printing|Printing]]
*[[Universal Bibliography/Printers|Printers]]
*[[Universal Bibliography/Microform|Microform]]
*[[Universal Bibliography/Periodicals|Periodicals]]
*[[Universal Bibliography/Reference|Reference]]
*[[Universal Bibliography/Gazetteers|Gazetteers]]
*[[Universal Bibliography/Humanities|Humanities]]
*[[Universal Bibliography/Law|Law]]
*[[Universal Bibliography/History|History]]
*[[Universal Bibliography/Archaeology|Archaeology]]
*[[Universal Bibliography/Geography|Geography]]
*[[Universal Bibliography/Countries|Countries]]
*[[Universal Bibliography/Architecture|Architecture]]
*[[Universal Bibliography/Mathematics|Mathematics]]
*[[Universal Bibliography/Computers|Computers]]
*[[Universal Bibliography/Kites|Kites]]
*[[Universal Bibliography/Nostalgia|Nostalgia]]
*[[Universal Bibliography/Children's non-fiction|Children's non-fiction]]

===About===
*[[Universal Bibliography/About|About]]

==Online libraries==
Swedish:
*[[w:Swedish Literature Bank|Litteraturbanken]] (Swedish Literature Bank)
*[[w:Project Runeberg|Projekt Runeberg]] (Project Runeberg)

French
*[[w:Persée (web portal)|Persée]] (persee.fr)

Japanese
*[[w:Aozora Bunko|Aozora Bunko]] (aozora.gr.jp)

==Biographical dictionaries etc==
See [[w:Bibliography of encyclopedias: general biographies]] and [[w:List of biographical dictionaries]]

*Fox. 'True Biographies of Nations?': The Cultural Journeys of Dictionaries of National Biography. ANU Press. 2019 [https://books.google.co.uk/books?id=siSbDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Arthur, &quot;Biographical Dictionaries in the Digital Era&quot;. Advancing Digital Humanities: Research, Methods, Theories. 2014. Chapter 6. [https://books.google.co.uk/books?id=z7MaBgAAQBAJ&amp;pg=PA83#v=onepage&amp;q&amp;f=false Page 83] et seq.

Bibliographies, indexes, etc:
*Wynar. ARBA Guide to Biographical Dictionaries. Libraries Unlimited. 1986 [https://books.google.co.uk/books?id=5FfgAAAAMAAJ]
*Slocum, Robert B (ed). Biographical Dictionaries and Related Works. Gale Research Company. 2nd Ed: 1986 [https://books.google.co.uk/books?id=5uMpAQAAMAAJ]
*Biographical Dictionaries Master Index. (Gale Biographical Index Series). [https://books.google.co.uk/books?id=ZEshAQAAMAAJ] [https://books.google.co.uk/books?id=pPAzAQAAIAAJ] see also [https://books.google.co.uk/books?id=o_gPAQAAMAAJ]
*Children's Authors and Illustrators: An Index to Biographical Dictionaries. (Gale Biographical Index Series). 2nd Ed: 1978,  3rd Ed: 1981, 4th Ed: 1987 [https://books.google.co.uk/books?id=VIsWAQAAMAAJ] [https://books.google.co.uk/books?id=DFtGAQAAIAAJ] [https://books.google.co.uk/books?id=01wjAQAAIAAJ]
*Index to the Wilson Authors Series [https://books.google.co.uk/books?id=oNZkAAAAMAAJ]
*Auchterlonie. Arabic Biographical Dictionaries: A Summary Guide and Bibliography. 1987 [https://books.google.co.uk/books?id=rW59QgAACAAJ]
*Black Biographical Dictionaries, 1790-1950 [https://books.google.co.uk/books?id=laIUAQAAMAAJ]

Particular works:

*Oxford Dictionary of National Biography; [[w:Dictionary of National Biography|Dictionary of National Biography]]
*Boase. Modern English Biography. ([http://www.google.com/search?q=editions%3Auzt3-qMuFcMC&amp;btnG=Search+Books&amp;bksoutput=html_text&amp;tbm=bks&amp;tbo=1 editions:uzt3-qMuFcMC])
*A &amp; C Black's Who's Who
*Who Was Who
*The Academic Who's Who. A &amp; C Black. 1st Ed: 1973 [https://books.google.co.uk/books?id=dnUWAQAAMAAJ] [https://books.google.co.uk/books?id=fXJmAAAAMAAJ]. 2nd Ed: 1975. Commentary: [https://books.google.co.uk/books?id=7VyOANl2qxoC&amp;pg=PA208&amp;output=html_text]. GBooks: editions:INAP7GGD2gYC editions:tA0FkHC75FIC
*Dictionary of Edwardian Biography (Pike's New Century Series)

Works that comprise largely of biographies:
*The Penguin Companion to Literature

Theatres
*A Biographical Dictionary of Actors, Actresses, Musicians, Dancers, Managers &amp; Other Stage Personnel in London, 1660-1800. [https://books.google.co.uk/books?id=TGgS9VxWJ0oC vol 15]

==Dictionaries of dates==
[https://archive.org/search.php?query=%22dictionary%20of%20dates%22 Archive.org]
*Baxter Dictionary of Dates and Events. 1st Ed: 1963: Napier, M (ed). 2nd Ed: 1971: Sanders and Laffin. Commentary: 92 Library Journal 1819 [https://books.google.co.uk/books?id=CExVAAAAYAAJ]
*Beeching, Cyril Leslie. A Dictionary of Dates. OUP. 1st Ed: 1993. 2nd Ed: 1997. [https://www.google.co.uk/search?hl=en&amp;tbm=bks&amp;q=editions:UGGp0EexZdcC editions:UGGp0EexZdcC]
*Bolton, John. Bolton's Dictionary of Dates, arranged in alphabetical order. Foulsham. 1958. Review: [https://books.google.co.uk/books?id=awJPAAAAIAAJ 172] The Publisher 880
*[[w:William Darling (politician)|William Young Darling]]. A Book of Days: A Dictionary of Dates, a Chronology of Circumstance, the Face of Time. Richards Press. 1951. [https://books.google.co.uk/books?id=PLkfAAAAMAAJ]
*Everyman's Dictionary of Dates. 1st Ed: 1911. 6th Ed: 1971. Review: (1971) 11 RQ 164 [http://www.jstor.org/stable/25824440]
*Platt, Charles. Foulsham's Dictionary of Dates and General Information. 1930.
*[[w:Haydn's Dictionary of Dates|Haydn's Dictionary of Dates]]
*Hamlyn Dictionary of Dates and Anniversaries. Newnes Dictionary of Dates.
*Williams, Henry Llewellyn. Hurst's Dictionary of Dates. 1891. [https://archive.org/details/hurstsdictionary00will]
*Keller, Helen Rex. The Dictionary of Dates. Macmillan. 1934. Commentary: [https://books.google.co.uk/books?id=Utcb32E7rsMC&amp;pg=PA93&amp;output=html_text] [https://books.google.co.uk/books?id=sAHfY6QbOEwC&amp;pg=PA351&amp;output=html_text]
*Nelson's Dictionary of Dates. A Dictionary of Dates. (Nelson's Encyclopaedic Library). 1912 [https://books.google.co.uk/books?id=Mp9lvwEACAAJ]. Reviews: (June 1912) Journal of Education, vol 34 (New Series), vol 44 (Old Series), p 392 [https://books.google.co.uk/books?id=QIRFAQAAMAAJ]; (1912) [https://books.google.co.uk/books?id=9i4_AQAAIAAJ 108] The Spectator [http://archive.spectator.co.uk/article/18th-may-1912/25/a-dictionary-of-dates-vol-i-and-english-idioms-nel 805] (18 May)
*Pulman, George Palmer. The World's Progress: A Dictionary of Dates. New York. 1861. [https://books.google.co.uk/books?printsec=frontcover&amp;id=k3dJAAAAYAAJ&amp;output=html]
*Urdang, Laurence. The World Almanac Dictionary of Dates. Longman. 1982. [https://books.google.co.uk/books?id=I4IRAQAAMAAJ] Review: (1982) 22 RQ 101 [http://www.jstor.org/stable/25826880]

Australia

*John Henniker Heaton. Australian Dictionary of Dates and Men of the Time. 1879. [https://archive.org/details/australiandicti00heatgoog]
*John James Knight. In the Early Days; History and Incident of Pioneer Queensland, with Dictionary of Dates in Chronological Order. Sapsford &amp; Co. Brisbane. 1895.

America

*Damon, Charles Ripley. The American Dictionary of Dates, 458-1920. R G Badger. 1921.

==Commodity dictionaries==
*Statistical Classification of Domestic and Foreign Commodities Exported from the United States. Commentary: [https://books.google.co.uk/books?id=91GLhsJSBj8C&amp;pg=PR22#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=RPwhAQAAMAAJ&amp;pg=RA15-PA7#v=onepage&amp;q&amp;f=false]
*Tovarnyi slovar'. (Commodity Dictionary). Reviews and commentary: Petrov, &quot;Commodity Dictionary&quot;, Ekonomicheskaya Gazeta, No 13, 30 October 1961, p 45; CDSP , 13 December 1961, p 46; (1962) [https://books.google.co.uk/books?id=2vMRAAAAIAAJ 13] Current Digest of the Soviet Press 47; (1958) 15 Quarterly Journal of Current Acquisitions 210 [https://books.google.co.uk/books?id=ZcvozpZAfpEC] [https://books.google.co.uk/books?id=S47qEIfyCr0C]; Fitzpatrick, Stalinism: New Directions, [https://books.google.co.uk/books?id=rD5FzoKnTE0C&amp;pg=PA182#v=onepage&amp;q&amp;f=false p 182] &amp; 183
*Szilágyi. Commodity Dictionary in Five Languages. Budapest. Közgazdasági és Jogi Könyvkiadó (Publishing House for Economics and Law). 1963 or 1964. Commentary: Books from Hungary, vols 4-6, pp 26 &amp; 40 [https://books.google.co.uk/books?id=6kMiAQAAMAAJ]
*Dictionnaire des produits: appellations et caractéristiques des produits francais de consommation courante, 1960. Commentary: Walford (ed), Guide to Reference Material Supplement, 1963, p 106 [https://books.google.co.uk/books?id=ej-9pHGR67oC]
*Chūgoku Shōhin Jiten. (Chinese commodity dictionary). Tokyo. 1960. [https://books.google.co.uk/books?id=Wc61lS0xj6AC&amp;pg=PA78#v=onepage&amp;q&amp;f=false]

==Encyclopedias==
See [[s:Category:Encyclopedias]], [[w:Bibliography of encyclopedias]] and [[w:Lists of encyclopedias]]

*[[w:en:Encyclopædia Britannica Eleventh Edition|Encyclopædia Britannica Eleventh Edition]]
*Paton, John (ed). Knowledge Encyclopedia: 1979, 1981, 1988. New Discovery Encyclopedia: 1990.
*The Dorling Kindersley Illustrated Family Encyclopedia

==Almanacs==
See [[s:Category:Almanacs]], [[s:Portal:Almanacs]], [[w:List of almanacs]], [[w:Category:Almanacs]].
*Year Book and Almanac of Newfoundland. 
**For 1896. 1895. [https://archive.org/details/yearbooknfld189600newfuoft]
*Whiteley. On This Date: A Day-by-Day Listing of Holidays, Birthday and Historic Events, and Special Days, Weeks and Months. 2002. [https://books.google.co.uk/books?id=sKCfomKSa74C]

==Censuses==
*Census of New Zealand and Labrador
**1901 Census. Tables 2 and 3. 1903. [https://archive.org/details/censusnewfoundl00bondgoog]
**1911 Census. Table 1. 1914. [https://archive.org/details/1911981911fnfldv11914eng]
**1921 Census. Tables 4 and 5. 1923. [https://archive.org/details/1921981921fnfldv451923eng]

==Pilot guides==
*[[w:United States Coast Pilot|United States Coast Pilot]]
*American Coast Pilot [https://books.google.co.uk/books?id=8GoDAAAAYAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]

*Sailing Directions: Newfoundland. Canadian Hydrographic Service. [https://books.google.co.uk/books?id=A77fAAAAMAAJ]
*Newfoundland Pilot. Canadian Hydrographic Service. [https://books.google.co.uk/books?id=z7zfAAAAMAAJ]
*Maxwell. The Newfoundland Pilot. Hydrographic Office, Admiralty. London. 1878. [https://books.google.co.uk/books?id=vS4BAAAAQAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]
*Newfoundland Pilot. HO No 73. Hydrographic Office. Governement Printing Office, Washington. 4th Ed: 1919: [https://books.google.co.uk/books?id=YGoDAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]. Sailing Directions for Newfoundland. 5th Ed: 1931: [https://books.google.co.uk/books?id=cMUiGo3JK9QC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]

==Books of facts==
*The Reader's Digest Book of Facts. 1st Ed: 1985. Reprinted with amendments: 1987: [https://books.google.co.uk/books?id=B8PmM_5Zm1MC]. (Review: Library Journal, [https://books.google.co.uk/books?id=EPDgAAAAMAAJ v 9], p 102, 1 Dec 1987, [http://www.bookverdict.com/details.xqy?uri=Product-94667328910921.xml Book Verdict].) 3rd Revised Ed: 1995: [https://books.google.co.uk/books?id=E5YhAQAAIAAJ]. GBooks: editions:nnJlLybWxbIC
*Chambers Book of Facts
*Crystal, David (ed). Penguin Book of Facts. [https://books.google.co.uk/books?id=k0sZAQAAIAAJ 2004]. 2nd Ed: 2008
*Handy Book of Facts: Things Everyone Should Know. C.S. Hammond &amp; Company. 1914. [https://books.google.co.uk/books?id=h5wRAAAAIAAJ]

==Series of books==
See [[w:Category:Series of books]] and [[w:Category:Monographic series]]
*George M Sinkankas, &quot;Series&quot; in Kent, Lancour and Daily (eds).  Encyclopedia of Library and Information Science. Volume 27. Marcel Dekker. 1979. Pages [https://books.google.co.uk/books?id=jU3fwyjqS5UC&amp;pg=PA250#v=onepage&amp;q&amp;f=false 250] to 273.
*&quot;Publishing in Series, 1896-1916&quot; in Eliot, Simon (ed). History of Oxford University Press. Louis,  Wm Roger (ed). Volume 3: 1896-1970. Oxford University Press. 2013. [https://books.google.co.uk/books?id=YbcJAgAAQBAJ&amp;pg=PA539#v=onepage&amp;q&amp;f=false Page 539] et seq.
*Spiers, John. The Culture of the Publisher’s Series. Palgrave Macmillan. 2011. [https://books.google.co.uk/books?id=ASaHDAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 1]. [https://books.google.co.uk/books?id=XCl-DAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 2].
*Spiers, John. Serious about Series: American 'Cheap' Libraries, British 'Railway' Libraries and Some Literary Series of the 1890's. 2007. [https://books.google.co.uk/books?id=1hRXAAAAYAAJ] [https://books.google.co.uk/books?id=AS4yQwAACAAJ]
*Rooney, Paul Raphael. Railway Reading and Late-Victorian Literary Series. Routledge. 2018. [https://books.google.co.uk/books?id=uX5aDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Khan. &quot;Monographs in series&quot;. The Principles and Practice of Library Science. 1996. Pages [https://books.google.co.uk/books?id=sAHfY6QbOEwC&amp;pg=PA208#v=onepage&amp;q&amp;f=false 207] to 209.
*Friskney. New Canadian Library: The Ross-McClelland Years, 1952-1978. Pages [https://books.google.co.uk/books?id=jHIjCCXBX9kC&amp;pg=PA6#v=onepage&amp;q&amp;f=false 6] and 7.

*Books in Series. R R Bowker Company. Commentary: [https://books.google.co.uk/books?id=uQe04OSlA7YC&amp;pg=PA11#v=onepage&amp;q&amp;f=false]
**Books in Series in the United States, 1966-1975. R R Bowker. 1977. Review: (1977) 14 Choice [https://books.google.co.uk/books?id=_e08AQAAIAAJ&amp;pg=PA1190#v=onepage&amp;q&amp;f=false 1190] (No 8, November). Commentary: [https://books.google.co.uk/books?id=LYAhAAAAQBAJ&amp;pg=PA53#v=onepage&amp;q&amp;f=false]
***Books in Series Supplement: A Supplement to Books in Series in the United States, 1966-1975. 1978. [https://books.google.co.uk/books?id=hOAaAQAAMAAJ]
**Books in Series. 3rd Ed. 1980. [https://books.google.co.uk/books?id=d_kaAQAAMAAJ]
**Books in Series, 1876-1949. R R Bowker Company. 1982. [https://books.google.co.uk/books?id=TngvAQAAIAAJ] [https://books.google.co.uk/books?id=iVIyAQAAMAAJ] [https://books.google.co.uk/books?id=R2AjAQAAIAAJ]
**Books in Series, 1985-89. [https://books.google.co.uk/books?id=yEkxAQAAIAAJ]
*Baer, Eleanora Agnes. Titles in Series: A Handbook for Librarians and Students. Scarecrow Press. Vol 1 (Books Published Prior to January 1953). 1953: [https://books.google.co.uk/books?id=GgAYAAAAMAAJ]. Vol 2 (Books Published Prior to January 1957). 1957: [https://books.google.co.uk/books?id=oqsXAAAAMAAJ]
**2nd Ed: 1964. [https://books.google.co.uk/books?id=gWlAAAAAIAAJ Vol 1]. [https://books.google.co.uk/books?id=tWpAAAAAIAAJ Vol 2]. Supplement to the Second Edition. 1967: [https://books.google.co.uk/books?id=zGARAQAAMAAJ]. Second Supplement to the Second Edition. 1971: [https://books.google.co.uk/books?id=WwXhAAAAMAAJ]
**3rd Ed: 1978. Commentary: [https://books.google.co.uk/books?id=h_wfYKnMfOkC&amp;pg=PA63#v=onepage&amp;q&amp;f=false]
*Ocran, Emmanuel Benjamin. Scientific &amp; Technical Series: A Select Bibliography. 1973: [https://books.google.co.uk/books?id=oy0EAAAAMAAJ] Review: [https://books.google.co.uk/books?id=fTCw_DQH6zkC&amp;pg=PA949#v=onepage&amp;q&amp;f=false]

*Rosenberg and Nichols. Young People's Books in Series: Fiction and Non-fiction, 1975-1991. Libraries Unlimited. 1992. [https://books.google.co.uk/books?id=REHhAAAAMAAJ]
*Young People's Literature in Series

*Catalog of Reprints in Series. (sometimes called &quot;Catalogue of Reprints in Series&quot;). 1940 onwards. [https://books.google.co.uk/books?id=MSI4AAAAIAAJ] [https://books.google.co.uk/books?id=6n1EAAAAMAAJ] Commentary: [https://books.google.co.uk/books?id=h_wfYKnMfOkC&amp;pg=PA73#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=1RxuAAAAMAAJ]

*Kuitert, Lisa. Het ene boek in vele delen. De Uitgave van Literaire Series in Nederland 1850-1900. Uitgeverij de Buitenkant. Amsterdam. 1993. Commentary: [https://books.google.co.uk/books?id=jSDnRo7YrWwC&amp;pg=PA656#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=szBcAAAAMAAJ] [https://books.google.co.uk/books?id=SVcVAQAAIAAJ] [https://books.google.co.uk/books?id=R8Pfs146nUAC&amp;pg=PA367#v=onepage&amp;q&amp;f=false]

==Series of classics==
*Penguin Classics (Penguin Modern Classics, Penguin English Library)
*Oxford World Classics
*Everyman's Library
*Wordsworth Classics
*Macmillan Collectors Library
*Bantam Classics
*Minster Classics
*The Literary Heritage Collection (Heron Books, London. William Collins Sons &amp; Co, Glasgow)
*Chandos Classics
*Temple Classics
*Longmans Heritage of Literature Series

Russian
*Greatest Masterpieces of Russian Literature (Heron Books, London)

SF
*Corgi SF Collectors Library

Children's and shorter classics etc 
*Shorter Classics. Ginn and Company.
*Ladybird Children's Classics.
*Mini Classics. Parragon Books.
*Bonny Books. Peter Haddock Ltd.
*A series published by Dean &amp; Son Ltd

==Non-fiction general series==
*[[w:Oxford Companions|Oxford Companions]]
*[[w:Cambridge Companions|Cambridge Companions]]
*Princeton Companions
*Blackwell Companions. Wiley Blackwell Companions
*Routledge Companions. Routledge Research Companions
*Ashgate Companions. Ashgate Research Companions
*Brill's Companions
*Facts on File Companions
*Guides to Information Sources. Bowker-Saur
*Butterworths Guides to Information Sources.
*Columbia Guides
*Blackwell Guides
*Edinburgh Critical Guides
*Collins Reference Dictionaries
*New Horizons. Thames and Hudson. ([[w:Découvertes Gallimard|Découvertes Gallimard]])
*Collins Gem (see [[w:List of Collins GEM books]])
*Concise Encyclopedias. Collins.
*Time Life Books (see [[w:Time Life#Book series]])
*[[w:Teach Yourself|Teach Yourself Books]]. English Universities Press. 
*[[w:Teach Yourself|Teach Yourself Books]]. Hodder and Stoughton.
*Made Simple Books. W H Allen.
*Palgrave Master Series
*Harrap's Mini Series
*Shire Albums. Shire Publications.
*Fax Pax: Knowledge in a Nutshell. Fax Pax Ltd.
*The Wonderful World Books. Macdonald and Company
*Harper's ABC series. Includes A-B-C of Housekeeping, A-B-C of Electricity, A-B-C of Gardening and A-B-C of Manners.
*Hamlyn Pocket Guides
*Oxford Monograph Series
*Study Outline Series. H W Wilson. [[s:Page:Russian Literature - A Study Outline.djvu/61|(wikisource)]]
*Helpmate Handbooks. Willow Books

University
*University Paperbacks. Meuthen &amp; Co
*World Student Series. Addison Wesley
*Unibooks. Hodder and Stoughton
*International Student Editions. Van Nostrand Reinhold
*Hutchinson University Library

Imprints
*Pelican Books

Pictorials
*Salmon Cameracolour series
*Pitkin Pictorials 

United Kingdom
*Aspects of Britain. HMSO.

Places
*The Little Guides. Meuthen [[s:Page:Cornwall (Salmon).djvu/336|(wikisource)]]
*G.W.R. Series of Travel Books [[s:Page:The Cornwall coast.djvu/391|(wikisource)]]

Art
*Movements in World Art. Meuthen.
*Movements in Modern Art. Meuthen.
*How to Draw and Paint. New Burlington.

Film
*BFI Companions

Popular science
*Contemporary Science Paperbacks. Oliver and Boyd.
*Pan Piper Science Series

Science and mathematics
*Simon and Schuster Tech Outlines
*Schaum's Outline Series

Military
*Illustrated Military Guides. Illustrated Guides. &quot;An Illustrated Guide to ...&quot;. Salamander Books.
*Combat Arms. Arco Military Books. Salamander Books. Prentice Hall Press.
*Osprey Men-at-Arms
*Jane's Pocket Books

Communication
*The Library of Communication Techniques. Focal Press.
*John Fiske (ed). Studies in Culture and Communication. Routledge.
*The Media. Wayland.

Cookery
*ABC series. Peter Pauper Press.

Gardening
*Pan Piper Small Gardens Series.

Mythology
*Series on mythology published by Southwater (imprint of Anness)

==History and Geography==
See also [[Universal Bibliography/History|History]] and [[Universal Bibliography/Geography|Geography]].
*Baker. Geography and History: Bridging the Divide. 2003. [https://books.google.co.uk/books?id=e8yf5JcefpAC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Darby. Relations of History and Geography: Studies in England, France and the United States. 2002. [https://books.google.co.uk/books?id=Vl4ZfpnP7NwC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

General series
*Cambridge Studies in Historical Geography

Atlases
*The Times Atlas of World History
*Philip's Atlas of World History

History of geography:
*Dunbar, Gary S. The History of Modern Geography: An Annotated Bibliography of Selected Works. Garland. 1985. [https://books.google.co.uk/books?id=FX4WAQAAIAAJ]

==Chronology==
See also [[Universal Bibliography/History#Millennia, centuries and decades]]

General
*Chronology of World History.
**Neville Williams. Chronology of the Modern World: 1763 to the present time. 1st Ed: 1966. (1763 to 1992). 2nd Ed: 1994.
**Neville Williams. Chronology of the Expanding World 1492 to 1762. 1969. Reissued 1994.
**Storey. Chronology of the Medieval World 800 to 1491. 1973. Reissued 1994.
**Mellersh. Chronology of the Ancient World 10,000 BC to AD 799. Barrie and Jenkins. 1976. Helicon. Simon &amp; Schuster. Reissued 1994.

Centuries
*Chronology of the 20th Century. Helicon. 1995. [https://books.google.com/books?id=pjsOAQAAMAAJ]
*Brownstone and Franck. Timelines of the 20th Century. [https://books.google.com/books?id=IZ6SQgAACAAJ]
*Beal. 20th Century Timeline. 1985. [https://books.google.com/books?id=cFrG7LBObGoC]
*20th Century Day by Day [https://books.google.com/books?id=kyxaAAAAYAAJ] [https://books.google.com/books?id=WiOAAAAACAAJ]
*Chronicle of the 20th Century [https://books.google.co.uk/books?id=pt3DYbnZO8sC] [https://books.google.co.uk/books?id=Gd1WPQAACAAJ]
*Boyle. The Chronology of the Eighteenth and Nineteenth Centuries. 1826. [https://books.google.co.uk/books?id=wDENAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]

Decades
*Series:
**Day by Day. Facts on File. [https://books.google.com/books?id=WfClvwEACAAJ] [https://books.google.com/books?id=CWNvQgAACAAJ]

Years
*Brown, D Kinnear. History of the Year. (1884 to 1885). [https://books.google.co.uk/books?id=DmRWAAAAYAAJ&amp;pg=PA113#v=onepage&amp;q&amp;f=false Catalogue].
*The History of the Year: A Narrative of the Chief Events and Topics of Interest. [https://books.google.co.uk/books?id=ljgIAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false 1881 to 1882]. [https://books.google.co.uk/books?id=1DgIAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false 1882 to 1883].
*James Mason. The History of the Year 1876. [https://books.google.co.uk/books?id=6DoIAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*[[w:The Annual Register|The Annual Register]]. [A View of the History Politics and Literature of the Year YYYY.] [https://books.google.co.uk/books?id=SrJNAAAAcAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false 1821].
*Giusto Traina. 428AD: An Ordinary Year at the End of the Roman Empire. [https://books.google.co.uk/books?id=gLumDwAAQBAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

Ancient
*Bickerman. Chronology of the Ancient World. 1968.
*Smithsonian Timelines of the Ancient World: A Visual Chronology from the Origins of Life. Dorling Kindersley. 1st American Ed: 1993.

==Anniversaries==
*Sian Facer (ed). On this Day: The History of the World in 366 Days. Octopus Illustrated Publishing, London. Crescent Books, New York and Avenel. 1992: [https://books.google.com/books?id=SYGQgwHTuE0C]. Other: [https://books.google.co.uk/books?id=W687MAEACAAJ] [https://books.google.co.uk/books?id=7ujArQEACAAJ]
*On this Day: A History of the World in 366 Days. DK. 2021. [https://books.google.co.uk/books?id=x4I5EAAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]

==Egyptology==
*Annual Egyptological Bibliography [https://books.google.co.uk/books?id=8MoUAAAAIAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=-eUUAAAAIAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

==Battlefields==
*[[w:War Walks|War Walks]]. BBC2. 1996 to 1997. [Television series]
*&quot;The Times Guide to Battlefields of Britain&quot;. Day 1: The Times, 1 August 1994, p 8. Day 2: The Times, 2 August 1994, p 8. Day 3: The Times, 3 August 1994, p 6. Day 4: The Times, 4 August 1994, p 9. Day 5: The Times, 5 August 1994, p 9. Day 6: The Times, 6 August 1994, p 6. There was also a colour wall chart.

==Armed forces==
Periodicals:
*[[w:NATO Review|NATO Review]]

Military
*The Journal of Military History

*Journal of the Royal United Service Institution [Google editions:lMJAgUvBWAEC editions:dcFNqS8JFjoC]

*The Monthly Army List [Google editions:I0t2L4ElznEC]
*The Army Quarterly and Defence Journal [Google editions:c7UjQ-q7SbUC]

*Journal of the Society for Army Historical Research [Google editions:9HZkbMTl6mcC]

*The Royal Armoured Corps Journal [https://www.google.com/search?tbm=bks&amp;q=editions:dEauCcI7kssC&amp;biw=534&amp;bih=736&amp;dpr=1.5#sbfbu=1]
*The Royal Tank Corps Journal
*The Tank [https://www.google.com/search?sa=N&amp;cs=0&amp;tbm=bks&amp;q=editions:Dv-RbpoM7acC&amp;biw=534&amp;bih=736&amp;dpr=1.5#ip=1] Editorial office at the Royal Tank Regiment
*The Cavalry Journal [https://www.google.com/search?sa=N&amp;cs=0&amp;tbm=bks&amp;q=editions:cVQlfkRl6KUC&amp;biw=534&amp;bih=688&amp;dpr=1.5#sbfbu=1]
*The Journal of the Royal Artillery [https://www.google.com/search?tbm=bks&amp;q=editions:liFy4uc0ggYC&amp;biw=534&amp;bih=736&amp;dpr=1.5]
*Minutes of Proceedings of the Royal Artillery Institution [Google editions:wdjZ588FbtMC]
*The Royal Engineers Journal [https://www.google.com/search?tbm=bks&amp;q=editions:8XobinXLbD0C&amp;biw=534&amp;bih=736&amp;dpr=1.5]
*Journal of the Royal Electrical and Mechanical Engineers [https://books.google.com/books?id=dz0cmA1jnv4C]
*Journal of the Royal Army Medical Corps [Google editions:FyUJx2dEWcQC]

United States
*Military Review
*The Coast Artillery Journal [Google editions:nMCogSJ_rlkC]
*Infantry Journal [Google editions:ULqoLmbUR5cC]
*The Reserve Officer [Google editions:JQDRDrnD1QQC]

Naval
*[[w:Navy News|Navy News]]

==Armour==
Armoured warfare; tank warfare
*Harris and Toase. Armoured Warfare. 1990. [https://books.google.com/books?id=KYPfAAAAMAAJ]
*Carver. The Apostles of Mobility: The Theory and Practice of Armoured Warfare. 1979. [https://books.google.com/books?id=8qcgAAAAMAAJ]
*Fuller. Armoured Warfare: An Annotated Edition of Fifteen Lectures on Operations between Mechanized Forces. 1943. [https://books.google.co.uk/books?id=2E4tAQAAMAAJ]
*Black. Tank Warfare. 2020. [https://books.google.co.uk/books?id=oFP5DwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Jorgensen and Mann. Tank Warfare. 2001. [https://books.google.co.uk/books?id=0AghAQAAIAAJ]
*Searle. Armoured Warfare: A Military, Political and Global History. 2017. [https://books.google.co.uk/books?id=HN4CDgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Willey. Tanks: The History of Armoured Warfare. 2018. [https://books.google.com/books?id=AXTltAEACAAJ]
*Perrett. Iron Fist: Classic Armoured Warfare Case Studies. [https://books.google.co.uk/books?id=pKGyeWqJcCEC]. Iron Fist: Classic Armoured Warfare. [https://books.google.co.uk/books?id=KKcKI4dG0VUC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Tom Clancy. Armoured Warfare: Guided Tour of an Armoured Cavalry Regiment. [https://books.google.co.uk/books?id=UxhONAAACAAJ]

Atlas
*Stephen Hart (ed). Atlas of Armored Warfare: From 1916 to the Present Day. Metro Books. 2012. [https://search.worldcat.org/title/1391166759]. Atlas of Tank Warfare. [https://books.google.com/books?id=KWqppwAACAAJ]

Armored forces
*Ogorkiewicz. Armoured Forces: A History of Armoured Forces and Their Vehicles. 1970. [https://books.google.co.uk/books?id=qIHfAAAAMAAJ]

==Mesoamerica==
*James. Aztecs &amp; Maya: The Ancient Peoples of Middle America. Tempus. 2001. 2005. History Press. [https://books.google.co.uk/books?id=XOXNhTY6TCYC 2009]. Reviews: &quot;Books Received&quot; (2003) [https://books.google.co.uk/books?id=3dozAQAAIAAJ 14] Minerva 57 (No 1); and &quot;Overviews for the general reader&quot; (2002) [https://books.google.co.uk/books?id=qShmAAAAMAAJ 76] Antiquity 252.
*Weaver. The Aztecs, Maya, and Their Predecessors. 1972. 2nd Ed: 1981: [https://books.google.co.uk/books?id=0mQkAQAAIAAJ] [https://books.google.com/books?id=OWQkAQAAIAAJ]

==Accounting==
See [[s:Category:Accounting]]

Periodicals
*[[s:The Accountant|The Accountant]] (1874 onwards)
*Accountant's Magazine (1897 onwards) Aberdeen

==Arts==
*Murray (ed).The Hutchinson Dictionary of the Arts. Helicon Publishing. 1994. Paperback Ed: 1995. Reprinted 1997.

==Biography==
*Parke. Biography: Writing Lives. 2002 [https://books.google.co.uk/books?id=6bAz2K98MeYC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Caine. Biography and History. (Theory and History). 1st Ed: 2010, 2nd Ed: 2019 [https://books.google.co.uk/books?id=h3dvDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Periodicals
*Biography. Biography: An Interdisciplinary Quarterly. 1978 onwards. Published by the University Press of Hawaii for the Biographical Research Center. [https://books.google.co.uk/books?id=s84ZAAAAYAAJ]
*Biography News. 1974 to 1975. Gale Research Company. [https://books.google.co.uk/books?id=RRsXAQAAIAAJ]

Yearbooks
*Current Biography Yearbook [https://books.google.com/books?id=Zcml63jalMIC]
*Dictionary of Literary Biography Yearbook [https://books.google.com/books?id=gNNlAAAAMAAJ]

==Information technology==
*Haynes, David (ed). Information Sources in Information Technology. (Guides to Information Sources). Bowker Saur. 1990. [https://books.google.co.uk/books?id=0hYjAAAAQBAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]

==Economics==
General series:
*Dryden Press Series in Economics
*Hurl, Bryan (ed). Studies in the UK Economy. Heinemann Educational
*Nuffield Economics &amp; Business. Nuffield Foundation. Longman.

Other:
*Bannock, Baxter and Davis. The Penguin Dictionary of Economics. Penguin Books. 4th Ed: 1987. Bannock, Baxter and Rees. 1972. 2nd Ed: 1978. 3rd Ed: 1984.

*Begg, Fischer and Dornbusch. Economics. McGraw Hill. 1984. 2nd Ed: 1987. 3rd Ed: 1991.
*Anderton, Alain. Economics. Causeway Press. 1991.
*Maile, Roger. Economics. (Core Business Studies). Mitchell Beazly. 1983.
*Maunder, Myers, Wall and Miller. Economics Explained. Collins Educational. 1987. 2nd Ed: 1991.
*Tibbitt, Andrew. A guide to A Level Economics. Thomas Nelson and Sons. 1986.

*Lipsey, Richard G. An Introduction to Positive Economics. Weidenfeld and Nicolson. 1963. 2nd Ed: 1966. 3rd Ed: 1971. 4th Ed: 1975. 5th Ed: 1979. 6th Ed: 1983. 7th Ed: 1989.

*Nicolson, Walter. Microeconomic Theory: Basic Principles and Extensions. (Dryden Press Series in Economics). Dryden Press, Holt-Saunders. 3rd Ed: 1985. 

*Caves and Jones. World Trade and Payments: An Introduction. Little, Brown and Company. 1973. 1977. 3rd Ed: 1981.

*National Institute of Economic and Social Research. The UK economy. (Studies in the UK Economy). Heinemann Educational. 1990.
*Smith, Charles. UK trade and sterling. (Studies in the UK Economy). Heinemann Educational. 1992.

==Games==
Chess
*Hooper and Whyld. The Oxford Companion to Chess. Oxford University Press. 1984. Paperback: 1987.
*Golombek, Harry. The Game of Chess. 1954. 2nd Ed: 1963. 3rd Ed: 1980.
*Pritchard, D. Brine. The Right Way to Play Chess. 1950. 8th Ed: 1971. 10th Ed: 1974. 11th Ed: 1977.
*Horowitz, Al. From Morphy to Fischer: A history of the World Chess Championship. B T Batsford. 1973. The World Chess Championship: A History. Macmillan. 1973. 

General series
*Batsford Chess Books
**Discovering Chess Series. B T Batsford.

Periodicals

See [[Universal Bibliography/Periodicals#Chess|Periodicals, Chess]]
*British Chess Magazine

Othello
*Goro Hasegawa with Maxine Brady. How to Win at Othello. (A Harvest/HBJ book). Jove Publications. 1977. ISBN 0-15-642215-8. [https://books.google.co.uk/books?id=mTdhlwVeyCcC]

Wargames
*Battleground. Tyne Tees. (ITV). 1978. [Television]. 6 episodes, with Edward Woodward.
**Laurie Taylor. &quot;Attila the Hun invades Tyne Tees&quot;. TV Times. 1978. pp 28 &amp; 29.
**Terry Wise. &quot;Battleground&quot;. Battle for Wargamers. June 1978. pp 261 &amp; 262.
*[[w:Game of War|Game of War]]. Channel 4. 1997. [Television].

==Toys==
Periodicals
*Games &amp; Toys: The Leading Trade Journal for Home &amp; Export. (H Richard Simmons Limited). [https://books.google.co.uk/books?id=pMmbZ_JTnXYC] Google: editions:UO8GID_4Ck0C
*Toys and Novelties. (Sporting Goods Pub Co). [https://books.google.co.uk/books?id=zKdAAQAAMAAJ] [https://archive.org/details/toys-and-novelties-volume-9-1913/page/n53/mode/1up] (Toys and Novelties Publishing Company) [https://archive.org/details/toys-and-novelties-volume-19-issue-no.-1-6-january-june-1922/page/n173/mode/1up]. Cf. &quot;Harcourt To Buy Journals From Haire Publishing Co&quot; [https://books.google.co.uk/books?id=J7hEAQAAIAAJ 194] Publishers Weekly 29
*[[w:Playthings (magazine)|Playthings: The National Magazine of the Toy Trade]]. (McCready Publishing Co) [https://books.google.co.uk/books?id=eCQHzuYWDY4C] [https://books.google.co.uk/books?id=mnRO5WFXDfEC]. (Geyer-McAllister Publications). Cf. &quot;Playthings bought by Geyer-McAllister&quot; [https://books.google.co.uk/books?id=itAaAQAAMAAJ 52] Industrial Marketing

==Cricket==
See [[w:Bibliography of cricket]]

*Peter Arnold and Peter Wynne-Thomas. The Complete Encyclopedia of Cricket. 2006. 4th Ed: 2011: [https://books.google.co.uk/books?id=2R_pXwAACAAJ].
**Peter Arnold. The Illustrated Encyclopedia of World Cricket.
*Morgan. The Encyclopedia of World Cricket. 2007. [https://books.google.co.uk/books?id=gFCbkgEACAAJ]

Scores and biographies
*Marylebone Club Cricket Scores and Biographies. [https://books.google.co.uk/books?id=dl8IAAAAQAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
**See [[w:Arthur Haygarth]] and [[w:Fred Lillywhite]]

Periodicals
*[[w:Cricket: A Weekly Record of the Game|Cricket: A Weekly Record of the Game]]. [https://books.google.co.uk/books?id=eX9QAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false].

Australia
*Malcolm Andrews. The Encyclopaedia of Australian Cricket. 1980. [https://catalogue.nla.gov.au/Record/1531463]
*The Oxford Companion to Australian Cricket

India 
*The Encyclopaedia of Indian Cricket, 1965. [https://books.google.com/books?id=CE4Joad6iwAC] [Includes biographies]

Annuals
*[[w:Indian Cricket (annual)|Indian Cricket]].  [https://books.google.co.uk/books?id=ioRLAAAAYAAJ 1966].

===Cricketers===
Cricketers, including biographical dictionaries and collections of biographies
*[[w:ESPNcricinfo|ESPNcricinfo]]
*[[w:CricketArchive|CricketArchive]]

*John Arlott's Book of Cricketers. 1979. [https://books.google.co.uk/books?id=8-WBAAAAMAAJ]

*World Cricketers: A Biographical Dictionary [https://books.google.com/books?id=IpBLAAAAYAAJ]
*Carr's Dictionary of Extraordinary Cricketers. 1977. Aurum Press. 2005. [https://books.google.com/books?id=CfwsAAAACAAJ]

*Sproat. Debrett's Cricketers' Who's Who. 1980.
*S Canynge Caple. The Cricketer's Who's Who. Williams. Lincoln. 1934.
*Cricket Who's Who: The Cricket Blue Book. 1909. [https://catalogue.nla.gov.au/Record/119715]. 1912. Bibliography: [https://books.google.co.uk/books?id=IjQyAQAAMAAJ]

*Who's Who in Test Cricket: A Biographical Dictionary of Test Cricketers [https://books.google.com/books?id=5uF5PQAACAAJ]

*Frindall. England Test Cricketers: The Complete Record from 1877. 1989. [https://books.google.com/books?id=2zHYLIW7h9UC]
*Brooke. The Collins Who's Who of English First-Class Cricket, 1945-1984. 1985. [https://books.google.com/books?id=NGSPAAAACAAJ]. Review: [https://books.google.co.uk/books?id=iHMsAAAAYAAJ]. Commentary: [https://books.google.co.uk/books?id=wPg5AQAAIAAJ]

Gloucestershire
*Gloucestershire Cricketers, 1870-1979. (ACS Cricketers Series [https://archive.acscricket.com/cricketers_series/index.html]). The Association of Cricket Statisticians. Cleethorpes. 1979. [https://archive.acscricket.com/cricketers_series/gloucestershire_cricketers_1870-1979/index.html]
*Rex Pogson. Gloucestershire Cricket and Cricketers, 1919-1939. Lytham St Annes. 1944. Catalogues: [https://catalogue.nla.gov.au/Record/850643] [https://books.google.co.uk/books?id=CS83vXlB1ZIC] [https://www.worldcat.org/title/504354999]. Also printed as microfilm: [https://books.google.co.uk/books?id=iqXeDTKUEl4C].
*Dean Hayes. Gloucestershire Cricketing Greats: 46 of the Best Cricketers for Gloucestershire. Tunbridge Wells. 1990. Catalogues: [https://books.google.co.uk/books?id=OmsqAQAAIAAJ] [https://www.worldcat.org/title/25202795]

Australia
*The A-Z of Australian Cricketers [https://books.google.com/books?id=w-0zAAAACAAJ]
*Piesse. Encyclopedia of Australian Cricket Players. 2012. [https://books.google.com/books?id=Jsh4MAEACAAJ]
*C P Moody. Australian Cricket and Cricketers 1856-1893-4. Melbourne. 1894.
*Jack Pollard. Australian Cricket: The Game and the Players. Hodder and Stoughton. ABC Books. Sydney. Lane Cove, New South Wales. 1982. Angus &amp; Robertson. London. North Ryde, New South Wales. Sydney. Revised Ed: 1988. Commentary: [https://books.google.co.uk/books?id=WotYAAAAYAAJ]. Review: [https://books.google.co.uk/books?id=KzNYAAAAMAAJ].

==Geology==
*Read and Watson. Introduction to Geology. Macmillan Education. 1962. 2nd Ed: 1968. Volume 1: Principles. Volume 2: Earth History.

==Mineralogy==
*Bibliography of Mineralogy for 1886. Annual Report of the Board of Regents of the Smithsonian Institution. Year Ending 30 June 1887. 1889. Pages [https://books.google.co.uk/books?id=wDcWAAAAYAAJ&amp;pg=PA473#v=onepage&amp;q&amp;f=false 473] to 476.

*Battey, Maurice Hugh. Mineralogy for students. Oliver &amp; Boyd. 1972. 2nd Ed. Longman. 1981.

==Paper==
See [[s:Category:Paper]]

*Surface. Bibliography of the Pulp and Paper Industries. Forest Service. Bulletin 123. 1913. [https://archive.org/details/bibliographyofpu12surf]
*West. Reading List on Papermaking Materials. 1920 to 1921. [https://archive.org/details/readinglistonpa00westgoog] [https://archive.org/details/readinglistonpa01westgoog]

==Books==
*British Book News [https://books.google.co.uk/books?id=2oFTAAAAIAAJ]
*Australasian Book News and Literary Journal. Australasian Book News and Library Journal. [https://books.google.co.uk/books?id=QVQPAQAAIAAJ]

*Book News. 1882 to 1918. (John Wanamaker). Called &quot;Book News Monthly&quot; from 1906. [https://books.google.co.uk/books?id=KtwRAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Stechert-Hafner Book News [https://books.google.co.uk/books?id=BmDqAAAAMAAJ]
*U.S.A. Book News [https://books.google.co.uk/books?id=36gVAQAAIAAJ]
*Branch Library Book News. [https://books.google.co.uk/books?id=NM8aAAAAMAAJ]

*Hungarian Book Review [https://books.google.co.uk/books?id=6U85AQAAIAAJ]
*Soviet Book News. (Earl Browder). 1947 [https://books.google.co.uk/books?id=QrXQ6LYSOF4C]

*Miniature Book News. [https://books.google.co.uk/books?id=MascAQAAMAAJ]

Rare
*Berger. Rare Books and Special Collections. American Library Association. 2014. [https://books.google.co.uk/books?id=IFUangEACAAJ]

Printed
*Annual Bibliography of the History of the Printed Book and Libraries. [https://books.google.co.uk/books?id=GLigoebhrd8C&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 30] [https://books.google.co.uk/books?id=UBN-IUZlF4gC&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 31]

==Paperback and Paperbound==
*Swados, &quot;Paper Books: What do they Promise?&quot; (1953) [https://books.google.co.uk/books?id=TwaJtQzwj1gC 173] The Nation 114
*Wagman, &quot;The Paperbound Book Business&quot; (1957) 9 Michigan Business Review [https://books.google.co.uk/books?id=9pA8uolQjnkC&amp;pg=RA4-PA9#v=onepage&amp;q&amp;f=false 9] (No 5, November)

==Science==
*Lafferty and Rowe. The Hutchinson Dictionary of Science. Helicon Publishing. 1993. 2nd Ed: 1998.

==Entertainment==
*The Directory (The Times, 1996 onwards) Commentary: [https://www.marketingweek.com/as-times-starts-listings-supplement/]

==Comedy and tragedy==
*E H Mikhail. Comedy and Tragedy: A Bibliography of Critical Studies. 1972. [https://books.google.co.uk/books?id=5bgEAAAAMAAJ]

===Comedy===
*James E Evans. Comedy: An Annotated Bibliography of Theory and Criticism. 1987. [https://books.google.co.uk/books?id=s9ZgthAs1t8C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Meghan Duffy (ed). Daniel Gerould (senior ed). Comedy: A Bibliography of Critical Studies in English on the Theory and Practice of Comedy in Drama, Theatre, and Performance. New York. 2006. [https://books.google.co.uk/books?id=fI0jAQAAIAAJ]
*David Humphrey. The Time of Laughter: Comedy and the Media Cultures of Japan. University of Michigan Press. 2023. [https://books.google.co.uk/books?id=CkTLEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

==Radio and television==
*William E McCavitt. Radio and Television: A Selected Annotated Bibliography. Scarecrow Press. 1978. [https://books.google.com/books?id=DAQVAQAAIAAJ]
*Gertrude G Broderick. Radio and Television Bibliography. Bulletin 1948 No 17. [https://books.google.co.uk/books?id=yIPP1dsmNtAC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
*Patricia Beall Hamill. Radio and Television: A Selected Bibliography. Bulletin 1960 No 25. [https://books.google.co.uk/books?id=AJhGAQAAMAAJ&amp;pg=PP3#v=onepage&amp;q&amp;f=false]

==Film and television==
*Jean Mitry. Bibliographie internationale du cinéma et de la télévision. 1966 onwards. [https://books.google.co.uk/books?id=SC3gAAAAMAAJ] Commentary: A Reference Guide for English Studies, [https://books.google.co.uk/books?id=h_wfYKnMfOkC&amp;pg=PA439#v=onepage&amp;q&amp;f=false p 439].

==Animation==
*John Halas and Roger Manvell. The Technique of Film Animation. 4th Ed: 1976. Focal Press. ISBN 0240509005.
*Clements and McCarthy. The Anime Encyclopedia. 3rd Rev Ed: [https://books.google.co.uk/books?id=E03KBgAAQBAJ&amp;pg=PA1958#v=onepage&amp;q&amp;f=false].

==Colours==
*Eiseman and Recker. Pantone: The 20th Century in Color. [https://books.google.co.uk/books?id=j3H7nSVS3UMC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. Reviews: [https://www.theguardian.com/books/2011/nov/13/pantone-20th-century-color-review][https://www.theatlantic.com/entertainment/archive/2011/11/pantone-100-years-of-color/249016/][https://eu.vvdailypress.com/story/lifestyle/health-fitness/2012/01/16/color-reel-20th-century-s/37119883007/]

==Bilateral==
Britain and Japan
*Pearse. Companion to Japanese Britain and Ireland. In Print. 1991. [https://books.google.co.uk/books?id=KtAxAAAAIAAJ]

==Prehistoric life==
Prehistoric animals
*[[w:Michael Benton|Michael Benton]]. Prehistoric Animals: An A-Z Guide. Kingfisher Books. 1989. Derrydale Books, New York. 1989. [Illustrations: Jim Channell and Kevin Maddison.]
*Ellis Owen. Prehistoric Animals: The Extraordinary Story of Life before Man. Octopus Books Limited. London. 1975. [Sculptures: Arthur Hayward.] Review: [https://books.google.co.uk/books?id=II-B8R-8Ov8C 17] Wildlife 422. Commentary: [https://books.google.co.uk/books?id=aUbYAAAAQBAJ&amp;pg=PA269#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=jFNBAAAAIBAJ&amp;pg=PA5#v=onepage&amp;q&amp;f=false].
**Prehistorische dieren: de geschiedenis van het leven vóór de mens. Translated by JJ Hoedeman. In den Toren, Baarn. Westland, Schoten. 1977.  Commentary: [https://books.google.co.uk/books?id=ToVMAQAAIAAJ]
**Les Animaux préhistoriques: l'extraordinaire histoire de la vie avant l'homme.

Dinosaurs
*Michael Benton. Dinosaurs: An A-Z Guide. Kingfisher Books. 1988. Derrydale Books, New York. 1988. [Illustrations: Jim Channell and Kevin Maddison.]

==Continents==
===Asia===

*Winston L Y Yang and Teresa S Yang. Asian Resources in American Libraries: Essays and Bibliographies. 1968. [https://books.google.com/books?id=76OkUAbkd4oC]

Periodicals
*Asian Bibliography [https://books.google.co.uk/books?id=EDq22yvuCb4C]

Asian studies and languages
*Pauline Haldane. Bibliography of Asian Studies and Languages. 1990. [https://books.google.com/books?id=9pQLAQAAIAAJ]

Asian studies
*Bibliography of Asian Studies. Association for Asian Studies. [https://books.google.co.uk/books?id=7NskAAAAMAAJ 1974].
*Cumulative Bibliography of Asian Studies, 1941-1965. GK Hall &amp; Co. [https://books.google.co.uk/books?id=p_UqAAAAMAAJ]
**Cumulative Bibliography of Asian Studies, 1966-1970. GK Hall &amp; Co. [https://books.google.com/books?id=Tg8rAAAAMAAJ]

East Asia
*G Raymond Nunn. East Asia: A Bibliography of Bibliographies. (Occasional Papers of East-West Center Library, No 7). Honolulu. 1967. [https://books.google.co.uk/books?id=XWOTAAAAIAAJ]
*East Asia: A Selected Functional Bibliography. Foreign Service Institute, Center for Area and Country Studies. [https://books.google.co.uk/books?id=ByXkdOpCwF8C&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*Donald Gillin. East Asia: A Bibliography for Undergraduate Libraries. [https://books.google.co.uk/books?id=Q7cIAAAAIAAJ]
*Thomas C Kuo and John W Chiang. East Asian Periodicals and Serials: A Descriptive Bibliography [https://books.google.co.uk/books?id=eA1GAAAAMAAJ]

====Far East====
Bibliography
*Kuniyoshi. Far East. (PACAF Basic Bibliographies). 1957. [https://books.google.co.uk/books?id=Q5TLdCbP2HcC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]

====Japan and Korea====
Bibliography
*Bernard S Silberman. Japan and Korea: A Critical Bibliography. University of Arizona Press. 1962. [https://books.google.co.uk/books?id=y6UIAAAAIAAJ]
*Frank J Shulman. Japan and Korea: An Annotated Bibliography of Doctoral Dissertations in Western Languages 1877-1969. American Library Association. 1970. Routledge. 2013. [https://books.google.co.uk/books?id=xs62AQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

====South Asia====
*South Asian Bibliography: A Handbook and Guide. Harvester Press. [https://books.google.co.uk/books?id=aqwNAQAAIAAJ]
*The Bibliography of South Asian Periodicals: A Union-list of Periodicals in South Asian Languages. Harvester Press. [https://books.google.co.uk/books?id=COV0nIUK0bgC]

==Culture and society==
*Victoria Lyon Bestor, Theodore C Bestor and Akiko Yamagata (eds). Routledge Handbook of Japanese Culture and Society. 2011. [https://books.google.co.uk/books?id=0cBYffHp5L4C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Josef Kreiner and Hans-Dieter Ölschleger (eds). Japanese Culture and Society: Models of Interpretation. 1996. [https://books.google.co.uk/books?id=6skwAQAAIAAJ]
*Dolores P Martinez. Modern Japanese Culture and Society. 2007. [https://books.google.co.uk/books?id=l6kMAQAAMAAJ vol 1]
*C Andrew Gerstle. 18th Century Japan: Culture and Society. 1989. [https://books.google.co.uk/books?id=ViglDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Periodicals
*Review of Japanese Culture and Society [https://books.google.co.uk/books?id=W_o-AQAAIAAJ]

==See also==
*[[Bibliography]]

==Notes==
{{Reflist}}
{{subpagesif}}
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{{Bibliography}}
{{research}}

If this resource is ever completed, it will be a universal bibliography.&lt;ref&gt;See [[w:Bibliography]].&lt;/ref&gt; Until then, it will be an approximation of a universal bibliography.

This bibliography is arranged as an index of topics.

==Index==
*[[Universal Bibliography/Bibliography|Bibliography]]
*[[Universal Bibliography/Libraries|Libraries]]
*[[Universal Bibliography/Literature|Literature]]
*[[Universal Bibliography/Languages|Languages]]
*[[Universal Bibliography/SF|SF]]
*[[Universal Bibliography/Music|Music]]
*[[Universal Bibliography/Cinema|Cinema]]
*[[Universal Bibliography/Television|Television]]
*[[Universal Bibliography/Culture|Culture]]
*[[Universal Bibliography/Publishers and imprints|Publishers and imprints]]
*[[Universal Bibliography/Printing|Printing]]
*[[Universal Bibliography/Printers|Printers]]
*[[Universal Bibliography/Microform|Microform]]
*[[Universal Bibliography/Periodicals|Periodicals]]
*[[Universal Bibliography/Reference|Reference]]
*[[Universal Bibliography/Gazetteers|Gazetteers]]
*[[Universal Bibliography/Humanities|Humanities]]
*[[Universal Bibliography/Law|Law]]
*[[Universal Bibliography/History|History]]
*[[Universal Bibliography/Archaeology|Archaeology]]
*[[Universal Bibliography/Geography|Geography]]
*[[Universal Bibliography/Countries|Countries]]
*[[Universal Bibliography/Architecture|Architecture]]
*[[Universal Bibliography/Mathematics|Mathematics]]
*[[Universal Bibliography/Computers|Computers]]
*[[Universal Bibliography/Kites|Kites]]
*[[Universal Bibliography/Nostalgia|Nostalgia]]
*[[Universal Bibliography/Children's non-fiction|Children's non-fiction]]

===About===
*[[Universal Bibliography/About|About]]

==Online libraries==
Swedish:
*[[w:Swedish Literature Bank|Litteraturbanken]] (Swedish Literature Bank)
*[[w:Project Runeberg|Projekt Runeberg]] (Project Runeberg)

French
*[[w:Persée (web portal)|Persée]] (persee.fr)

Japanese
*[[w:Aozora Bunko|Aozora Bunko]] (aozora.gr.jp)

==Biographical dictionaries etc==
See [[w:Bibliography of encyclopedias: general biographies]] and [[w:List of biographical dictionaries]]

*Fox. 'True Biographies of Nations?': The Cultural Journeys of Dictionaries of National Biography. ANU Press. 2019 [https://books.google.co.uk/books?id=siSbDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Arthur, &quot;Biographical Dictionaries in the Digital Era&quot;. Advancing Digital Humanities: Research, Methods, Theories. 2014. Chapter 6. [https://books.google.co.uk/books?id=z7MaBgAAQBAJ&amp;pg=PA83#v=onepage&amp;q&amp;f=false Page 83] et seq.

Bibliographies, indexes, etc:
*Wynar. ARBA Guide to Biographical Dictionaries. Libraries Unlimited. 1986 [https://books.google.co.uk/books?id=5FfgAAAAMAAJ]
*Slocum, Robert B (ed). Biographical Dictionaries and Related Works. Gale Research Company. 2nd Ed: 1986 [https://books.google.co.uk/books?id=5uMpAQAAMAAJ]
*Biographical Dictionaries Master Index. (Gale Biographical Index Series). [https://books.google.co.uk/books?id=ZEshAQAAMAAJ] [https://books.google.co.uk/books?id=pPAzAQAAIAAJ] see also [https://books.google.co.uk/books?id=o_gPAQAAMAAJ]
*Children's Authors and Illustrators: An Index to Biographical Dictionaries. (Gale Biographical Index Series). 2nd Ed: 1978,  3rd Ed: 1981, 4th Ed: 1987 [https://books.google.co.uk/books?id=VIsWAQAAMAAJ] [https://books.google.co.uk/books?id=DFtGAQAAIAAJ] [https://books.google.co.uk/books?id=01wjAQAAIAAJ]
*Index to the Wilson Authors Series [https://books.google.co.uk/books?id=oNZkAAAAMAAJ]
*Auchterlonie. Arabic Biographical Dictionaries: A Summary Guide and Bibliography. 1987 [https://books.google.co.uk/books?id=rW59QgAACAAJ]
*Black Biographical Dictionaries, 1790-1950 [https://books.google.co.uk/books?id=laIUAQAAMAAJ]

Particular works:

*Oxford Dictionary of National Biography; [[w:Dictionary of National Biography|Dictionary of National Biography]]
*Boase. Modern English Biography. ([http://www.google.com/search?q=editions%3Auzt3-qMuFcMC&amp;btnG=Search+Books&amp;bksoutput=html_text&amp;tbm=bks&amp;tbo=1 editions:uzt3-qMuFcMC])
*A &amp; C Black's Who's Who
*Who Was Who
*The Academic Who's Who. A &amp; C Black. 1st Ed: 1973 [https://books.google.co.uk/books?id=dnUWAQAAMAAJ] [https://books.google.co.uk/books?id=fXJmAAAAMAAJ]. 2nd Ed: 1975. Commentary: [https://books.google.co.uk/books?id=7VyOANl2qxoC&amp;pg=PA208&amp;output=html_text]. GBooks: editions:INAP7GGD2gYC editions:tA0FkHC75FIC
*Dictionary of Edwardian Biography (Pike's New Century Series)

Works that comprise largely of biographies:
*The Penguin Companion to Literature

Theatres
*A Biographical Dictionary of Actors, Actresses, Musicians, Dancers, Managers &amp; Other Stage Personnel in London, 1660-1800. [https://books.google.co.uk/books?id=TGgS9VxWJ0oC vol 15]

==Dictionaries of dates==
[https://archive.org/search.php?query=%22dictionary%20of%20dates%22 Archive.org]
*Baxter Dictionary of Dates and Events. 1st Ed: 1963: Napier, M (ed). 2nd Ed: 1971: Sanders and Laffin. Commentary: 92 Library Journal 1819 [https://books.google.co.uk/books?id=CExVAAAAYAAJ]
*Beeching, Cyril Leslie. A Dictionary of Dates. OUP. 1st Ed: 1993. 2nd Ed: 1997. [https://www.google.co.uk/search?hl=en&amp;tbm=bks&amp;q=editions:UGGp0EexZdcC editions:UGGp0EexZdcC]
*Bolton, John. Bolton's Dictionary of Dates, arranged in alphabetical order. Foulsham. 1958. Review: [https://books.google.co.uk/books?id=awJPAAAAIAAJ 172] The Publisher 880
*[[w:William Darling (politician)|William Young Darling]]. A Book of Days: A Dictionary of Dates, a Chronology of Circumstance, the Face of Time. Richards Press. 1951. [https://books.google.co.uk/books?id=PLkfAAAAMAAJ]
*Everyman's Dictionary of Dates. 1st Ed: 1911. 6th Ed: 1971. Review: (1971) 11 RQ 164 [http://www.jstor.org/stable/25824440]
*Platt, Charles. Foulsham's Dictionary of Dates and General Information. 1930.
*[[w:Haydn's Dictionary of Dates|Haydn's Dictionary of Dates]]
*Hamlyn Dictionary of Dates and Anniversaries. Newnes Dictionary of Dates.
*Williams, Henry Llewellyn. Hurst's Dictionary of Dates. 1891. [https://archive.org/details/hurstsdictionary00will]
*Keller, Helen Rex. The Dictionary of Dates. Macmillan. 1934. Commentary: [https://books.google.co.uk/books?id=Utcb32E7rsMC&amp;pg=PA93&amp;output=html_text] [https://books.google.co.uk/books?id=sAHfY6QbOEwC&amp;pg=PA351&amp;output=html_text]
*Nelson's Dictionary of Dates. A Dictionary of Dates. (Nelson's Encyclopaedic Library). 1912 [https://books.google.co.uk/books?id=Mp9lvwEACAAJ]. Reviews: (June 1912) Journal of Education, vol 34 (New Series), vol 44 (Old Series), p 392 [https://books.google.co.uk/books?id=QIRFAQAAMAAJ]; (1912) [https://books.google.co.uk/books?id=9i4_AQAAIAAJ 108] The Spectator [http://archive.spectator.co.uk/article/18th-may-1912/25/a-dictionary-of-dates-vol-i-and-english-idioms-nel 805] (18 May)
*Pulman, George Palmer. The World's Progress: A Dictionary of Dates. New York. 1861. [https://books.google.co.uk/books?printsec=frontcover&amp;id=k3dJAAAAYAAJ&amp;output=html]
*Urdang, Laurence. The World Almanac Dictionary of Dates. Longman. 1982. [https://books.google.co.uk/books?id=I4IRAQAAMAAJ] Review: (1982) 22 RQ 101 [http://www.jstor.org/stable/25826880]

Australia

*John Henniker Heaton. Australian Dictionary of Dates and Men of the Time. 1879. [https://archive.org/details/australiandicti00heatgoog]
*John James Knight. In the Early Days; History and Incident of Pioneer Queensland, with Dictionary of Dates in Chronological Order. Sapsford &amp; Co. Brisbane. 1895.

America

*Damon, Charles Ripley. The American Dictionary of Dates, 458-1920. R G Badger. 1921.

==Commodity dictionaries==
*Statistical Classification of Domestic and Foreign Commodities Exported from the United States. Commentary: [https://books.google.co.uk/books?id=91GLhsJSBj8C&amp;pg=PR22#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=RPwhAQAAMAAJ&amp;pg=RA15-PA7#v=onepage&amp;q&amp;f=false]
*Tovarnyi slovar'. (Commodity Dictionary). Reviews and commentary: Petrov, &quot;Commodity Dictionary&quot;, Ekonomicheskaya Gazeta, No 13, 30 October 1961, p 45; CDSP , 13 December 1961, p 46; (1962) [https://books.google.co.uk/books?id=2vMRAAAAIAAJ 13] Current Digest of the Soviet Press 47; (1958) 15 Quarterly Journal of Current Acquisitions 210 [https://books.google.co.uk/books?id=ZcvozpZAfpEC] [https://books.google.co.uk/books?id=S47qEIfyCr0C]; Fitzpatrick, Stalinism: New Directions, [https://books.google.co.uk/books?id=rD5FzoKnTE0C&amp;pg=PA182#v=onepage&amp;q&amp;f=false p 182] &amp; 183
*Szilágyi. Commodity Dictionary in Five Languages. Budapest. Közgazdasági és Jogi Könyvkiadó (Publishing House for Economics and Law). 1963 or 1964. Commentary: Books from Hungary, vols 4-6, pp 26 &amp; 40 [https://books.google.co.uk/books?id=6kMiAQAAMAAJ]
*Dictionnaire des produits: appellations et caractéristiques des produits francais de consommation courante, 1960. Commentary: Walford (ed), Guide to Reference Material Supplement, 1963, p 106 [https://books.google.co.uk/books?id=ej-9pHGR67oC]
*Chūgoku Shōhin Jiten. (Chinese commodity dictionary). Tokyo. 1960. [https://books.google.co.uk/books?id=Wc61lS0xj6AC&amp;pg=PA78#v=onepage&amp;q&amp;f=false]

==Encyclopedias==
See [[s:Category:Encyclopedias]], [[w:Bibliography of encyclopedias]] and [[w:Lists of encyclopedias]]

*[[w:en:Encyclopædia Britannica Eleventh Edition|Encyclopædia Britannica Eleventh Edition]]
*Paton, John (ed). Knowledge Encyclopedia: 1979, 1981, 1988. New Discovery Encyclopedia: 1990.
*The Dorling Kindersley Illustrated Family Encyclopedia

==Almanacs==
See [[s:Category:Almanacs]], [[s:Portal:Almanacs]], [[w:List of almanacs]], [[w:Category:Almanacs]].
*Year Book and Almanac of Newfoundland. 
**For 1896. 1895. [https://archive.org/details/yearbooknfld189600newfuoft]
*Whiteley. On This Date: A Day-by-Day Listing of Holidays, Birthday and Historic Events, and Special Days, Weeks and Months. 2002. [https://books.google.co.uk/books?id=sKCfomKSa74C]

==Censuses==
*Census of New Zealand and Labrador
**1901 Census. Tables 2 and 3. 1903. [https://archive.org/details/censusnewfoundl00bondgoog]
**1911 Census. Table 1. 1914. [https://archive.org/details/1911981911fnfldv11914eng]
**1921 Census. Tables 4 and 5. 1923. [https://archive.org/details/1921981921fnfldv451923eng]

==Pilot guides==
*[[w:United States Coast Pilot|United States Coast Pilot]]
*American Coast Pilot [https://books.google.co.uk/books?id=8GoDAAAAYAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]

*Sailing Directions: Newfoundland. Canadian Hydrographic Service. [https://books.google.co.uk/books?id=A77fAAAAMAAJ]
*Newfoundland Pilot. Canadian Hydrographic Service. [https://books.google.co.uk/books?id=z7zfAAAAMAAJ]
*Maxwell. The Newfoundland Pilot. Hydrographic Office, Admiralty. London. 1878. [https://books.google.co.uk/books?id=vS4BAAAAQAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]
*Newfoundland Pilot. HO No 73. Hydrographic Office. Governement Printing Office, Washington. 4th Ed: 1919: [https://books.google.co.uk/books?id=YGoDAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]. Sailing Directions for Newfoundland. 5th Ed: 1931: [https://books.google.co.uk/books?id=cMUiGo3JK9QC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]

==Books of facts==
*The Reader's Digest Book of Facts. 1st Ed: 1985. Reprinted with amendments: 1987: [https://books.google.co.uk/books?id=B8PmM_5Zm1MC]. (Review: Library Journal, [https://books.google.co.uk/books?id=EPDgAAAAMAAJ v 9], p 102, 1 Dec 1987, [http://www.bookverdict.com/details.xqy?uri=Product-94667328910921.xml Book Verdict].) 3rd Revised Ed: 1995: [https://books.google.co.uk/books?id=E5YhAQAAIAAJ]. GBooks: editions:nnJlLybWxbIC
*Chambers Book of Facts
*Crystal, David (ed). Penguin Book of Facts. [https://books.google.co.uk/books?id=k0sZAQAAIAAJ 2004]. 2nd Ed: 2008
*Handy Book of Facts: Things Everyone Should Know. C.S. Hammond &amp; Company. 1914. [https://books.google.co.uk/books?id=h5wRAAAAIAAJ]

==Series of books==
See [[w:Category:Series of books]] and [[w:Category:Monographic series]]
*George M Sinkankas, &quot;Series&quot; in Kent, Lancour and Daily (eds).  Encyclopedia of Library and Information Science. Volume 27. Marcel Dekker. 1979. Pages [https://books.google.co.uk/books?id=jU3fwyjqS5UC&amp;pg=PA250#v=onepage&amp;q&amp;f=false 250] to 273.
*&quot;Publishing in Series, 1896-1916&quot; in Eliot, Simon (ed). History of Oxford University Press. Louis,  Wm Roger (ed). Volume 3: 1896-1970. Oxford University Press. 2013. [https://books.google.co.uk/books?id=YbcJAgAAQBAJ&amp;pg=PA539#v=onepage&amp;q&amp;f=false Page 539] et seq.
*Spiers, John. The Culture of the Publisher’s Series. Palgrave Macmillan. 2011. [https://books.google.co.uk/books?id=ASaHDAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 1]. [https://books.google.co.uk/books?id=XCl-DAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 2].
*Spiers, John. Serious about Series: American 'Cheap' Libraries, British 'Railway' Libraries and Some Literary Series of the 1890's. 2007. [https://books.google.co.uk/books?id=1hRXAAAAYAAJ] [https://books.google.co.uk/books?id=AS4yQwAACAAJ]
*Rooney, Paul Raphael. Railway Reading and Late-Victorian Literary Series. Routledge. 2018. [https://books.google.co.uk/books?id=uX5aDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Khan. &quot;Monographs in series&quot;. The Principles and Practice of Library Science. 1996. Pages [https://books.google.co.uk/books?id=sAHfY6QbOEwC&amp;pg=PA208#v=onepage&amp;q&amp;f=false 207] to 209.
*Friskney. New Canadian Library: The Ross-McClelland Years, 1952-1978. Pages [https://books.google.co.uk/books?id=jHIjCCXBX9kC&amp;pg=PA6#v=onepage&amp;q&amp;f=false 6] and 7.

*Books in Series. R R Bowker Company. Commentary: [https://books.google.co.uk/books?id=uQe04OSlA7YC&amp;pg=PA11#v=onepage&amp;q&amp;f=false]
**Books in Series in the United States, 1966-1975. R R Bowker. 1977. Review: (1977) 14 Choice [https://books.google.co.uk/books?id=_e08AQAAIAAJ&amp;pg=PA1190#v=onepage&amp;q&amp;f=false 1190] (No 8, November). Commentary: [https://books.google.co.uk/books?id=LYAhAAAAQBAJ&amp;pg=PA53#v=onepage&amp;q&amp;f=false]
***Books in Series Supplement: A Supplement to Books in Series in the United States, 1966-1975. 1978. [https://books.google.co.uk/books?id=hOAaAQAAMAAJ]
**Books in Series. 3rd Ed. 1980. [https://books.google.co.uk/books?id=d_kaAQAAMAAJ]
**Books in Series, 1876-1949. R R Bowker Company. 1982. [https://books.google.co.uk/books?id=TngvAQAAIAAJ] [https://books.google.co.uk/books?id=iVIyAQAAMAAJ] [https://books.google.co.uk/books?id=R2AjAQAAIAAJ]
**Books in Series, 1985-89. [https://books.google.co.uk/books?id=yEkxAQAAIAAJ]
*Baer, Eleanora Agnes. Titles in Series: A Handbook for Librarians and Students. Scarecrow Press. Vol 1 (Books Published Prior to January 1953). 1953: [https://books.google.co.uk/books?id=GgAYAAAAMAAJ]. Vol 2 (Books Published Prior to January 1957). 1957: [https://books.google.co.uk/books?id=oqsXAAAAMAAJ]
**2nd Ed: 1964. [https://books.google.co.uk/books?id=gWlAAAAAIAAJ Vol 1]. [https://books.google.co.uk/books?id=tWpAAAAAIAAJ Vol 2]. Supplement to the Second Edition. 1967: [https://books.google.co.uk/books?id=zGARAQAAMAAJ]. Second Supplement to the Second Edition. 1971: [https://books.google.co.uk/books?id=WwXhAAAAMAAJ]
**3rd Ed: 1978. Commentary: [https://books.google.co.uk/books?id=h_wfYKnMfOkC&amp;pg=PA63#v=onepage&amp;q&amp;f=false]
*Ocran, Emmanuel Benjamin. Scientific &amp; Technical Series: A Select Bibliography. 1973: [https://books.google.co.uk/books?id=oy0EAAAAMAAJ] Review: [https://books.google.co.uk/books?id=fTCw_DQH6zkC&amp;pg=PA949#v=onepage&amp;q&amp;f=false]

*Rosenberg and Nichols. Young People's Books in Series: Fiction and Non-fiction, 1975-1991. Libraries Unlimited. 1992. [https://books.google.co.uk/books?id=REHhAAAAMAAJ]
*Young People's Literature in Series

*Catalog of Reprints in Series. (sometimes called &quot;Catalogue of Reprints in Series&quot;). 1940 onwards. [https://books.google.co.uk/books?id=MSI4AAAAIAAJ] [https://books.google.co.uk/books?id=6n1EAAAAMAAJ] Commentary: [https://books.google.co.uk/books?id=h_wfYKnMfOkC&amp;pg=PA73#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=1RxuAAAAMAAJ]

*Kuitert, Lisa. Het ene boek in vele delen. De Uitgave van Literaire Series in Nederland 1850-1900. Uitgeverij de Buitenkant. Amsterdam. 1993. Commentary: [https://books.google.co.uk/books?id=jSDnRo7YrWwC&amp;pg=PA656#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=szBcAAAAMAAJ] [https://books.google.co.uk/books?id=SVcVAQAAIAAJ] [https://books.google.co.uk/books?id=R8Pfs146nUAC&amp;pg=PA367#v=onepage&amp;q&amp;f=false]

==Series of classics==
*Penguin Classics (Penguin Modern Classics, Penguin English Library)
*Oxford World Classics
*Everyman's Library
*Wordsworth Classics
*Macmillan Collectors Library
*Bantam Classics
*Minster Classics
*The Literary Heritage Collection (Heron Books, London. William Collins Sons &amp; Co, Glasgow)
*Chandos Classics
*Temple Classics
*Longmans Heritage of Literature Series

Russian
*Greatest Masterpieces of Russian Literature (Heron Books, London)

SF
*Corgi SF Collectors Library

Children's and shorter classics etc 
*Shorter Classics. Ginn and Company.
*Ladybird Children's Classics.
*Mini Classics. Parragon Books.
*Bonny Books. Peter Haddock Ltd.
*A series published by Dean &amp; Son Ltd

==Non-fiction general series==
*[[w:Oxford Companions|Oxford Companions]]
*[[w:Cambridge Companions|Cambridge Companions]]
*Princeton Companions
*Blackwell Companions. Wiley Blackwell Companions
*Routledge Companions. Routledge Research Companions
*Ashgate Companions. Ashgate Research Companions
*Brill's Companions
*Facts on File Companions
*Guides to Information Sources. Bowker-Saur
*Butterworths Guides to Information Sources.
*Columbia Guides
*Blackwell Guides
*Edinburgh Critical Guides
*Collins Reference Dictionaries
*New Horizons. Thames and Hudson. ([[w:Découvertes Gallimard|Découvertes Gallimard]])
*Collins Gem (see [[w:List of Collins GEM books]])
*Concise Encyclopedias. Collins.
*Time Life Books (see [[w:Time Life#Book series]])
*[[w:Teach Yourself|Teach Yourself Books]]. English Universities Press. 
*[[w:Teach Yourself|Teach Yourself Books]]. Hodder and Stoughton.
*Made Simple Books. W H Allen.
*Palgrave Master Series
*Harrap's Mini Series
*Shire Albums. Shire Publications.
*Fax Pax: Knowledge in a Nutshell. Fax Pax Ltd.
*The Wonderful World Books. Macdonald and Company
*Harper's ABC series. Includes A-B-C of Housekeeping, A-B-C of Electricity, A-B-C of Gardening and A-B-C of Manners.
*Hamlyn Pocket Guides
*Oxford Monograph Series
*Study Outline Series. H W Wilson. [[s:Page:Russian Literature - A Study Outline.djvu/61|(wikisource)]]
*Helpmate Handbooks. Willow Books

University
*University Paperbacks. Meuthen &amp; Co
*World Student Series. Addison Wesley
*Unibooks. Hodder and Stoughton
*International Student Editions. Van Nostrand Reinhold
*Hutchinson University Library

Imprints
*Pelican Books

Pictorials
*Salmon Cameracolour series
*Pitkin Pictorials 

United Kingdom
*Aspects of Britain. HMSO.

Places
*The Little Guides. Meuthen [[s:Page:Cornwall (Salmon).djvu/336|(wikisource)]]
*G.W.R. Series of Travel Books [[s:Page:The Cornwall coast.djvu/391|(wikisource)]]

Art
*Movements in World Art. Meuthen.
*Movements in Modern Art. Meuthen.
*How to Draw and Paint. New Burlington.

Film
*BFI Companions

Popular science
*Contemporary Science Paperbacks. Oliver and Boyd.
*Pan Piper Science Series

Science and mathematics
*Simon and Schuster Tech Outlines
*Schaum's Outline Series

Military
*Illustrated Military Guides. Illustrated Guides. &quot;An Illustrated Guide to ...&quot;. Salamander Books.
*Combat Arms. Arco Military Books. Salamander Books. Prentice Hall Press.
*Osprey Men-at-Arms
*Jane's Pocket Books

Communication
*The Library of Communication Techniques. Focal Press.
*John Fiske (ed). Studies in Culture and Communication. Routledge.
*The Media. Wayland.

Cookery
*ABC series. Peter Pauper Press.

Gardening
*Pan Piper Small Gardens Series.

Mythology
*Series on mythology published by Southwater (imprint of Anness)

==History and Geography==
See also [[Universal Bibliography/History|History]] and [[Universal Bibliography/Geography|Geography]].
*Baker. Geography and History: Bridging the Divide. 2003. [https://books.google.co.uk/books?id=e8yf5JcefpAC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Darby. Relations of History and Geography: Studies in England, France and the United States. 2002. [https://books.google.co.uk/books?id=Vl4ZfpnP7NwC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

General series
*Cambridge Studies in Historical Geography

Atlases
*The Times Atlas of World History
*Philip's Atlas of World History

History of geography:
*Dunbar, Gary S. The History of Modern Geography: An Annotated Bibliography of Selected Works. Garland. 1985. [https://books.google.co.uk/books?id=FX4WAQAAIAAJ]

==Chronology==
See also [[Universal Bibliography/History#Millennia, centuries and decades]]

General
*Chronology of World History.
**Neville Williams. Chronology of the Modern World: 1763 to the present time. 1st Ed: 1966. (1763 to 1992). 2nd Ed: 1994.
**Neville Williams. Chronology of the Expanding World 1492 to 1762. 1969. Reissued 1994.
**Storey. Chronology of the Medieval World 800 to 1491. 1973. Reissued 1994.
**Mellersh. Chronology of the Ancient World 10,000 BC to AD 799. Barrie and Jenkins. 1976. Helicon. Simon &amp; Schuster. Reissued 1994.

Centuries
*Chronology of the 20th Century. Helicon. 1995. [https://books.google.com/books?id=pjsOAQAAMAAJ]
*Brownstone and Franck. Timelines of the 20th Century. [https://books.google.com/books?id=IZ6SQgAACAAJ]
*Beal. 20th Century Timeline. 1985. [https://books.google.com/books?id=cFrG7LBObGoC]
*20th Century Day by Day [https://books.google.com/books?id=kyxaAAAAYAAJ] [https://books.google.com/books?id=WiOAAAAACAAJ]
*Chronicle of the 20th Century [https://books.google.co.uk/books?id=pt3DYbnZO8sC] [https://books.google.co.uk/books?id=Gd1WPQAACAAJ]
*Boyle. The Chronology of the Eighteenth and Nineteenth Centuries. 1826. [https://books.google.co.uk/books?id=wDENAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]

Decades
*Series:
**Day by Day. Facts on File. [https://books.google.com/books?id=WfClvwEACAAJ] [https://books.google.com/books?id=CWNvQgAACAAJ]

Years
*Brown, D Kinnear. History of the Year. (1884 to 1885). [https://books.google.co.uk/books?id=DmRWAAAAYAAJ&amp;pg=PA113#v=onepage&amp;q&amp;f=false Catalogue].
*The History of the Year: A Narrative of the Chief Events and Topics of Interest. [https://books.google.co.uk/books?id=ljgIAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false 1881 to 1882]. [https://books.google.co.uk/books?id=1DgIAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false 1882 to 1883].
*James Mason. The History of the Year 1876. [https://books.google.co.uk/books?id=6DoIAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*[[w:The Annual Register|The Annual Register]]. [A View of the History Politics and Literature of the Year YYYY.] [https://books.google.co.uk/books?id=SrJNAAAAcAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false 1821].
*Giusto Traina. 428AD: An Ordinary Year at the End of the Roman Empire. [https://books.google.co.uk/books?id=gLumDwAAQBAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

Ancient
*Bickerman. Chronology of the Ancient World. 1968.
*Smithsonian Timelines of the Ancient World: A Visual Chronology from the Origins of Life. Dorling Kindersley. 1st American Ed: 1993.

==Anniversaries==
*Sian Facer (ed). On this Day: The History of the World in 366 Days. Octopus Illustrated Publishing, London. Crescent Books, New York and Avenel. 1992: [https://books.google.com/books?id=SYGQgwHTuE0C]. Other: [https://books.google.co.uk/books?id=W687MAEACAAJ] [https://books.google.co.uk/books?id=7ujArQEACAAJ]
*On this Day: A History of the World in 366 Days. DK. 2021. [https://books.google.co.uk/books?id=x4I5EAAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]

==Egyptology==
*Annual Egyptological Bibliography [https://books.google.co.uk/books?id=8MoUAAAAIAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=-eUUAAAAIAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

==Battlefields==
*[[w:War Walks|War Walks]]. BBC2. 1996 to 1997. [Television series]
*&quot;The Times Guide to Battlefields of Britain&quot;. Day 1: The Times, 1 August 1994, p 8. Day 2: The Times, 2 August 1994, p 8. Day 3: The Times, 3 August 1994, p 6. Day 4: The Times, 4 August 1994, p 9. Day 5: The Times, 5 August 1994, p 9. Day 6: The Times, 6 August 1994, p 6. There was also a colour wall chart.

==Armed forces==
Periodicals:
*[[w:NATO Review|NATO Review]]

Military
*The Journal of Military History

*Journal of the Royal United Service Institution [Google editions:lMJAgUvBWAEC editions:dcFNqS8JFjoC]

*The Monthly Army List [Google editions:I0t2L4ElznEC]
*The Army Quarterly and Defence Journal [Google editions:c7UjQ-q7SbUC]

*Journal of the Society for Army Historical Research [Google editions:9HZkbMTl6mcC]

*The Royal Armoured Corps Journal [https://www.google.com/search?tbm=bks&amp;q=editions:dEauCcI7kssC&amp;biw=534&amp;bih=736&amp;dpr=1.5#sbfbu=1]
*The Royal Tank Corps Journal
*The Tank [https://www.google.com/search?sa=N&amp;cs=0&amp;tbm=bks&amp;q=editions:Dv-RbpoM7acC&amp;biw=534&amp;bih=736&amp;dpr=1.5#ip=1] Editorial office at the Royal Tank Regiment
*The Cavalry Journal [https://www.google.com/search?sa=N&amp;cs=0&amp;tbm=bks&amp;q=editions:cVQlfkRl6KUC&amp;biw=534&amp;bih=688&amp;dpr=1.5#sbfbu=1]
*The Journal of the Royal Artillery [https://www.google.com/search?tbm=bks&amp;q=editions:liFy4uc0ggYC&amp;biw=534&amp;bih=736&amp;dpr=1.5]
*Minutes of Proceedings of the Royal Artillery Institution [Google editions:wdjZ588FbtMC]
*The Royal Engineers Journal [https://www.google.com/search?tbm=bks&amp;q=editions:8XobinXLbD0C&amp;biw=534&amp;bih=736&amp;dpr=1.5]
*Journal of the Royal Electrical and Mechanical Engineers [https://books.google.com/books?id=dz0cmA1jnv4C]
*Journal of the Royal Army Medical Corps [Google editions:FyUJx2dEWcQC]

United States
*Military Review
*The Coast Artillery Journal [Google editions:nMCogSJ_rlkC]
*Infantry Journal [Google editions:ULqoLmbUR5cC]
*The Reserve Officer [Google editions:JQDRDrnD1QQC]

Naval
*[[w:Navy News|Navy News]]

==Armour==
Armoured warfare; tank warfare
*Harris and Toase. Armoured Warfare. 1990. [https://books.google.com/books?id=KYPfAAAAMAAJ]
*Carver. The Apostles of Mobility: The Theory and Practice of Armoured Warfare. 1979. [https://books.google.com/books?id=8qcgAAAAMAAJ]
*Fuller. Armoured Warfare: An Annotated Edition of Fifteen Lectures on Operations between Mechanized Forces. 1943. [https://books.google.co.uk/books?id=2E4tAQAAMAAJ]
*Black. Tank Warfare. 2020. [https://books.google.co.uk/books?id=oFP5DwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Jorgensen and Mann. Tank Warfare. 2001. [https://books.google.co.uk/books?id=0AghAQAAIAAJ]
*Searle. Armoured Warfare: A Military, Political and Global History. 2017. [https://books.google.co.uk/books?id=HN4CDgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Willey. Tanks: The History of Armoured Warfare. 2018. [https://books.google.com/books?id=AXTltAEACAAJ]
*Perrett. Iron Fist: Classic Armoured Warfare Case Studies. [https://books.google.co.uk/books?id=pKGyeWqJcCEC]. Iron Fist: Classic Armoured Warfare. [https://books.google.co.uk/books?id=KKcKI4dG0VUC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Tom Clancy. Armoured Warfare: Guided Tour of an Armoured Cavalry Regiment. [https://books.google.co.uk/books?id=UxhONAAACAAJ]

Atlas
*Stephen Hart (ed). Atlas of Armored Warfare: From 1916 to the Present Day. Metro Books. 2012. [https://search.worldcat.org/title/1391166759]. Atlas of Tank Warfare. [https://books.google.com/books?id=KWqppwAACAAJ]

Armored forces
*Ogorkiewicz. Armoured Forces: A History of Armoured Forces and Their Vehicles. 1970. [https://books.google.co.uk/books?id=qIHfAAAAMAAJ]

==Mesoamerica==
*James. Aztecs &amp; Maya: The Ancient Peoples of Middle America. Tempus. 2001. 2005. History Press. [https://books.google.co.uk/books?id=XOXNhTY6TCYC 2009]. Reviews: &quot;Books Received&quot; (2003) [https://books.google.co.uk/books?id=3dozAQAAIAAJ 14] Minerva 57 (No 1); and &quot;Overviews for the general reader&quot; (2002) [https://books.google.co.uk/books?id=qShmAAAAMAAJ 76] Antiquity 252.
*Weaver. The Aztecs, Maya, and Their Predecessors. 1972. 2nd Ed: 1981: [https://books.google.co.uk/books?id=0mQkAQAAIAAJ] [https://books.google.com/books?id=OWQkAQAAIAAJ]

==Accounting==
See [[s:Category:Accounting]]

Periodicals
*[[s:The Accountant|The Accountant]] (1874 onwards)
*Accountant's Magazine (1897 onwards) Aberdeen

==Arts==
*Murray (ed).The Hutchinson Dictionary of the Arts. Helicon Publishing. 1994. Paperback Ed: 1995. Reprinted 1997.

==Biography==
*Parke. Biography: Writing Lives. 2002 [https://books.google.co.uk/books?id=6bAz2K98MeYC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Caine. Biography and History. (Theory and History). 1st Ed: 2010, 2nd Ed: 2019 [https://books.google.co.uk/books?id=h3dvDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Periodicals
*Biography. Biography: An Interdisciplinary Quarterly. 1978 onwards. Published by the University Press of Hawaii for the Biographical Research Center. [https://books.google.co.uk/books?id=s84ZAAAAYAAJ]
*Biography News. 1974 to 1975. Gale Research Company. [https://books.google.co.uk/books?id=RRsXAQAAIAAJ]

Yearbooks
*Current Biography Yearbook [https://books.google.com/books?id=Zcml63jalMIC]
*Dictionary of Literary Biography Yearbook [https://books.google.com/books?id=gNNlAAAAMAAJ]

==Information technology==
*Haynes, David (ed). Information Sources in Information Technology. (Guides to Information Sources). Bowker Saur. 1990. [https://books.google.co.uk/books?id=0hYjAAAAQBAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]

==Economics==
General series:
*Dryden Press Series in Economics
*Hurl, Bryan (ed). Studies in the UK Economy. Heinemann Educational
*Nuffield Economics &amp; Business. Nuffield Foundation. Longman.

Other:
*Bannock, Baxter and Davis. The Penguin Dictionary of Economics. Penguin Books. 4th Ed: 1987. Bannock, Baxter and Rees. 1972. 2nd Ed: 1978. 3rd Ed: 1984.

*Begg, Fischer and Dornbusch. Economics. McGraw Hill. 1984. 2nd Ed: 1987. 3rd Ed: 1991.
*Anderton, Alain. Economics. Causeway Press. 1991.
*Maile, Roger. Economics. (Core Business Studies). Mitchell Beazly. 1983.
*Maunder, Myers, Wall and Miller. Economics Explained. Collins Educational. 1987. 2nd Ed: 1991.
*Tibbitt, Andrew. A guide to A Level Economics. Thomas Nelson and Sons. 1986.

*Lipsey, Richard G. An Introduction to Positive Economics. Weidenfeld and Nicolson. 1963. 2nd Ed: 1966. 3rd Ed: 1971. 4th Ed: 1975. 5th Ed: 1979. 6th Ed: 1983. 7th Ed: 1989.

*Nicolson, Walter. Microeconomic Theory: Basic Principles and Extensions. (Dryden Press Series in Economics). Dryden Press, Holt-Saunders. 3rd Ed: 1985. 

*Caves and Jones. World Trade and Payments: An Introduction. Little, Brown and Company. 1973. 1977. 3rd Ed: 1981.

*National Institute of Economic and Social Research. The UK economy. (Studies in the UK Economy). Heinemann Educational. 1990.
*Smith, Charles. UK trade and sterling. (Studies in the UK Economy). Heinemann Educational. 1992.

==Games==
Chess
*Hooper and Whyld. The Oxford Companion to Chess. Oxford University Press. 1984. Paperback: 1987.
*Golombek, Harry. The Game of Chess. 1954. 2nd Ed: 1963. 3rd Ed: 1980.
*Pritchard, D. Brine. The Right Way to Play Chess. 1950. 8th Ed: 1971. 10th Ed: 1974. 11th Ed: 1977.
*Horowitz, Al. From Morphy to Fischer: A history of the World Chess Championship. B T Batsford. 1973. The World Chess Championship: A History. Macmillan. 1973. 

General series
*Batsford Chess Books
**Discovering Chess Series. B T Batsford.

Periodicals

See [[Universal Bibliography/Periodicals#Chess|Periodicals, Chess]]
*British Chess Magazine

Othello
*Goro Hasegawa with Maxine Brady. How to Win at Othello. (A Harvest/HBJ book). Jove Publications. 1977. ISBN 0-15-642215-8. [https://books.google.co.uk/books?id=mTdhlwVeyCcC]

Wargames
*Battleground. Tyne Tees. (ITV). 1978. [Television]. 6 episodes, with Edward Woodward.
**Laurie Taylor. &quot;Attila the Hun invades Tyne Tees&quot;. TV Times. 1978. pp 28 &amp; 29.
**Terry Wise. &quot;Battleground&quot;. Battle for Wargamers. June 1978. pp 261 &amp; 262.
*[[w:Game of War|Game of War]]. Channel 4. 1997. [Television].

==Toys==
Periodicals
*Games &amp; Toys: The Leading Trade Journal for Home &amp; Export. (H Richard Simmons Limited). [https://books.google.co.uk/books?id=pMmbZ_JTnXYC] Google: editions:UO8GID_4Ck0C
*Toys and Novelties. (Sporting Goods Pub Co). [https://books.google.co.uk/books?id=zKdAAQAAMAAJ] [https://archive.org/details/toys-and-novelties-volume-9-1913/page/n53/mode/1up] (Toys and Novelties Publishing Company) [https://archive.org/details/toys-and-novelties-volume-19-issue-no.-1-6-january-june-1922/page/n173/mode/1up]. Cf. &quot;Harcourt To Buy Journals From Haire Publishing Co&quot; [https://books.google.co.uk/books?id=J7hEAQAAIAAJ 194] Publishers Weekly 29
*[[w:Playthings (magazine)|Playthings: The National Magazine of the Toy Trade]]. (McCready Publishing Co) [https://books.google.co.uk/books?id=eCQHzuYWDY4C] [https://books.google.co.uk/books?id=mnRO5WFXDfEC]. (Geyer-McAllister Publications). Cf. &quot;Playthings bought by Geyer-McAllister&quot; [https://books.google.co.uk/books?id=itAaAQAAMAAJ 52] Industrial Marketing

==Cricket==
See [[w:Bibliography of cricket]]

*Peter Arnold and Peter Wynne-Thomas. The Complete Encyclopedia of Cricket. 2006. 4th Ed: 2011: [https://books.google.co.uk/books?id=2R_pXwAACAAJ].
**Peter Arnold. The Illustrated Encyclopedia of World Cricket.
*Morgan. The Encyclopedia of World Cricket. 2007. [https://books.google.co.uk/books?id=gFCbkgEACAAJ]

Scores and biographies
*Marylebone Club Cricket Scores and Biographies. [https://books.google.co.uk/books?id=dl8IAAAAQAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
**See [[w:Arthur Haygarth]] and [[w:Fred Lillywhite]]

Periodicals
*[[w:Cricket: A Weekly Record of the Game|Cricket: A Weekly Record of the Game]]. [https://books.google.co.uk/books?id=eX9QAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false].

Australia
*Malcolm Andrews. The Encyclopaedia of Australian Cricket. 1980. [https://catalogue.nla.gov.au/Record/1531463]
*The Oxford Companion to Australian Cricket

India 
*The Encyclopaedia of Indian Cricket, 1965. [https://books.google.com/books?id=CE4Joad6iwAC] [Includes biographies]

Annuals
*[[w:Indian Cricket (annual)|Indian Cricket]].  [https://books.google.co.uk/books?id=ioRLAAAAYAAJ 1966].

===Cricketers===
Cricketers, including biographical dictionaries and collections of biographies
*[[w:ESPNcricinfo|ESPNcricinfo]]
*[[w:CricketArchive|CricketArchive]]

*John Arlott's Book of Cricketers. 1979. [https://books.google.co.uk/books?id=8-WBAAAAMAAJ]

*World Cricketers: A Biographical Dictionary [https://books.google.com/books?id=IpBLAAAAYAAJ]
*Carr's Dictionary of Extraordinary Cricketers. 1977. Aurum Press. 2005. [https://books.google.com/books?id=CfwsAAAACAAJ]

*Sproat. Debrett's Cricketers' Who's Who. 1980.
*S Canynge Caple. The Cricketer's Who's Who. Williams. Lincoln. 1934.
*Cricket Who's Who: The Cricket Blue Book. 1909. [https://catalogue.nla.gov.au/Record/119715]. 1912. Bibliography: [https://books.google.co.uk/books?id=IjQyAQAAMAAJ]

*Who's Who in Test Cricket: A Biographical Dictionary of Test Cricketers [https://books.google.com/books?id=5uF5PQAACAAJ]

*Frindall. England Test Cricketers: The Complete Record from 1877. 1989. [https://books.google.com/books?id=2zHYLIW7h9UC]
*Brooke. The Collins Who's Who of English First-Class Cricket, 1945-1984. 1985. [https://books.google.com/books?id=NGSPAAAACAAJ]. Review: [https://books.google.co.uk/books?id=iHMsAAAAYAAJ]. Commentary: [https://books.google.co.uk/books?id=wPg5AQAAIAAJ]

Gloucestershire
*Gloucestershire Cricketers, 1870-1979. (ACS Cricketers Series [https://archive.acscricket.com/cricketers_series/index.html]). The Association of Cricket Statisticians. Cleethorpes. 1979. [https://archive.acscricket.com/cricketers_series/gloucestershire_cricketers_1870-1979/index.html]
*Rex Pogson. Gloucestershire Cricket and Cricketers, 1919-1939. Lytham St Annes. 1944. Catalogues: [https://catalogue.nla.gov.au/Record/850643] [https://books.google.co.uk/books?id=CS83vXlB1ZIC] [https://www.worldcat.org/title/504354999]. Also printed as microfilm: [https://books.google.co.uk/books?id=iqXeDTKUEl4C].
*Dean Hayes. Gloucestershire Cricketing Greats: 46 of the Best Cricketers for Gloucestershire. Tunbridge Wells. 1990. Catalogues: [https://books.google.co.uk/books?id=OmsqAQAAIAAJ] [https://www.worldcat.org/title/25202795]

Australia
*The A-Z of Australian Cricketers [https://books.google.com/books?id=w-0zAAAACAAJ]
*Piesse. Encyclopedia of Australian Cricket Players. 2012. [https://books.google.com/books?id=Jsh4MAEACAAJ]
*C P Moody. Australian Cricket and Cricketers 1856-1893-4. Melbourne. 1894.
*Jack Pollard. Australian Cricket: The Game and the Players. Hodder and Stoughton. ABC Books. Sydney. Lane Cove, New South Wales. 1982. Angus &amp; Robertson. London. North Ryde, New South Wales. Sydney. Revised Ed: 1988. Commentary: [https://books.google.co.uk/books?id=WotYAAAAYAAJ]. Review: [https://books.google.co.uk/books?id=KzNYAAAAMAAJ].

==Geology==
*Read and Watson. Introduction to Geology. Macmillan Education. 1962. 2nd Ed: 1968. Volume 1: Principles. Volume 2: Earth History.

==Mineralogy==
*Bibliography of Mineralogy for 1886. Annual Report of the Board of Regents of the Smithsonian Institution. Year Ending 30 June 1887. 1889. Pages [https://books.google.co.uk/books?id=wDcWAAAAYAAJ&amp;pg=PA473#v=onepage&amp;q&amp;f=false 473] to 476.

*Battey, Maurice Hugh. Mineralogy for students. Oliver &amp; Boyd. 1972. 2nd Ed. Longman. 1981.

==Paper==
See [[s:Category:Paper]]

*Surface. Bibliography of the Pulp and Paper Industries. Forest Service. Bulletin 123. 1913. [https://archive.org/details/bibliographyofpu12surf]
*West. Reading List on Papermaking Materials. 1920 to 1921. [https://archive.org/details/readinglistonpa00westgoog] [https://archive.org/details/readinglistonpa01westgoog]

==Books==
*British Book News [https://books.google.co.uk/books?id=2oFTAAAAIAAJ]
*Australasian Book News and Literary Journal. Australasian Book News and Library Journal. [https://books.google.co.uk/books?id=QVQPAQAAIAAJ]

*Book News. 1882 to 1918. (John Wanamaker). Called &quot;Book News Monthly&quot; from 1906. [https://books.google.co.uk/books?id=KtwRAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Stechert-Hafner Book News [https://books.google.co.uk/books?id=BmDqAAAAMAAJ]
*U.S.A. Book News [https://books.google.co.uk/books?id=36gVAQAAIAAJ]
*Branch Library Book News. [https://books.google.co.uk/books?id=NM8aAAAAMAAJ]

*Hungarian Book Review [https://books.google.co.uk/books?id=6U85AQAAIAAJ]
*Soviet Book News. (Earl Browder). 1947 [https://books.google.co.uk/books?id=QrXQ6LYSOF4C]

*Miniature Book News. [https://books.google.co.uk/books?id=MascAQAAMAAJ]

Rare
*Berger. Rare Books and Special Collections. American Library Association. 2014. [https://books.google.co.uk/books?id=IFUangEACAAJ]

Printed
*Annual Bibliography of the History of the Printed Book and Libraries. [https://books.google.co.uk/books?id=GLigoebhrd8C&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 30] [https://books.google.co.uk/books?id=UBN-IUZlF4gC&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 31]

==Paperback and Paperbound==
*Swados, &quot;Paper Books: What do they Promise?&quot; (1953) [https://books.google.co.uk/books?id=TwaJtQzwj1gC 173] The Nation 114
*Wagman, &quot;The Paperbound Book Business&quot; (1957) 9 Michigan Business Review [https://books.google.co.uk/books?id=9pA8uolQjnkC&amp;pg=RA4-PA9#v=onepage&amp;q&amp;f=false 9] (No 5, November)

==Science==
*Lafferty and Rowe. The Hutchinson Dictionary of Science. Helicon Publishing. 1993. 2nd Ed: 1998.

==Entertainment==
*The Directory (The Times, 1996 onwards) Commentary: [https://www.marketingweek.com/as-times-starts-listings-supplement/]

==Comedy and tragedy==
*E H Mikhail. Comedy and Tragedy: A Bibliography of Critical Studies. 1972. [https://books.google.co.uk/books?id=5bgEAAAAMAAJ]

===Comedy===
*James E Evans. Comedy: An Annotated Bibliography of Theory and Criticism. 1987. [https://books.google.co.uk/books?id=s9ZgthAs1t8C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Meghan Duffy (ed). Daniel Gerould (senior ed). Comedy: A Bibliography of Critical Studies in English on the Theory and Practice of Comedy in Drama, Theatre, and Performance. New York. 2006. [https://books.google.co.uk/books?id=fI0jAQAAIAAJ]
*David Humphrey. The Time of Laughter: Comedy and the Media Cultures of Japan. University of Michigan Press. 2023. [https://books.google.co.uk/books?id=CkTLEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

==Radio and television==
*William E McCavitt. Radio and Television: A Selected Annotated Bibliography. Scarecrow Press. 1978. [https://books.google.com/books?id=DAQVAQAAIAAJ]
*Gertrude G Broderick. Radio and Television Bibliography. Bulletin 1948 No 17. [https://books.google.co.uk/books?id=yIPP1dsmNtAC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
*Patricia Beall Hamill. Radio and Television: A Selected Bibliography. Bulletin 1960 No 25. [https://books.google.co.uk/books?id=AJhGAQAAMAAJ&amp;pg=PP3#v=onepage&amp;q&amp;f=false]

==Film and television==
*Jean Mitry. Bibliographie internationale du cinéma et de la télévision. 1966 onwards. [https://books.google.co.uk/books?id=SC3gAAAAMAAJ] Commentary: A Reference Guide for English Studies, [https://books.google.co.uk/books?id=h_wfYKnMfOkC&amp;pg=PA439#v=onepage&amp;q&amp;f=false p 439].

==Animation==
*John Halas and Roger Manvell. The Technique of Film Animation. 4th Ed: 1976. Focal Press. ISBN 0240509005.
*Clements and McCarthy. The Anime Encyclopedia. 3rd Rev Ed: [https://books.google.co.uk/books?id=E03KBgAAQBAJ&amp;pg=PA1958#v=onepage&amp;q&amp;f=false].

==Colours==
*Eiseman and Recker. Pantone: The 20th Century in Color. [https://books.google.co.uk/books?id=j3H7nSVS3UMC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. Reviews: [https://www.theguardian.com/books/2011/nov/13/pantone-20th-century-color-review][https://www.theatlantic.com/entertainment/archive/2011/11/pantone-100-years-of-color/249016/][https://eu.vvdailypress.com/story/lifestyle/health-fitness/2012/01/16/color-reel-20th-century-s/37119883007/]

==Bilateral==
Britain and Japan
*Pearse. Companion to Japanese Britain and Ireland. In Print. 1991. [https://books.google.co.uk/books?id=KtAxAAAAIAAJ]

==Prehistoric life==
Prehistoric animals
*[[w:Michael Benton|Michael Benton]]. Prehistoric Animals: An A-Z Guide. Kingfisher Books. 1989. Derrydale Books, New York. 1989. [Illustrations: Jim Channell and Kevin Maddison.]
*Ellis Owen. Prehistoric Animals: The Extraordinary Story of Life before Man. Octopus Books Limited. London. 1975. [Sculptures: Arthur Hayward.] Review: [https://books.google.co.uk/books?id=II-B8R-8Ov8C 17] Wildlife 422. Commentary: [https://books.google.co.uk/books?id=aUbYAAAAQBAJ&amp;pg=PA269#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=jFNBAAAAIBAJ&amp;pg=PA5#v=onepage&amp;q&amp;f=false].
**Prehistorische dieren: de geschiedenis van het leven vóór de mens. Translated by JJ Hoedeman. In den Toren, Baarn. Westland, Schoten. 1977.  Commentary: [https://books.google.co.uk/books?id=ToVMAQAAIAAJ]
**Les Animaux préhistoriques: l'extraordinaire histoire de la vie avant l'homme.

Dinosaurs
*Michael Benton. Dinosaurs: An A-Z Guide. Kingfisher Books. 1988. Derrydale Books, New York. 1988. [Illustrations: Jim Channell and Kevin Maddison.]

==Continents==
===Asia===

*Winston L Y Yang and Teresa S Yang. Asian Resources in American Libraries: Essays and Bibliographies. 1968. [https://books.google.com/books?id=76OkUAbkd4oC]
*Noriko Asato (ed). Handbook for Asian Studies Specialists: A Guide to Research Materials and Collection Building Tools. Libraries Unlimited. 2013. [https://books.google.co.uk/books?id=jkzEEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. Review: [https://www.emerald.com/rr/article-abstract/29/3/51/335520/Handbook-for-Asian-Studies-Specialists-A-Guide-to].

Periodicals
*Asian Bibliography [https://books.google.co.uk/books?id=EDq22yvuCb4C]

Asian studies and languages
*Pauline Haldane. Bibliography of Asian Studies and Languages. 1990. [https://books.google.com/books?id=9pQLAQAAIAAJ]

Asian studies
*Bibliography of Asian Studies. Association for Asian Studies. [https://books.google.co.uk/books?id=7NskAAAAMAAJ 1974].
*Cumulative Bibliography of Asian Studies, 1941-1965. GK Hall &amp; Co. [https://books.google.co.uk/books?id=p_UqAAAAMAAJ]
**Cumulative Bibliography of Asian Studies, 1966-1970. GK Hall &amp; Co. [https://books.google.com/books?id=Tg8rAAAAMAAJ]

East Asia
*G Raymond Nunn. East Asia: A Bibliography of Bibliographies. (Occasional Papers of East-West Center Library, No 7). Honolulu. 1967. [https://books.google.co.uk/books?id=XWOTAAAAIAAJ]
*East Asia: A Selected Functional Bibliography. Foreign Service Institute, Center for Area and Country Studies. [https://books.google.co.uk/books?id=ByXkdOpCwF8C&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*Donald Gillin. East Asia: A Bibliography for Undergraduate Libraries. [https://books.google.co.uk/books?id=Q7cIAAAAIAAJ]
*Thomas C Kuo and John W Chiang. East Asian Periodicals and Serials: A Descriptive Bibliography [https://books.google.co.uk/books?id=eA1GAAAAMAAJ]
*Bibliographic Guide to East Asian Studies. [https://books.google.co.uk/books?id=t7WFAAAAIAAJ 1996].

====Far East====
Bibliography
*Kuniyoshi. Far East. (PACAF Basic Bibliographies). 1957. [https://books.google.co.uk/books?id=Q5TLdCbP2HcC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]

====Japan and Korea====
Bibliography
*Bernard S Silberman. Japan and Korea: A Critical Bibliography. University of Arizona Press. 1962. [https://books.google.co.uk/books?id=y6UIAAAAIAAJ]
*Frank J Shulman. Japan and Korea: An Annotated Bibliography of Doctoral Dissertations in Western Languages 1877-1969. American Library Association. 1970. Routledge. 2013. [https://books.google.co.uk/books?id=xs62AQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

====South Asia====
*South Asian Bibliography: A Handbook and Guide. Harvester Press. [https://books.google.co.uk/books?id=aqwNAQAAIAAJ]
*The Bibliography of South Asian Periodicals: A Union-list of Periodicals in South Asian Languages. Harvester Press. [https://books.google.co.uk/books?id=COV0nIUK0bgC]

==Culture and society==
*Victoria Lyon Bestor, Theodore C Bestor and Akiko Yamagata (eds). Routledge Handbook of Japanese Culture and Society. 2011. [https://books.google.co.uk/books?id=0cBYffHp5L4C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Josef Kreiner and Hans-Dieter Ölschleger (eds). Japanese Culture and Society: Models of Interpretation. 1996. [https://books.google.co.uk/books?id=6skwAQAAIAAJ]
*Dolores P Martinez. Modern Japanese Culture and Society. 2007. [https://books.google.co.uk/books?id=l6kMAQAAMAAJ vol 1]
*C Andrew Gerstle. 18th Century Japan: Culture and Society. 1989. [https://books.google.co.uk/books?id=ViglDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Periodicals
*Review of Japanese Culture and Society [https://books.google.co.uk/books?id=W_o-AQAAIAAJ]

==See also==
*[[Bibliography]]

==Notes==
{{Reflist}}
{{subpagesif}}
[[Category:Bibliographies]]
[[Category:Research]]</text>
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{{Bibliography}}
{{research}}

If this resource is ever completed, it will be a universal bibliography.&lt;ref&gt;See [[w:Bibliography]].&lt;/ref&gt; Until then, it will be an approximation of a universal bibliography.

This bibliography is arranged as an index of topics.

==Index==
*[[Universal Bibliography/Bibliography|Bibliography]]
*[[Universal Bibliography/Libraries|Libraries]]
*[[Universal Bibliography/Literature|Literature]]
*[[Universal Bibliography/Languages|Languages]]
*[[Universal Bibliography/SF|SF]]
*[[Universal Bibliography/Music|Music]]
*[[Universal Bibliography/Cinema|Cinema]]
*[[Universal Bibliography/Television|Television]]
*[[Universal Bibliography/Culture|Culture]]
*[[Universal Bibliography/Publishers and imprints|Publishers and imprints]]
*[[Universal Bibliography/Printing|Printing]]
*[[Universal Bibliography/Printers|Printers]]
*[[Universal Bibliography/Microform|Microform]]
*[[Universal Bibliography/Periodicals|Periodicals]]
*[[Universal Bibliography/Reference|Reference]]
*[[Universal Bibliography/Gazetteers|Gazetteers]]
*[[Universal Bibliography/Humanities|Humanities]]
*[[Universal Bibliography/Law|Law]]
*[[Universal Bibliography/History|History]]
*[[Universal Bibliography/Archaeology|Archaeology]]
*[[Universal Bibliography/Geography|Geography]]
*[[Universal Bibliography/Countries|Countries]]
*[[Universal Bibliography/Architecture|Architecture]]
*[[Universal Bibliography/Mathematics|Mathematics]]
*[[Universal Bibliography/Computers|Computers]]
*[[Universal Bibliography/Kites|Kites]]
*[[Universal Bibliography/Nostalgia|Nostalgia]]
*[[Universal Bibliography/Children's non-fiction|Children's non-fiction]]

===About===
*[[Universal Bibliography/About|About]]

==Online libraries==
Swedish:
*[[w:Swedish Literature Bank|Litteraturbanken]] (Swedish Literature Bank)
*[[w:Project Runeberg|Projekt Runeberg]] (Project Runeberg)

French
*[[w:Persée (web portal)|Persée]] (persee.fr)

Japanese
*[[w:Aozora Bunko|Aozora Bunko]] (aozora.gr.jp)

==Biographical dictionaries etc==
See [[w:Bibliography of encyclopedias: general biographies]] and [[w:List of biographical dictionaries]]

*Fox. 'True Biographies of Nations?': The Cultural Journeys of Dictionaries of National Biography. ANU Press. 2019 [https://books.google.co.uk/books?id=siSbDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Arthur, &quot;Biographical Dictionaries in the Digital Era&quot;. Advancing Digital Humanities: Research, Methods, Theories. 2014. Chapter 6. [https://books.google.co.uk/books?id=z7MaBgAAQBAJ&amp;pg=PA83#v=onepage&amp;q&amp;f=false Page 83] et seq.

Bibliographies, indexes, etc:
*Wynar. ARBA Guide to Biographical Dictionaries. Libraries Unlimited. 1986 [https://books.google.co.uk/books?id=5FfgAAAAMAAJ]
*Slocum, Robert B (ed). Biographical Dictionaries and Related Works. Gale Research Company. 2nd Ed: 1986 [https://books.google.co.uk/books?id=5uMpAQAAMAAJ]
*Biographical Dictionaries Master Index. (Gale Biographical Index Series). [https://books.google.co.uk/books?id=ZEshAQAAMAAJ] [https://books.google.co.uk/books?id=pPAzAQAAIAAJ] see also [https://books.google.co.uk/books?id=o_gPAQAAMAAJ]
*Children's Authors and Illustrators: An Index to Biographical Dictionaries. (Gale Biographical Index Series). 2nd Ed: 1978,  3rd Ed: 1981, 4th Ed: 1987 [https://books.google.co.uk/books?id=VIsWAQAAMAAJ] [https://books.google.co.uk/books?id=DFtGAQAAIAAJ] [https://books.google.co.uk/books?id=01wjAQAAIAAJ]
*Index to the Wilson Authors Series [https://books.google.co.uk/books?id=oNZkAAAAMAAJ]
*Auchterlonie. Arabic Biographical Dictionaries: A Summary Guide and Bibliography. 1987 [https://books.google.co.uk/books?id=rW59QgAACAAJ]
*Black Biographical Dictionaries, 1790-1950 [https://books.google.co.uk/books?id=laIUAQAAMAAJ]

Particular works:

*Oxford Dictionary of National Biography; [[w:Dictionary of National Biography|Dictionary of National Biography]]
*Boase. Modern English Biography. ([http://www.google.com/search?q=editions%3Auzt3-qMuFcMC&amp;btnG=Search+Books&amp;bksoutput=html_text&amp;tbm=bks&amp;tbo=1 editions:uzt3-qMuFcMC])
*A &amp; C Black's Who's Who
*Who Was Who
*The Academic Who's Who. A &amp; C Black. 1st Ed: 1973 [https://books.google.co.uk/books?id=dnUWAQAAMAAJ] [https://books.google.co.uk/books?id=fXJmAAAAMAAJ]. 2nd Ed: 1975. Commentary: [https://books.google.co.uk/books?id=7VyOANl2qxoC&amp;pg=PA208&amp;output=html_text]. GBooks: editions:INAP7GGD2gYC editions:tA0FkHC75FIC
*Dictionary of Edwardian Biography (Pike's New Century Series)

Works that comprise largely of biographies:
*The Penguin Companion to Literature

Theatres
*A Biographical Dictionary of Actors, Actresses, Musicians, Dancers, Managers &amp; Other Stage Personnel in London, 1660-1800. [https://books.google.co.uk/books?id=TGgS9VxWJ0oC vol 15]

==Dictionaries of dates==
[https://archive.org/search.php?query=%22dictionary%20of%20dates%22 Archive.org]
*Baxter Dictionary of Dates and Events. 1st Ed: 1963: Napier, M (ed). 2nd Ed: 1971: Sanders and Laffin. Commentary: 92 Library Journal 1819 [https://books.google.co.uk/books?id=CExVAAAAYAAJ]
*Beeching, Cyril Leslie. A Dictionary of Dates. OUP. 1st Ed: 1993. 2nd Ed: 1997. [https://www.google.co.uk/search?hl=en&amp;tbm=bks&amp;q=editions:UGGp0EexZdcC editions:UGGp0EexZdcC]
*Bolton, John. Bolton's Dictionary of Dates, arranged in alphabetical order. Foulsham. 1958. Review: [https://books.google.co.uk/books?id=awJPAAAAIAAJ 172] The Publisher 880
*[[w:William Darling (politician)|William Young Darling]]. A Book of Days: A Dictionary of Dates, a Chronology of Circumstance, the Face of Time. Richards Press. 1951. [https://books.google.co.uk/books?id=PLkfAAAAMAAJ]
*Everyman's Dictionary of Dates. 1st Ed: 1911. 6th Ed: 1971. Review: (1971) 11 RQ 164 [http://www.jstor.org/stable/25824440]
*Platt, Charles. Foulsham's Dictionary of Dates and General Information. 1930.
*[[w:Haydn's Dictionary of Dates|Haydn's Dictionary of Dates]]
*Hamlyn Dictionary of Dates and Anniversaries. Newnes Dictionary of Dates.
*Williams, Henry Llewellyn. Hurst's Dictionary of Dates. 1891. [https://archive.org/details/hurstsdictionary00will]
*Keller, Helen Rex. The Dictionary of Dates. Macmillan. 1934. Commentary: [https://books.google.co.uk/books?id=Utcb32E7rsMC&amp;pg=PA93&amp;output=html_text] [https://books.google.co.uk/books?id=sAHfY6QbOEwC&amp;pg=PA351&amp;output=html_text]
*Nelson's Dictionary of Dates. A Dictionary of Dates. (Nelson's Encyclopaedic Library). 1912 [https://books.google.co.uk/books?id=Mp9lvwEACAAJ]. Reviews: (June 1912) Journal of Education, vol 34 (New Series), vol 44 (Old Series), p 392 [https://books.google.co.uk/books?id=QIRFAQAAMAAJ]; (1912) [https://books.google.co.uk/books?id=9i4_AQAAIAAJ 108] The Spectator [http://archive.spectator.co.uk/article/18th-may-1912/25/a-dictionary-of-dates-vol-i-and-english-idioms-nel 805] (18 May)
*Pulman, George Palmer. The World's Progress: A Dictionary of Dates. New York. 1861. [https://books.google.co.uk/books?printsec=frontcover&amp;id=k3dJAAAAYAAJ&amp;output=html]
*Urdang, Laurence. The World Almanac Dictionary of Dates. Longman. 1982. [https://books.google.co.uk/books?id=I4IRAQAAMAAJ] Review: (1982) 22 RQ 101 [http://www.jstor.org/stable/25826880]

Australia

*John Henniker Heaton. Australian Dictionary of Dates and Men of the Time. 1879. [https://archive.org/details/australiandicti00heatgoog]
*John James Knight. In the Early Days; History and Incident of Pioneer Queensland, with Dictionary of Dates in Chronological Order. Sapsford &amp; Co. Brisbane. 1895.

America

*Damon, Charles Ripley. The American Dictionary of Dates, 458-1920. R G Badger. 1921.

==Commodity dictionaries==
*Statistical Classification of Domestic and Foreign Commodities Exported from the United States. Commentary: [https://books.google.co.uk/books?id=91GLhsJSBj8C&amp;pg=PR22#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=RPwhAQAAMAAJ&amp;pg=RA15-PA7#v=onepage&amp;q&amp;f=false]
*Tovarnyi slovar'. (Commodity Dictionary). Reviews and commentary: Petrov, &quot;Commodity Dictionary&quot;, Ekonomicheskaya Gazeta, No 13, 30 October 1961, p 45; CDSP , 13 December 1961, p 46; (1962) [https://books.google.co.uk/books?id=2vMRAAAAIAAJ 13] Current Digest of the Soviet Press 47; (1958) 15 Quarterly Journal of Current Acquisitions 210 [https://books.google.co.uk/books?id=ZcvozpZAfpEC] [https://books.google.co.uk/books?id=S47qEIfyCr0C]; Fitzpatrick, Stalinism: New Directions, [https://books.google.co.uk/books?id=rD5FzoKnTE0C&amp;pg=PA182#v=onepage&amp;q&amp;f=false p 182] &amp; 183
*Szilágyi. Commodity Dictionary in Five Languages. Budapest. Közgazdasági és Jogi Könyvkiadó (Publishing House for Economics and Law). 1963 or 1964. Commentary: Books from Hungary, vols 4-6, pp 26 &amp; 40 [https://books.google.co.uk/books?id=6kMiAQAAMAAJ]
*Dictionnaire des produits: appellations et caractéristiques des produits francais de consommation courante, 1960. Commentary: Walford (ed), Guide to Reference Material Supplement, 1963, p 106 [https://books.google.co.uk/books?id=ej-9pHGR67oC]
*Chūgoku Shōhin Jiten. (Chinese commodity dictionary). Tokyo. 1960. [https://books.google.co.uk/books?id=Wc61lS0xj6AC&amp;pg=PA78#v=onepage&amp;q&amp;f=false]

==Encyclopedias==
See [[s:Category:Encyclopedias]], [[w:Bibliography of encyclopedias]] and [[w:Lists of encyclopedias]]

*[[w:en:Encyclopædia Britannica Eleventh Edition|Encyclopædia Britannica Eleventh Edition]]
*Paton, John (ed). Knowledge Encyclopedia: 1979, 1981, 1988. New Discovery Encyclopedia: 1990.
*The Dorling Kindersley Illustrated Family Encyclopedia

==Almanacs==
See [[s:Category:Almanacs]], [[s:Portal:Almanacs]], [[w:List of almanacs]], [[w:Category:Almanacs]].
*Year Book and Almanac of Newfoundland. 
**For 1896. 1895. [https://archive.org/details/yearbooknfld189600newfuoft]
*Whiteley. On This Date: A Day-by-Day Listing of Holidays, Birthday and Historic Events, and Special Days, Weeks and Months. 2002. [https://books.google.co.uk/books?id=sKCfomKSa74C]

==Censuses==
*Census of New Zealand and Labrador
**1901 Census. Tables 2 and 3. 1903. [https://archive.org/details/censusnewfoundl00bondgoog]
**1911 Census. Table 1. 1914. [https://archive.org/details/1911981911fnfldv11914eng]
**1921 Census. Tables 4 and 5. 1923. [https://archive.org/details/1921981921fnfldv451923eng]

==Pilot guides==
*[[w:United States Coast Pilot|United States Coast Pilot]]
*American Coast Pilot [https://books.google.co.uk/books?id=8GoDAAAAYAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]

*Sailing Directions: Newfoundland. Canadian Hydrographic Service. [https://books.google.co.uk/books?id=A77fAAAAMAAJ]
*Newfoundland Pilot. Canadian Hydrographic Service. [https://books.google.co.uk/books?id=z7zfAAAAMAAJ]
*Maxwell. The Newfoundland Pilot. Hydrographic Office, Admiralty. London. 1878. [https://books.google.co.uk/books?id=vS4BAAAAQAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]
*Newfoundland Pilot. HO No 73. Hydrographic Office. Governement Printing Office, Washington. 4th Ed: 1919: [https://books.google.co.uk/books?id=YGoDAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]. Sailing Directions for Newfoundland. 5th Ed: 1931: [https://books.google.co.uk/books?id=cMUiGo3JK9QC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]

==Books of facts==
*The Reader's Digest Book of Facts. 1st Ed: 1985. Reprinted with amendments: 1987: [https://books.google.co.uk/books?id=B8PmM_5Zm1MC]. (Review: Library Journal, [https://books.google.co.uk/books?id=EPDgAAAAMAAJ v 9], p 102, 1 Dec 1987, [http://www.bookverdict.com/details.xqy?uri=Product-94667328910921.xml Book Verdict].) 3rd Revised Ed: 1995: [https://books.google.co.uk/books?id=E5YhAQAAIAAJ]. GBooks: editions:nnJlLybWxbIC
*Chambers Book of Facts
*Crystal, David (ed). Penguin Book of Facts. [https://books.google.co.uk/books?id=k0sZAQAAIAAJ 2004]. 2nd Ed: 2008
*Handy Book of Facts: Things Everyone Should Know. C.S. Hammond &amp; Company. 1914. [https://books.google.co.uk/books?id=h5wRAAAAIAAJ]

==Series of books==
See [[w:Category:Series of books]] and [[w:Category:Monographic series]]
*George M Sinkankas, &quot;Series&quot; in Kent, Lancour and Daily (eds).  Encyclopedia of Library and Information Science. Volume 27. Marcel Dekker. 1979. Pages [https://books.google.co.uk/books?id=jU3fwyjqS5UC&amp;pg=PA250#v=onepage&amp;q&amp;f=false 250] to 273.
*&quot;Publishing in Series, 1896-1916&quot; in Eliot, Simon (ed). History of Oxford University Press. Louis,  Wm Roger (ed). Volume 3: 1896-1970. Oxford University Press. 2013. [https://books.google.co.uk/books?id=YbcJAgAAQBAJ&amp;pg=PA539#v=onepage&amp;q&amp;f=false Page 539] et seq.
*Spiers, John. The Culture of the Publisher’s Series. Palgrave Macmillan. 2011. [https://books.google.co.uk/books?id=ASaHDAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 1]. [https://books.google.co.uk/books?id=XCl-DAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 2].
*Spiers, John. Serious about Series: American 'Cheap' Libraries, British 'Railway' Libraries and Some Literary Series of the 1890's. 2007. [https://books.google.co.uk/books?id=1hRXAAAAYAAJ] [https://books.google.co.uk/books?id=AS4yQwAACAAJ]
*Rooney, Paul Raphael. Railway Reading and Late-Victorian Literary Series. Routledge. 2018. [https://books.google.co.uk/books?id=uX5aDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Khan. &quot;Monographs in series&quot;. The Principles and Practice of Library Science. 1996. Pages [https://books.google.co.uk/books?id=sAHfY6QbOEwC&amp;pg=PA208#v=onepage&amp;q&amp;f=false 207] to 209.
*Friskney. New Canadian Library: The Ross-McClelland Years, 1952-1978. Pages [https://books.google.co.uk/books?id=jHIjCCXBX9kC&amp;pg=PA6#v=onepage&amp;q&amp;f=false 6] and 7.

*Books in Series. R R Bowker Company. Commentary: [https://books.google.co.uk/books?id=uQe04OSlA7YC&amp;pg=PA11#v=onepage&amp;q&amp;f=false]
**Books in Series in the United States, 1966-1975. R R Bowker. 1977. Review: (1977) 14 Choice [https://books.google.co.uk/books?id=_e08AQAAIAAJ&amp;pg=PA1190#v=onepage&amp;q&amp;f=false 1190] (No 8, November). Commentary: [https://books.google.co.uk/books?id=LYAhAAAAQBAJ&amp;pg=PA53#v=onepage&amp;q&amp;f=false]
***Books in Series Supplement: A Supplement to Books in Series in the United States, 1966-1975. 1978. [https://books.google.co.uk/books?id=hOAaAQAAMAAJ]
**Books in Series. 3rd Ed. 1980. [https://books.google.co.uk/books?id=d_kaAQAAMAAJ]
**Books in Series, 1876-1949. R R Bowker Company. 1982. [https://books.google.co.uk/books?id=TngvAQAAIAAJ] [https://books.google.co.uk/books?id=iVIyAQAAMAAJ] [https://books.google.co.uk/books?id=R2AjAQAAIAAJ]
**Books in Series, 1985-89. [https://books.google.co.uk/books?id=yEkxAQAAIAAJ]
*Baer, Eleanora Agnes. Titles in Series: A Handbook for Librarians and Students. Scarecrow Press. Vol 1 (Books Published Prior to January 1953). 1953: [https://books.google.co.uk/books?id=GgAYAAAAMAAJ]. Vol 2 (Books Published Prior to January 1957). 1957: [https://books.google.co.uk/books?id=oqsXAAAAMAAJ]
**2nd Ed: 1964. [https://books.google.co.uk/books?id=gWlAAAAAIAAJ Vol 1]. [https://books.google.co.uk/books?id=tWpAAAAAIAAJ Vol 2]. Supplement to the Second Edition. 1967: [https://books.google.co.uk/books?id=zGARAQAAMAAJ]. Second Supplement to the Second Edition. 1971: [https://books.google.co.uk/books?id=WwXhAAAAMAAJ]
**3rd Ed: 1978. Commentary: [https://books.google.co.uk/books?id=h_wfYKnMfOkC&amp;pg=PA63#v=onepage&amp;q&amp;f=false]
*Ocran, Emmanuel Benjamin. Scientific &amp; Technical Series: A Select Bibliography. 1973: [https://books.google.co.uk/books?id=oy0EAAAAMAAJ] Review: [https://books.google.co.uk/books?id=fTCw_DQH6zkC&amp;pg=PA949#v=onepage&amp;q&amp;f=false]

*Rosenberg and Nichols. Young People's Books in Series: Fiction and Non-fiction, 1975-1991. Libraries Unlimited. 1992. [https://books.google.co.uk/books?id=REHhAAAAMAAJ]
*Young People's Literature in Series

*Catalog of Reprints in Series. (sometimes called &quot;Catalogue of Reprints in Series&quot;). 1940 onwards. [https://books.google.co.uk/books?id=MSI4AAAAIAAJ] [https://books.google.co.uk/books?id=6n1EAAAAMAAJ] Commentary: [https://books.google.co.uk/books?id=h_wfYKnMfOkC&amp;pg=PA73#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=1RxuAAAAMAAJ]

*Kuitert, Lisa. Het ene boek in vele delen. De Uitgave van Literaire Series in Nederland 1850-1900. Uitgeverij de Buitenkant. Amsterdam. 1993. Commentary: [https://books.google.co.uk/books?id=jSDnRo7YrWwC&amp;pg=PA656#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=szBcAAAAMAAJ] [https://books.google.co.uk/books?id=SVcVAQAAIAAJ] [https://books.google.co.uk/books?id=R8Pfs146nUAC&amp;pg=PA367#v=onepage&amp;q&amp;f=false]

==Series of classics==
*Penguin Classics (Penguin Modern Classics, Penguin English Library)
*Oxford World Classics
*Everyman's Library
*Wordsworth Classics
*Macmillan Collectors Library
*Bantam Classics
*Minster Classics
*The Literary Heritage Collection (Heron Books, London. William Collins Sons &amp; Co, Glasgow)
*Chandos Classics
*Temple Classics
*Longmans Heritage of Literature Series

Russian
*Greatest Masterpieces of Russian Literature (Heron Books, London)

SF
*Corgi SF Collectors Library

Children's and shorter classics etc 
*Shorter Classics. Ginn and Company.
*Ladybird Children's Classics.
*Mini Classics. Parragon Books.
*Bonny Books. Peter Haddock Ltd.
*A series published by Dean &amp; Son Ltd

==Non-fiction general series==
*[[w:Oxford Companions|Oxford Companions]]
*[[w:Cambridge Companions|Cambridge Companions]]
*Princeton Companions
*Blackwell Companions. Wiley Blackwell Companions
*Routledge Companions. Routledge Research Companions
*Ashgate Companions. Ashgate Research Companions
*Brill's Companions
*Facts on File Companions
*Guides to Information Sources. Bowker-Saur
*Butterworths Guides to Information Sources.
*Columbia Guides
*Blackwell Guides
*Edinburgh Critical Guides
*Collins Reference Dictionaries
*New Horizons. Thames and Hudson. ([[w:Découvertes Gallimard|Découvertes Gallimard]])
*Collins Gem (see [[w:List of Collins GEM books]])
*Concise Encyclopedias. Collins.
*Time Life Books (see [[w:Time Life#Book series]])
*[[w:Teach Yourself|Teach Yourself Books]]. English Universities Press. 
*[[w:Teach Yourself|Teach Yourself Books]]. Hodder and Stoughton.
*Made Simple Books. W H Allen.
*Palgrave Master Series
*Harrap's Mini Series
*Shire Albums. Shire Publications.
*Fax Pax: Knowledge in a Nutshell. Fax Pax Ltd.
*The Wonderful World Books. Macdonald and Company
*Harper's ABC series. Includes A-B-C of Housekeeping, A-B-C of Electricity, A-B-C of Gardening and A-B-C of Manners.
*Hamlyn Pocket Guides
*Oxford Monograph Series
*Study Outline Series. H W Wilson. [[s:Page:Russian Literature - A Study Outline.djvu/61|(wikisource)]]
*Helpmate Handbooks. Willow Books

University
*University Paperbacks. Meuthen &amp; Co
*World Student Series. Addison Wesley
*Unibooks. Hodder and Stoughton
*International Student Editions. Van Nostrand Reinhold
*Hutchinson University Library

Imprints
*Pelican Books

Pictorials
*Salmon Cameracolour series
*Pitkin Pictorials 

United Kingdom
*Aspects of Britain. HMSO.

Places
*The Little Guides. Meuthen [[s:Page:Cornwall (Salmon).djvu/336|(wikisource)]]
*G.W.R. Series of Travel Books [[s:Page:The Cornwall coast.djvu/391|(wikisource)]]

Art
*Movements in World Art. Meuthen.
*Movements in Modern Art. Meuthen.
*How to Draw and Paint. New Burlington.

Film
*BFI Companions

Popular science
*Contemporary Science Paperbacks. Oliver and Boyd.
*Pan Piper Science Series

Science and mathematics
*Simon and Schuster Tech Outlines
*Schaum's Outline Series

Military
*Illustrated Military Guides. Illustrated Guides. &quot;An Illustrated Guide to ...&quot;. Salamander Books.
*Combat Arms. Arco Military Books. Salamander Books. Prentice Hall Press.
*Osprey Men-at-Arms
*Jane's Pocket Books

Communication
*The Library of Communication Techniques. Focal Press.
*John Fiske (ed). Studies in Culture and Communication. Routledge.
*The Media. Wayland.

Cookery
*ABC series. Peter Pauper Press.

Gardening
*Pan Piper Small Gardens Series.

Mythology
*Series on mythology published by Southwater (imprint of Anness)

==History and Geography==
See also [[Universal Bibliography/History|History]] and [[Universal Bibliography/Geography|Geography]].
*Baker. Geography and History: Bridging the Divide. 2003. [https://books.google.co.uk/books?id=e8yf5JcefpAC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Darby. Relations of History and Geography: Studies in England, France and the United States. 2002. [https://books.google.co.uk/books?id=Vl4ZfpnP7NwC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

General series
*Cambridge Studies in Historical Geography

Atlases
*The Times Atlas of World History
*Philip's Atlas of World History

History of geography:
*Dunbar, Gary S. The History of Modern Geography: An Annotated Bibliography of Selected Works. Garland. 1985. [https://books.google.co.uk/books?id=FX4WAQAAIAAJ]

==Chronology==
See also [[Universal Bibliography/History#Millennia, centuries and decades]]

General
*Chronology of World History.
**Neville Williams. Chronology of the Modern World: 1763 to the present time. 1st Ed: 1966. (1763 to 1992). 2nd Ed: 1994.
**Neville Williams. Chronology of the Expanding World 1492 to 1762. 1969. Reissued 1994.
**Storey. Chronology of the Medieval World 800 to 1491. 1973. Reissued 1994.
**Mellersh. Chronology of the Ancient World 10,000 BC to AD 799. Barrie and Jenkins. 1976. Helicon. Simon &amp; Schuster. Reissued 1994.

Centuries
*Chronology of the 20th Century. Helicon. 1995. [https://books.google.com/books?id=pjsOAQAAMAAJ]
*Brownstone and Franck. Timelines of the 20th Century. [https://books.google.com/books?id=IZ6SQgAACAAJ]
*Beal. 20th Century Timeline. 1985. [https://books.google.com/books?id=cFrG7LBObGoC]
*20th Century Day by Day [https://books.google.com/books?id=kyxaAAAAYAAJ] [https://books.google.com/books?id=WiOAAAAACAAJ]
*Chronicle of the 20th Century [https://books.google.co.uk/books?id=pt3DYbnZO8sC] [https://books.google.co.uk/books?id=Gd1WPQAACAAJ]
*Boyle. The Chronology of the Eighteenth and Nineteenth Centuries. 1826. [https://books.google.co.uk/books?id=wDENAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]

Decades
*Series:
**Day by Day. Facts on File. [https://books.google.com/books?id=WfClvwEACAAJ] [https://books.google.com/books?id=CWNvQgAACAAJ]

Years
*Brown, D Kinnear. History of the Year. (1884 to 1885). [https://books.google.co.uk/books?id=DmRWAAAAYAAJ&amp;pg=PA113#v=onepage&amp;q&amp;f=false Catalogue].
*The History of the Year: A Narrative of the Chief Events and Topics of Interest. [https://books.google.co.uk/books?id=ljgIAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false 1881 to 1882]. [https://books.google.co.uk/books?id=1DgIAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false 1882 to 1883].
*James Mason. The History of the Year 1876. [https://books.google.co.uk/books?id=6DoIAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*[[w:The Annual Register|The Annual Register]]. [A View of the History Politics and Literature of the Year YYYY.] [https://books.google.co.uk/books?id=SrJNAAAAcAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false 1821].
*Giusto Traina. 428AD: An Ordinary Year at the End of the Roman Empire. [https://books.google.co.uk/books?id=gLumDwAAQBAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

Ancient
*Bickerman. Chronology of the Ancient World. 1968.
*Smithsonian Timelines of the Ancient World: A Visual Chronology from the Origins of Life. Dorling Kindersley. 1st American Ed: 1993.

==Anniversaries==
*Sian Facer (ed). On this Day: The History of the World in 366 Days. Octopus Illustrated Publishing, London. Crescent Books, New York and Avenel. 1992: [https://books.google.com/books?id=SYGQgwHTuE0C]. Other: [https://books.google.co.uk/books?id=W687MAEACAAJ] [https://books.google.co.uk/books?id=7ujArQEACAAJ]
*On this Day: A History of the World in 366 Days. DK. 2021. [https://books.google.co.uk/books?id=x4I5EAAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]

==Egyptology==
*Annual Egyptological Bibliography [https://books.google.co.uk/books?id=8MoUAAAAIAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=-eUUAAAAIAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

==Battlefields==
*[[w:War Walks|War Walks]]. BBC2. 1996 to 1997. [Television series]
*&quot;The Times Guide to Battlefields of Britain&quot;. Day 1: The Times, 1 August 1994, p 8. Day 2: The Times, 2 August 1994, p 8. Day 3: The Times, 3 August 1994, p 6. Day 4: The Times, 4 August 1994, p 9. Day 5: The Times, 5 August 1994, p 9. Day 6: The Times, 6 August 1994, p 6. There was also a colour wall chart.

==Armed forces==
Periodicals:
*[[w:NATO Review|NATO Review]]

Military
*The Journal of Military History

*Journal of the Royal United Service Institution [Google editions:lMJAgUvBWAEC editions:dcFNqS8JFjoC]

*The Monthly Army List [Google editions:I0t2L4ElznEC]
*The Army Quarterly and Defence Journal [Google editions:c7UjQ-q7SbUC]

*Journal of the Society for Army Historical Research [Google editions:9HZkbMTl6mcC]

*The Royal Armoured Corps Journal [https://www.google.com/search?tbm=bks&amp;q=editions:dEauCcI7kssC&amp;biw=534&amp;bih=736&amp;dpr=1.5#sbfbu=1]
*The Royal Tank Corps Journal
*The Tank [https://www.google.com/search?sa=N&amp;cs=0&amp;tbm=bks&amp;q=editions:Dv-RbpoM7acC&amp;biw=534&amp;bih=736&amp;dpr=1.5#ip=1] Editorial office at the Royal Tank Regiment
*The Cavalry Journal [https://www.google.com/search?sa=N&amp;cs=0&amp;tbm=bks&amp;q=editions:cVQlfkRl6KUC&amp;biw=534&amp;bih=688&amp;dpr=1.5#sbfbu=1]
*The Journal of the Royal Artillery [https://www.google.com/search?tbm=bks&amp;q=editions:liFy4uc0ggYC&amp;biw=534&amp;bih=736&amp;dpr=1.5]
*Minutes of Proceedings of the Royal Artillery Institution [Google editions:wdjZ588FbtMC]
*The Royal Engineers Journal [https://www.google.com/search?tbm=bks&amp;q=editions:8XobinXLbD0C&amp;biw=534&amp;bih=736&amp;dpr=1.5]
*Journal of the Royal Electrical and Mechanical Engineers [https://books.google.com/books?id=dz0cmA1jnv4C]
*Journal of the Royal Army Medical Corps [Google editions:FyUJx2dEWcQC]

United States
*Military Review
*The Coast Artillery Journal [Google editions:nMCogSJ_rlkC]
*Infantry Journal [Google editions:ULqoLmbUR5cC]
*The Reserve Officer [Google editions:JQDRDrnD1QQC]

Naval
*[[w:Navy News|Navy News]]

==Armour==
Armoured warfare; tank warfare
*Harris and Toase. Armoured Warfare. 1990. [https://books.google.com/books?id=KYPfAAAAMAAJ]
*Carver. The Apostles of Mobility: The Theory and Practice of Armoured Warfare. 1979. [https://books.google.com/books?id=8qcgAAAAMAAJ]
*Fuller. Armoured Warfare: An Annotated Edition of Fifteen Lectures on Operations between Mechanized Forces. 1943. [https://books.google.co.uk/books?id=2E4tAQAAMAAJ]
*Black. Tank Warfare. 2020. [https://books.google.co.uk/books?id=oFP5DwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Jorgensen and Mann. Tank Warfare. 2001. [https://books.google.co.uk/books?id=0AghAQAAIAAJ]
*Searle. Armoured Warfare: A Military, Political and Global History. 2017. [https://books.google.co.uk/books?id=HN4CDgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Willey. Tanks: The History of Armoured Warfare. 2018. [https://books.google.com/books?id=AXTltAEACAAJ]
*Perrett. Iron Fist: Classic Armoured Warfare Case Studies. [https://books.google.co.uk/books?id=pKGyeWqJcCEC]. Iron Fist: Classic Armoured Warfare. [https://books.google.co.uk/books?id=KKcKI4dG0VUC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Tom Clancy. Armoured Warfare: Guided Tour of an Armoured Cavalry Regiment. [https://books.google.co.uk/books?id=UxhONAAACAAJ]

Atlas
*Stephen Hart (ed). Atlas of Armored Warfare: From 1916 to the Present Day. Metro Books. 2012. [https://search.worldcat.org/title/1391166759]. Atlas of Tank Warfare. [https://books.google.com/books?id=KWqppwAACAAJ]

Armored forces
*Ogorkiewicz. Armoured Forces: A History of Armoured Forces and Their Vehicles. 1970. [https://books.google.co.uk/books?id=qIHfAAAAMAAJ]

==Mesoamerica==
*James. Aztecs &amp; Maya: The Ancient Peoples of Middle America. Tempus. 2001. 2005. History Press. [https://books.google.co.uk/books?id=XOXNhTY6TCYC 2009]. Reviews: &quot;Books Received&quot; (2003) [https://books.google.co.uk/books?id=3dozAQAAIAAJ 14] Minerva 57 (No 1); and &quot;Overviews for the general reader&quot; (2002) [https://books.google.co.uk/books?id=qShmAAAAMAAJ 76] Antiquity 252.
*Weaver. The Aztecs, Maya, and Their Predecessors. 1972. 2nd Ed: 1981: [https://books.google.co.uk/books?id=0mQkAQAAIAAJ] [https://books.google.com/books?id=OWQkAQAAIAAJ]

==Accounting==
See [[s:Category:Accounting]]

Periodicals
*[[s:The Accountant|The Accountant]] (1874 onwards)
*Accountant's Magazine (1897 onwards) Aberdeen

==Arts==
*Murray (ed).The Hutchinson Dictionary of the Arts. Helicon Publishing. 1994. Paperback Ed: 1995. Reprinted 1997.

==Biography==
*Parke. Biography: Writing Lives. 2002 [https://books.google.co.uk/books?id=6bAz2K98MeYC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Caine. Biography and History. (Theory and History). 1st Ed: 2010, 2nd Ed: 2019 [https://books.google.co.uk/books?id=h3dvDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Periodicals
*Biography. Biography: An Interdisciplinary Quarterly. 1978 onwards. Published by the University Press of Hawaii for the Biographical Research Center. [https://books.google.co.uk/books?id=s84ZAAAAYAAJ]
*Biography News. 1974 to 1975. Gale Research Company. [https://books.google.co.uk/books?id=RRsXAQAAIAAJ]

Yearbooks
*Current Biography Yearbook [https://books.google.com/books?id=Zcml63jalMIC]
*Dictionary of Literary Biography Yearbook [https://books.google.com/books?id=gNNlAAAAMAAJ]

==Information technology==
*Haynes, David (ed). Information Sources in Information Technology. (Guides to Information Sources). Bowker Saur. 1990. [https://books.google.co.uk/books?id=0hYjAAAAQBAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]

==Economics==
General series:
*Dryden Press Series in Economics
*Hurl, Bryan (ed). Studies in the UK Economy. Heinemann Educational
*Nuffield Economics &amp; Business. Nuffield Foundation. Longman.

Other:
*Bannock, Baxter and Davis. The Penguin Dictionary of Economics. Penguin Books. 4th Ed: 1987. Bannock, Baxter and Rees. 1972. 2nd Ed: 1978. 3rd Ed: 1984.

*Begg, Fischer and Dornbusch. Economics. McGraw Hill. 1984. 2nd Ed: 1987. 3rd Ed: 1991.
*Anderton, Alain. Economics. Causeway Press. 1991.
*Maile, Roger. Economics. (Core Business Studies). Mitchell Beazly. 1983.
*Maunder, Myers, Wall and Miller. Economics Explained. Collins Educational. 1987. 2nd Ed: 1991.
*Tibbitt, Andrew. A guide to A Level Economics. Thomas Nelson and Sons. 1986.

*Lipsey, Richard G. An Introduction to Positive Economics. Weidenfeld and Nicolson. 1963. 2nd Ed: 1966. 3rd Ed: 1971. 4th Ed: 1975. 5th Ed: 1979. 6th Ed: 1983. 7th Ed: 1989.

*Nicolson, Walter. Microeconomic Theory: Basic Principles and Extensions. (Dryden Press Series in Economics). Dryden Press, Holt-Saunders. 3rd Ed: 1985. 

*Caves and Jones. World Trade and Payments: An Introduction. Little, Brown and Company. 1973. 1977. 3rd Ed: 1981.

*National Institute of Economic and Social Research. The UK economy. (Studies in the UK Economy). Heinemann Educational. 1990.
*Smith, Charles. UK trade and sterling. (Studies in the UK Economy). Heinemann Educational. 1992.

==Games==
Chess
*Hooper and Whyld. The Oxford Companion to Chess. Oxford University Press. 1984. Paperback: 1987.
*Golombek, Harry. The Game of Chess. 1954. 2nd Ed: 1963. 3rd Ed: 1980.
*Pritchard, D. Brine. The Right Way to Play Chess. 1950. 8th Ed: 1971. 10th Ed: 1974. 11th Ed: 1977.
*Horowitz, Al. From Morphy to Fischer: A history of the World Chess Championship. B T Batsford. 1973. The World Chess Championship: A History. Macmillan. 1973. 

General series
*Batsford Chess Books
**Discovering Chess Series. B T Batsford.

Periodicals

See [[Universal Bibliography/Periodicals#Chess|Periodicals, Chess]]
*British Chess Magazine

Othello
*Goro Hasegawa with Maxine Brady. How to Win at Othello. (A Harvest/HBJ book). Jove Publications. 1977. ISBN 0-15-642215-8. [https://books.google.co.uk/books?id=mTdhlwVeyCcC]

Wargames
*Battleground. Tyne Tees. (ITV). 1978. [Television]. 6 episodes, with Edward Woodward.
**Laurie Taylor. &quot;Attila the Hun invades Tyne Tees&quot;. TV Times. 1978. pp 28 &amp; 29.
**Terry Wise. &quot;Battleground&quot;. Battle for Wargamers. June 1978. pp 261 &amp; 262.
*[[w:Game of War|Game of War]]. Channel 4. 1997. [Television].

==Toys==
Periodicals
*Games &amp; Toys: The Leading Trade Journal for Home &amp; Export. (H Richard Simmons Limited). [https://books.google.co.uk/books?id=pMmbZ_JTnXYC] Google: editions:UO8GID_4Ck0C
*Toys and Novelties. (Sporting Goods Pub Co). [https://books.google.co.uk/books?id=zKdAAQAAMAAJ] [https://archive.org/details/toys-and-novelties-volume-9-1913/page/n53/mode/1up] (Toys and Novelties Publishing Company) [https://archive.org/details/toys-and-novelties-volume-19-issue-no.-1-6-january-june-1922/page/n173/mode/1up]. Cf. &quot;Harcourt To Buy Journals From Haire Publishing Co&quot; [https://books.google.co.uk/books?id=J7hEAQAAIAAJ 194] Publishers Weekly 29
*[[w:Playthings (magazine)|Playthings: The National Magazine of the Toy Trade]]. (McCready Publishing Co) [https://books.google.co.uk/books?id=eCQHzuYWDY4C] [https://books.google.co.uk/books?id=mnRO5WFXDfEC]. (Geyer-McAllister Publications). Cf. &quot;Playthings bought by Geyer-McAllister&quot; [https://books.google.co.uk/books?id=itAaAQAAMAAJ 52] Industrial Marketing

==Cricket==
See [[w:Bibliography of cricket]]

*Peter Arnold and Peter Wynne-Thomas. The Complete Encyclopedia of Cricket. 2006. 4th Ed: 2011: [https://books.google.co.uk/books?id=2R_pXwAACAAJ].
**Peter Arnold. The Illustrated Encyclopedia of World Cricket.
*Morgan. The Encyclopedia of World Cricket. 2007. [https://books.google.co.uk/books?id=gFCbkgEACAAJ]

Scores and biographies
*Marylebone Club Cricket Scores and Biographies. [https://books.google.co.uk/books?id=dl8IAAAAQAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
**See [[w:Arthur Haygarth]] and [[w:Fred Lillywhite]]

Periodicals
*[[w:Cricket: A Weekly Record of the Game|Cricket: A Weekly Record of the Game]]. [https://books.google.co.uk/books?id=eX9QAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false].

Australia
*Malcolm Andrews. The Encyclopaedia of Australian Cricket. 1980. [https://catalogue.nla.gov.au/Record/1531463]
*The Oxford Companion to Australian Cricket

India 
*The Encyclopaedia of Indian Cricket, 1965. [https://books.google.com/books?id=CE4Joad6iwAC] [Includes biographies]

Annuals
*[[w:Indian Cricket (annual)|Indian Cricket]].  [https://books.google.co.uk/books?id=ioRLAAAAYAAJ 1966].

===Cricketers===
Cricketers, including biographical dictionaries and collections of biographies
*[[w:ESPNcricinfo|ESPNcricinfo]]
*[[w:CricketArchive|CricketArchive]]

*John Arlott's Book of Cricketers. 1979. [https://books.google.co.uk/books?id=8-WBAAAAMAAJ]

*World Cricketers: A Biographical Dictionary [https://books.google.com/books?id=IpBLAAAAYAAJ]
*Carr's Dictionary of Extraordinary Cricketers. 1977. Aurum Press. 2005. [https://books.google.com/books?id=CfwsAAAACAAJ]

*Sproat. Debrett's Cricketers' Who's Who. 1980.
*S Canynge Caple. The Cricketer's Who's Who. Williams. Lincoln. 1934.
*Cricket Who's Who: The Cricket Blue Book. 1909. [https://catalogue.nla.gov.au/Record/119715]. 1912. Bibliography: [https://books.google.co.uk/books?id=IjQyAQAAMAAJ]

*Who's Who in Test Cricket: A Biographical Dictionary of Test Cricketers [https://books.google.com/books?id=5uF5PQAACAAJ]

*Frindall. England Test Cricketers: The Complete Record from 1877. 1989. [https://books.google.com/books?id=2zHYLIW7h9UC]
*Brooke. The Collins Who's Who of English First-Class Cricket, 1945-1984. 1985. [https://books.google.com/books?id=NGSPAAAACAAJ]. Review: [https://books.google.co.uk/books?id=iHMsAAAAYAAJ]. Commentary: [https://books.google.co.uk/books?id=wPg5AQAAIAAJ]

Gloucestershire
*Gloucestershire Cricketers, 1870-1979. (ACS Cricketers Series [https://archive.acscricket.com/cricketers_series/index.html]). The Association of Cricket Statisticians. Cleethorpes. 1979. [https://archive.acscricket.com/cricketers_series/gloucestershire_cricketers_1870-1979/index.html]
*Rex Pogson. Gloucestershire Cricket and Cricketers, 1919-1939. Lytham St Annes. 1944. Catalogues: [https://catalogue.nla.gov.au/Record/850643] [https://books.google.co.uk/books?id=CS83vXlB1ZIC] [https://www.worldcat.org/title/504354999]. Also printed as microfilm: [https://books.google.co.uk/books?id=iqXeDTKUEl4C].
*Dean Hayes. Gloucestershire Cricketing Greats: 46 of the Best Cricketers for Gloucestershire. Tunbridge Wells. 1990. Catalogues: [https://books.google.co.uk/books?id=OmsqAQAAIAAJ] [https://www.worldcat.org/title/25202795]

Australia
*The A-Z of Australian Cricketers [https://books.google.com/books?id=w-0zAAAACAAJ]
*Piesse. Encyclopedia of Australian Cricket Players. 2012. [https://books.google.com/books?id=Jsh4MAEACAAJ]
*C P Moody. Australian Cricket and Cricketers 1856-1893-4. Melbourne. 1894.
*Jack Pollard. Australian Cricket: The Game and the Players. Hodder and Stoughton. ABC Books. Sydney. Lane Cove, New South Wales. 1982. Angus &amp; Robertson. London. North Ryde, New South Wales. Sydney. Revised Ed: 1988. Commentary: [https://books.google.co.uk/books?id=WotYAAAAYAAJ]. Review: [https://books.google.co.uk/books?id=KzNYAAAAMAAJ].

==Geology==
*Read and Watson. Introduction to Geology. Macmillan Education. 1962. 2nd Ed: 1968. Volume 1: Principles. Volume 2: Earth History.

==Mineralogy==
*Bibliography of Mineralogy for 1886. Annual Report of the Board of Regents of the Smithsonian Institution. Year Ending 30 June 1887. 1889. Pages [https://books.google.co.uk/books?id=wDcWAAAAYAAJ&amp;pg=PA473#v=onepage&amp;q&amp;f=false 473] to 476.

*Battey, Maurice Hugh. Mineralogy for students. Oliver &amp; Boyd. 1972. 2nd Ed. Longman. 1981.

==Paper==
See [[s:Category:Paper]]

*Surface. Bibliography of the Pulp and Paper Industries. Forest Service. Bulletin 123. 1913. [https://archive.org/details/bibliographyofpu12surf]
*West. Reading List on Papermaking Materials. 1920 to 1921. [https://archive.org/details/readinglistonpa00westgoog] [https://archive.org/details/readinglistonpa01westgoog]

==Books==
*British Book News [https://books.google.co.uk/books?id=2oFTAAAAIAAJ]
*Australasian Book News and Literary Journal. Australasian Book News and Library Journal. [https://books.google.co.uk/books?id=QVQPAQAAIAAJ]

*Book News. 1882 to 1918. (John Wanamaker). Called &quot;Book News Monthly&quot; from 1906. [https://books.google.co.uk/books?id=KtwRAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Stechert-Hafner Book News [https://books.google.co.uk/books?id=BmDqAAAAMAAJ]
*U.S.A. Book News [https://books.google.co.uk/books?id=36gVAQAAIAAJ]
*Branch Library Book News. [https://books.google.co.uk/books?id=NM8aAAAAMAAJ]

*Hungarian Book Review [https://books.google.co.uk/books?id=6U85AQAAIAAJ]
*Soviet Book News. (Earl Browder). 1947 [https://books.google.co.uk/books?id=QrXQ6LYSOF4C]

*Miniature Book News. [https://books.google.co.uk/books?id=MascAQAAMAAJ]

Rare
*Berger. Rare Books and Special Collections. American Library Association. 2014. [https://books.google.co.uk/books?id=IFUangEACAAJ]

Printed
*Annual Bibliography of the History of the Printed Book and Libraries. [https://books.google.co.uk/books?id=GLigoebhrd8C&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 30] [https://books.google.co.uk/books?id=UBN-IUZlF4gC&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 31]

==Paperback and Paperbound==
*Swados, &quot;Paper Books: What do they Promise?&quot; (1953) [https://books.google.co.uk/books?id=TwaJtQzwj1gC 173] The Nation 114
*Wagman, &quot;The Paperbound Book Business&quot; (1957) 9 Michigan Business Review [https://books.google.co.uk/books?id=9pA8uolQjnkC&amp;pg=RA4-PA9#v=onepage&amp;q&amp;f=false 9] (No 5, November)

==Science==
*Lafferty and Rowe. The Hutchinson Dictionary of Science. Helicon Publishing. 1993. 2nd Ed: 1998.

==Entertainment==
*The Directory (The Times, 1996 onwards) Commentary: [https://www.marketingweek.com/as-times-starts-listings-supplement/]

==Comedy and tragedy==
*E H Mikhail. Comedy and Tragedy: A Bibliography of Critical Studies. 1972. [https://books.google.co.uk/books?id=5bgEAAAAMAAJ]

===Comedy===
*James E Evans. Comedy: An Annotated Bibliography of Theory and Criticism. 1987. [https://books.google.co.uk/books?id=s9ZgthAs1t8C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Meghan Duffy (ed). Daniel Gerould (senior ed). Comedy: A Bibliography of Critical Studies in English on the Theory and Practice of Comedy in Drama, Theatre, and Performance. New York. 2006. [https://books.google.co.uk/books?id=fI0jAQAAIAAJ]
*David Humphrey. The Time of Laughter: Comedy and the Media Cultures of Japan. University of Michigan Press. 2023. [https://books.google.co.uk/books?id=CkTLEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

==Radio and television==
*William E McCavitt. Radio and Television: A Selected Annotated Bibliography. Scarecrow Press. 1978. [https://books.google.com/books?id=DAQVAQAAIAAJ]
*Gertrude G Broderick. Radio and Television Bibliography. Bulletin 1948 No 17. [https://books.google.co.uk/books?id=yIPP1dsmNtAC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
*Patricia Beall Hamill. Radio and Television: A Selected Bibliography. Bulletin 1960 No 25. [https://books.google.co.uk/books?id=AJhGAQAAMAAJ&amp;pg=PP3#v=onepage&amp;q&amp;f=false]

==Film and television==
*Jean Mitry. Bibliographie internationale du cinéma et de la télévision. 1966 onwards. [https://books.google.co.uk/books?id=SC3gAAAAMAAJ] Commentary: A Reference Guide for English Studies, [https://books.google.co.uk/books?id=h_wfYKnMfOkC&amp;pg=PA439#v=onepage&amp;q&amp;f=false p 439].

==Animation==
*John Halas and Roger Manvell. The Technique of Film Animation. 4th Ed: 1976. Focal Press. ISBN 0240509005.
*Clements and McCarthy. The Anime Encyclopedia. 3rd Rev Ed: [https://books.google.co.uk/books?id=E03KBgAAQBAJ&amp;pg=PA1958#v=onepage&amp;q&amp;f=false].

==Colours==
*Eiseman and Recker. Pantone: The 20th Century in Color. [https://books.google.co.uk/books?id=j3H7nSVS3UMC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. Reviews: [https://www.theguardian.com/books/2011/nov/13/pantone-20th-century-color-review][https://www.theatlantic.com/entertainment/archive/2011/11/pantone-100-years-of-color/249016/][https://eu.vvdailypress.com/story/lifestyle/health-fitness/2012/01/16/color-reel-20th-century-s/37119883007/]

==Bilateral==
Britain and Japan
*Pearse. Companion to Japanese Britain and Ireland. In Print. 1991. [https://books.google.co.uk/books?id=KtAxAAAAIAAJ]

==Prehistoric life==
Prehistoric animals
*[[w:Michael Benton|Michael Benton]]. Prehistoric Animals: An A-Z Guide. Kingfisher Books. 1989. Derrydale Books, New York. 1989. [Illustrations: Jim Channell and Kevin Maddison.]
*Ellis Owen. Prehistoric Animals: The Extraordinary Story of Life before Man. Octopus Books Limited. London. 1975. [Sculptures: Arthur Hayward.] Review: [https://books.google.co.uk/books?id=II-B8R-8Ov8C 17] Wildlife 422. Commentary: [https://books.google.co.uk/books?id=aUbYAAAAQBAJ&amp;pg=PA269#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=jFNBAAAAIBAJ&amp;pg=PA5#v=onepage&amp;q&amp;f=false].
**Prehistorische dieren: de geschiedenis van het leven vóór de mens. Translated by JJ Hoedeman. In den Toren, Baarn. Westland, Schoten. 1977.  Commentary: [https://books.google.co.uk/books?id=ToVMAQAAIAAJ]
**Les Animaux préhistoriques: l'extraordinaire histoire de la vie avant l'homme.

Dinosaurs
*Michael Benton. Dinosaurs: An A-Z Guide. Kingfisher Books. 1988. Derrydale Books, New York. 1988. [Illustrations: Jim Channell and Kevin Maddison.]

==Continents==
*John J W Rogers and M Santosh. Continents and Supercontinents. 2004. [https://books.google.co.uk/books?id=CI9Ig7DGvTMC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

===Asia===

*Winston L Y Yang and Teresa S Yang. Asian Resources in American Libraries: Essays and Bibliographies. 1968. [https://books.google.com/books?id=76OkUAbkd4oC]
*Noriko Asato (ed). Handbook for Asian Studies Specialists: A Guide to Research Materials and Collection Building Tools. Libraries Unlimited. 2013. [https://books.google.co.uk/books?id=jkzEEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. Review: [https://www.emerald.com/rr/article-abstract/29/3/51/335520/Handbook-for-Asian-Studies-Specialists-A-Guide-to].

Periodicals
*Asian Bibliography [https://books.google.co.uk/books?id=EDq22yvuCb4C]

Asian studies and languages
*Pauline Haldane. Bibliography of Asian Studies and Languages. 1990. [https://books.google.com/books?id=9pQLAQAAIAAJ]

Asian studies
*Bibliography of Asian Studies. Association for Asian Studies. [https://books.google.co.uk/books?id=7NskAAAAMAAJ 1974].
*Cumulative Bibliography of Asian Studies, 1941-1965. GK Hall &amp; Co. [https://books.google.co.uk/books?id=p_UqAAAAMAAJ]
**Cumulative Bibliography of Asian Studies, 1966-1970. GK Hall &amp; Co. [https://books.google.com/books?id=Tg8rAAAAMAAJ]

East Asia
*G Raymond Nunn. East Asia: A Bibliography of Bibliographies. (Occasional Papers of East-West Center Library, No 7). Honolulu. 1967. [https://books.google.co.uk/books?id=XWOTAAAAIAAJ]
*East Asia: A Selected Functional Bibliography. Foreign Service Institute, Center for Area and Country Studies. [https://books.google.co.uk/books?id=ByXkdOpCwF8C&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*Donald Gillin. East Asia: A Bibliography for Undergraduate Libraries. [https://books.google.co.uk/books?id=Q7cIAAAAIAAJ]
*Thomas C Kuo and John W Chiang. East Asian Periodicals and Serials: A Descriptive Bibliography [https://books.google.co.uk/books?id=eA1GAAAAMAAJ]
*Bibliographic Guide to East Asian Studies. [https://books.google.co.uk/books?id=t7WFAAAAIAAJ 1996].

====Far East====
Bibliography
*Kuniyoshi. Far East. (PACAF Basic Bibliographies). 1957. [https://books.google.co.uk/books?id=Q5TLdCbP2HcC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]

====Japan and Korea====
Bibliography
*Bernard S Silberman. Japan and Korea: A Critical Bibliography. University of Arizona Press. 1962. [https://books.google.co.uk/books?id=y6UIAAAAIAAJ]
*Frank J Shulman. Japan and Korea: An Annotated Bibliography of Doctoral Dissertations in Western Languages 1877-1969. American Library Association. 1970. Routledge. 2013. [https://books.google.co.uk/books?id=xs62AQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

====South Asia====
*South Asian Bibliography: A Handbook and Guide. Harvester Press. [https://books.google.co.uk/books?id=aqwNAQAAIAAJ]
*The Bibliography of South Asian Periodicals: A Union-list of Periodicals in South Asian Languages. Harvester Press. [https://books.google.co.uk/books?id=COV0nIUK0bgC]

==Culture and society==
*Victoria Lyon Bestor, Theodore C Bestor and Akiko Yamagata (eds). Routledge Handbook of Japanese Culture and Society. 2011. [https://books.google.co.uk/books?id=0cBYffHp5L4C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Josef Kreiner and Hans-Dieter Ölschleger (eds). Japanese Culture and Society: Models of Interpretation. 1996. [https://books.google.co.uk/books?id=6skwAQAAIAAJ]
*Dolores P Martinez. Modern Japanese Culture and Society. 2007. [https://books.google.co.uk/books?id=l6kMAQAAMAAJ vol 1]
*C Andrew Gerstle. 18th Century Japan: Culture and Society. 1989. [https://books.google.co.uk/books?id=ViglDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Periodicals
*Review of Japanese Culture and Society [https://books.google.co.uk/books?id=W_o-AQAAIAAJ]

==See also==
*[[Bibliography]]

==Notes==
{{Reflist}}
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{| style=&quot;width:65%;&quot;
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This is a list of cases involving copyright law:

;Indian copyright law
* [[Wikiversity Law Reports/Gramophone Co v Shanti Films|Gramophone Co v Shanti Films]]
* [[Wikiversity Law Reports/Civic Chandran v Ammini Amma|Civic Chandran v Ammini Amma]]

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* [[Wikiversity:Page creation requests]]


===To study more later ===
* [[Cost of crony capitalism in the United States]]
* [[Set up a professional blog and YouTube channel]]
* [[Using the internet for learning and research]]
* [[Action research]]

* [[Web development]]

* [[Pursuing Collective Wisdom]]


generate me

== Discussion questions, essay ideas, and AI prompt ideas== section....
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      <text bytes="27280" sha1="bercjqktxmhusr47gqvz716g24nhk3g" xml:space="preserve">&lt;!--Knowledge Module 04: Pre-dive Activities (Sub-module 3 of 3)--&gt;
&lt;!--KM-04-KT03 Basic introduction to dive support vessels and ROV support--&gt;
''Relevance: Scuba diving(?), Surface supplied diving(?), Surface oriented wet bell diving.''

Required outcomes:
#&lt;!--IAC0301--&gt; Identify various vessel types
#&lt;!--IAC0302--&gt; Describe the principles of dynamic positioning and the hazards specific to DPV operations
#&lt;!--IAC0303--&gt; Discuss the role of dive support vessels (DSV’s)
#&lt;!--IAC0304--&gt; Discuss the principles of ROV support in diving operations

==Introduction to diving support locations==
&lt;!--See also IMCA D022 Chapter 8--&gt;
Divers may work from a wide range of support locations, both shore based and waterborne, and platforms that are supported by the bottom, but not in contact with the shore.
The type of support location will influence the operation in several ways, and must be considered during the planning stages with reference to the mode of diving required and equipment it will be possible or necessary to use. Access to the water is one of the issues that is most strongly affected by the details of the support location, and another is the feasibility of making heavy equipment available on site.

==Diving support vessel types==
&lt;!--IAC0301 Identify various vessel types--&gt;
{{see also|Wikipedia:Diving support vessel}}
[[File:Skandi Achiever - geograph.org.uk - 946023.jpg|thumb|DSV Skandi Achiever in Aberdeen]]
A diving support vessel is a ship that is used as a floating base for professional diving projects.

===History===
Commercial Diving Support Vessels emerged during the 1960s and 1970s, when the need arose for diving operations to be performed below and around oil production platforms and associated installations in open water in the North Sea and Gulf of Mexico. Until that point, most diving operations were from mobile oil drilling platforms, pipe-lay, or crane barges. The diving system tended to be modularised and craned on and off the vessels as a package.

As permanent oil and gas production platforms emerged, the owners and operators were not keen to give over valuable deck space to diving systems because after they came on-line the expectation of continuing diving operations was low.

However, equipment fails or gets damaged, and there was a regular if not continuous need for diving operations in and around oil fields. The solution was to put diving packages on ships. Initially these tended to be oilfield supply ships or fishing vessels; however, keeping this kind of ship 'on station', particularly during uncertain weather, made the diving dangerous, problematic and seasonal. Furthermore, seabed operations usually entailed the raising and lowering of heavy equipment, and most such vessels were not equipped for this task.

This is when the dedicated commercial diving support vessel emerged. These were often built from scratch or heavily converted pipe carriers or other utility ships. The key components of the diving support vessel are:
*Dynamic Positioning - Controlled by a computer with input from position reference systems (DGPS, Transponders, Light Taut Wires or RadaScan), it will maintain the ships position over a dive site by using multi-directional thrusters, other sensors would compensate for swell, tide and prevailing wind.
*Saturation diving system - For diving operations below 50m, a mixture of helium and oxygen (heliox) is required to eliminate the narcotic effect of nitrogen under pressure. For extended diving operations at depth, saturation diving is the preferred approach. A saturation system would be installed within the ship. A diving bell would transport the divers between the saturation system and the work site lowered through a 'moon pool' in the bottom of the ship, usually with a support structure 'cursor' to support the diving bell through the turbulent waters near the surface. There are a number of support systems for the saturation system on a Diving Support Vessel, usually including a Remotely Operated Vehicle Remotely operated underwater vehicle (ROV) and heavy lifting equipment.

===Modern diving support vessels===
[[File:DSV Curtis Marshall.JPG|thumb|right|The 2015 launched DSV Curtis Marshall]]
Most of the vessels currently in the North Sea were built in the 1980s. The semi-submersible fleet, the Uncle John and similar, have proven to be too expensive to maintain and too slow to move between fields. Therefore, most existing designs are monohull vessels with either a single or a twin bell dive system. There has been little innovation since the 1980s. However, driven by high oil prices since 2004, the market for subsea developments in the North Sea grew significantly. This led to a scarcity of Diving Support Vessels and drove the price up, so contractors ordered a number of new-build vessels which were expected to enter the market in about 2008.

===Comparison between position-keeping options===
Methods of position-keeping include dynamic positioning, the use of an anchor spread and the use of a jack-up barge. All have their advantages and disadvantages.
{| class=&quot;wikitable&quot; style=&quot;width:100%&quot;
! colspan=&quot;3&quot; | '''Comparison of position-keeping options'''
|-
| style=&quot;;width:33.3%;text-align:center&quot;|'''Jack-up barge'''
| style=&quot;width:33.3%;text-align:center&quot;|'''Anchoring'''
| style=&quot;width:33.3%;text-align:center&quot;|'''Dynamic positioning'''
|-
| style=&quot;vertical-align:top&quot;|'''Advantages:'''
*No complex systems with thrusters, extra generators and controllers.
*No chance of running off position by system failures or blackouts.
*No underwater hazards from thrusters.
| style=&quot;vertical-align:top&quot;|'''Advantages:'''
*No complex systems with thrusters, extra generators and controllers.
*No chance of running off position by system failures or blackouts.
*No underwater hazards from thrusters.
| style=&quot;vertical-align:top&quot;|'''Advantages:'''
*Maneuverability is excellent; it is easy to change position.
*No anchor handling tugs are required.
*Not dependent on water depth.
*Quick set-up.
*Not limited by obstructed seabed.
|-
| style=&quot;vertical-align:top&quot;|'''Disadvantages:'''
*No maneuverability once positioned.
*Limited to water depths of 175 meters or less.
| style=&quot;vertical-align:top&quot;|'''Disadvantages:'''
*Limited maneuverability once anchored.
*Anchor handling tugs are required.
*Less suitable in deep water.
*Time to anchor out varies between several hours to several days.
*Limited by obstructed seabed (pipelines, seabed).
| style=&quot;vertical-align:top&quot;|'''Disadvantages:'''
*Complex systems with thrusters, extra generators and controllers.
*High initial costs of installation.
*High fuel costs.
*Chance of running off position in case of strong currents or winds, or due to system failures or blackouts.
*Underwater hazards from thrusters for divers and Remotely operated underwater vehicles.
*Higher maintenance of the mechanical systems.
|}

Although all methods have their own advantages, dynamic positioning has made many operations possible that were not feasible before.

The costs are falling due to newer and cheaper technologies, and the advantages are becoming more compelling as offshore work enters ever deeper water and the environment is given more respect.

==Dynamic positioning==
&lt;!--IAC0302 Describe the principles of dynamic positioning and the hazards specific to DPV operations--&gt;
{{see also|Wikipedia:Dynamic positioning}}
[[Image:Toisa Perseus&amp;Discoverer Enterprise.jpg|thumb|300px|Offshore support vessel ''Toisa Perseus'' with, in the background, the fifth-generation deepwater drillship ''Discoverer Enterprise'', over the Thunder Horse Oil Field. Both are equipped with DP systems.]]

Dynamic positioning (DP) is a computer-controlled system to automatically maintain a vessel's position and heading by using its own propellers and thrusters. Position reference sensors, combined with wind sensors, motion sensors and gyrocompasses, provide information to the computer pertaining to the vessel's position and the magnitude and direction of environmental forces affecting its position. Examples of vessel types that employ DP include, ships and semi-submersible mobile offshore drilling units (MODU) and oceanographic research vessels.

The computer program contains a mathematical model of the vessel that includes information pertaining to the wind and current drag of the vessel and the location of the thrusters. This information, combined with the sensor input, allows the computer to calculate the required steering angle and output for each thruster. This allows operations at sea where mooring or anchoring is not feasible due to deep water, congestion on the sea bottom or other problems.

Dynamic positioning may either be absolute in that the position is locked to a fixed point over the bottom, or relative to a moving object like another ship or an underwater vehicle. One may also position the ship at a favorable angle towards wind, waves and current, called weathervaning.

Dynamic positioning is used by much of the offshore oil industry. There are currently (2017) more than 1800 DP ships.

=== Scope ===
A ship can be considered to have six degrees of freedom in its motion, i.e., it can move in any of six axes.

Three of these involve translation:
*surge (forward/astern along longitudinal axis)
*sway (starboard/port along transverse axis)
*heave (up/down along vertical axis)

and the other three rotation:
*roll (rotation about longitudinal axis)
*pitch (rotation about transverse axis)
*yaw (rotation about vertical axis)

Dynamic positioning is concerned primarily with control of the ship in the horizontal plane, i.e., the three axes: surge, sway and yaw.

=== Requirements ===
A ship that is to be used for DP requires:
*to maintain position and heading, first of all the position and heading need to be known.
*a computer control system to calculate the required control actions to maintain position and correct for position errors.
*thrust elements to apply forces to the ship as demanded by the control system.

The position reference systems and thrust elements must be carefully considered when designing a DP ship. In particular, for good control of position in adverse weather, the thrust capability of the ship in three axes must be adequate.

===Reference systems===

====Position reference systems====
There are several means to determine a ship's position at sea. Most traditional methods used for ships navigation are not accurate enough for some modern requirements. For that reason, several positioning systems have been developed during the past decades. Producers of DP systems include Marine Technologies LLC, Kongsberg Maritime, GE, DCNS, Wartsila, MT-div.Chouest, Rolls-Royce plc, Praxis Automation Technology and others.  The applications and availability depends on the type of work and water depth. The most common Position reference/Measuring systems /Equipment (PRS/PME) are:

[[Image:GPS Satellite NASA art-iif.jpg|thumb|GPS satellite in orbit.]]
*'''Differential Global Positioning System (DGPS)'''. The position obtained by GPS is not accurate enough for use by DP. The position is improved by use of a fixed ground-based reference station (differential station) that compares the GPS position to the known position of the station. The correction is sent to the DGPS receiver by long wave radio frequency. For use in DP an even higher accuracy and reliability is needed. Companies such as Veripos, Fugro or C-Nav supply differential signals via satellite, enabling the combination of several differential stations. The advantage of DGPS is that it is almost always available. Disadvantages include degradation of the signal by ionospheric or atmospheric disturbances, blockage of satellites by cranes or structures and deterioration of the signal at high altitudes. There are also systems installed on vessels that use various Augmentation systems, as well as combining GPS position with GLONASS.
*'''Acoustics'''. This system consists of one or more transponders placed on the seabed and a transducer placed in the ship's hull. The transducer sends an acoustic signal (by means of piezoelectric elements) to the transponder, which is triggered to reply. As the velocity of sound through water is known (preferably a soundprofile is taken regularly), the distance is known. Because there are many elements on the transducer, the direction of the signal from the transponder can be determined. Now the position of the ship relative to the transponder can be calculated. Disadvantages are the vulnerability to noise by thrusters or other acoustic systems. The use is limited in shallow waters because of ray bending that occurs when sound travels through water horizontally. Three types of HPR systems are commonly used:
**'''Ultra- or super- short base line, USBL or SSBL'''. This works as described above. Because the angle to the transponder is measured, a correction needs to be made for the ship's roll and pitch. These are determined by Motion Reference Units. Because of the nature of angle measurement, the accuracy deteriorates with increasing water depth.
**'''Long base line, LBL'''. This consists of an array of at least three transponders. The initial position of the transponders is determined by USBL and/ or by measuring the baselines between the transponders. Once that is done, only the ranges to the transponders need to be measured to determine a relative position. The position should theoretically be located at the intersection of imaginary spheres, one around each transponder, with a radius equal to the time between transmission and reception multiplied by the speed of sound through water. Because angle measurement is not necessary, the accuracy in large water depths is better than USBL.
**'''Short baseline, SBL'''. This works with an array of transducers in the ship's hull. These determine their position to a transponder, so a solution is found in the same way as with LBL. As the array is located on the ship, it needs to be corrected for roll and pitch.
*'''Riser Angle Monitoring'''. On drillships, riser angle monitoring can be fed into the DP system. It may be an electrical inclinometer or based on USBL, where a riser angle monitoring transponder is fitted to the riser and a remote inclinometer unit is installed on the Blow Out Preventer (BOP) and interrogated through the ship’s HPR.

[[Image:Light Taut Wire.JPG|thumb|Light taut wire on the ''HOS Achiever'']]
*'''Light taut wire, LTW or LWTW'''. The oldest position reference system used for DP is still very accurate in relatively shallow water. A clumpweight is lowered to the seabed. By measuring the amount of wire paid out and the angle of the wire by a gimbal head, the relative position can be calculated. Care should be taken not to let the wire angle become too large to avoid dragging. For deeper water the system is less favourable, as current will curve the wire. There are however systems that counteract this with a gimbal head on the clumpweight. Horizontal LTW’s are also used when operating close to a structure. Objects falling on the wire are a risk here.
*'''Fanbeam''' and '''CyScan'''. These are laser based position reference systems. They are very straightforward system, as only a small prism needs to be installed on a nearby structure or ship. Risks are the system locking on other reflecting objects and blocking of the signal. Range depends on the weather, but is typically more than 500 meters.
*'''Artemis'''. A radar-based system. A unit is placed on a nearby structure and aimed at the unit on board the ship. The range is several kilometres. Advantage is the reliable, all-weather performance. Disadvantage is that the unit is rather heavy.
*'''DARPS, Differential, Absolute and Relative Positioning System'''. Commonly used on shuttle tankers while loading from a [[Floating Production Storage and Offloading|FPSO]]. Both will have a GPS receiver. As the errors are the same for the both of them, the signal does not need to be corrected. The position from the FPSO is transmitted to the shuttle tanker, so a range and bearing can be calculated and fed into the DP system.
*'''RADius''' and '''RadaScan'''. These are radar based system, but have no moving parts as Artemis. Another advantage is that the transponders are much smaller than the Artemis unit. The range is typically 500 – 1000 meters.
*'''Inertial navigation''' is used in combination with any of the above reference systems, but typically with gnss (Global Navigation Satellite System) and Hydroacoustics (USBL, LBL, or SBL).

====Heading reference systems====
*'''Gyrocompasses''' are normally used to determine heading.

More advanced methods are:
*'''Ring-Laser gyroscopes'''
*'''Fibre optic gyroscopes'''
*'''Seapath''', a combination of GPS and inertial sensors.

====Sensors====
Besides position and heading, other variables are fed into the DP system through sensors:
*'''Motion reference units, vertical reference units or vertical reference sensors, VRUs or MRUs or VRSs''', determine the ship's roll, pitch and heave.
*'''Wind sensors''' are fed into the DP system feedforward, so the system can anticipate wind gusts before the ship is blown off position.
*'''Draught sensors''', since a change of draught influences the effect of wind and current on the hull.
*Other sensors depend on the kind of ship. A pipelay ship may measure the force needed to pull on the pipe, large crane vessels will have sensors to determine the cranes position, as this changes the wind model, enabling the calculation of a more accurate model (see Control systems).
*Some external forces are not directly measured.  In these cases, the offset force is deduced over a period of time, allowing an average value of compensating thrust to be applied. All forces not attributable to direct measurement are lavelled &quot;current&quot;, as this is what they are assumed to be, but in reality this is a combination of current, waves, swell, and any errors in the system.  As is traditional in the maritime industry, DP &quot;current&quot; is always recorced in the direction that it is flowing towards.

===Control systems===
In the beginning PID controllers were used and today are still used in the simpler DP systems. But modern controllers use a mathematical model of the ship that is based on a hydrodynamic and aerodynamic description concerning some of the ship's characteristics such as mass and drag. Of course, this model is not entirely correct. The ship's position and heading are fed into the system and compared with the prediction made by the model. This difference is used to update the model by using Kalman filtering technique. For this reason, the model also has input from the wind sensors and feedback from the thrusters. This method even allows not having input from any PRS for some time, depending on the quality of the model and the weather. This process is known as dead reckoning.

The accuracy and precision of the different PRSs is not the same. While a DGPS has a high accuracy and precision, a USBL can have a much lower precision. For this reason, the PRS’s are weighted. Based on variance a PRS receives a weight between 0 and 1.

===Power and propulsion systems===
To maintain position azimuth thrusters (electric, L-drive or Z-drive) bow thrusters, stern thrusters, water jets, rudders and propellers are used. DP ships are usually at least partially diesel-electric, as this allows a more flexible set-up and is better able to handle the large changes in power demand, typical for DP operations. These fluctuations may be suitable for hybrid operation. An LNG-powered platform supply vessel started operation in 2016 with a 653 kWh/1600 kW battery acting as spinning reserve during DP2, saving 15-30% fuel.

The set-up depends on the DP class of the ship. A Class 1 can be relatively simple, whereas the system of a Class 3 ship is quite complex. On Class 2 and 3 ships, all computers and reference systems should be powered through an uninterruptible power supply (UPS).

===Class requirements===
Based on International Maritime Organization (IMO) publication 645&gt; the Classification Societies have issued rules for Dynamic Positioned Ships described as Class 1, Class 2 and Class 3.
*Equipment Class 1 has no redundancy. Loss of position may occur in the event of a single fault.
*Equipment Class 2 has redundancy so that no single fault in an active system will cause the system to fail. Loss of position should not occur from a single fault of an active component or system such as generators, thruster, switchboards, remote controlled valves etc., but may occur after failure of a static component such as cables, pipes, manual valves etc.
*Equipment Class 3 which also has to withstand fire or flood in any one compartment without the system failing. Loss of position should not occur from any single failure including a completely burnt fire sub division or flooded watertight compartment.

Classification Societies have their own Class notations:

{| class=&quot;wikitable&quot;
|- style=&quot;vertical-align:top&quot;
|style=&quot;background:#DDDDDD;{{text default color}};&quot;| Description ||style=&quot;background:#DDDDDD;{{text default color}};&quot;| IMO&lt;br&gt;Equipment Class||style=&quot;background:#DDDDDD;{{text default color}};&quot;| LR&lt;br&gt;Equipment Class ||style=&quot;background:#DDDDDD;{{text default color}};&quot;| DNV&lt;br&gt;Equipment Class ||style=&quot;background:#DDDDDD;{{text default color}};&quot;| GL&lt;br&gt;Equipment Class||style=&quot;background:#DDDDDD;{{text default color}};&quot;| ABS&lt;br&gt;Equipment Class||style=&quot;background:#DDDDDD;{{text default color}};&quot;| NKK&lt;br&gt;Equipment Class||style=&quot;background:#DDDDDD;{{text default color}};&quot;| BV&lt;br&gt;Equipment Class
|-
| style=&quot;background:#EEEEEE;{{text default color}};&quot;| Manual position control and automatic heading control under specified maximum environmental conditions || - || DP(CM) || DYNPOS-AUTS || - || DPS-0 || -
|-
|- style=&quot;vertical-align:top&quot;
| style=&quot;background:#EEEEEE;{{text default color}};&quot;| Automatic and manual position and heading control under specified maximum environmental conditions || Class 1 || DP(AM) || DYNPOS-AUT &amp; DPS1|| DP 1 || DPS-1 || DPS A || DYNAPOS AM/AT
|-
|- style=&quot;vertical-align:top&quot;
| style=&quot;background:#EEEEEE;{{text default color}};&quot;| Automatic and manual position and heading control under specified maximum environmental conditions, during and following any single fault excluding loss of a compartment. (Two independent computer systems). || Class 2 || DP(AA) || DYNPOS-AUTR &amp; DPS2 || DP 2 || DPS-2 || DPS B || DYNAPOS AM/AT R
|-
|- style=&quot;vertical-align:top&quot;
| style=&quot;background:#EEEEEE;{{text default color}};&quot;| Automatic and manual position and heading control under specified maximum environmental conditions, during and following any single fault including loss of a compartment due to fire or flood. (At least two independent computer systems with a separate backup system separated by A60 class division). || Class 3 || DP(AAA) || DYNPOS-AUTRO &amp; DPS3 || DP 3 || DPS-3 || DPS C || DYNAPOS AM/AT RS
|}
DNV rules 2011 Pt6 Ch7 introduced &quot;DPS&quot; series of classification to compete with ABS &quot;DPS&quot; series.

===NMA===
Where IMO leaves the decision of which class applies to what kind of operation to the operator of the DP ship and its client, the Norwegian Maritime Authority(NMA) has specified what Class should be used in regard to the risk of an operation. In the NMA Guidelines and Notes No. 28, enclosure A four classes are defined:

*Class 0 Operations where loss of position keeping capability is not considered to endanger human lives, or cause damage.
*Class 1 Operations where loss of position keeping capability may cause damage or pollution of small consequence.
*Class 2 Operations where loss of position keeping capability may cause personnel injury, pollution, or damage with large economic consequences.
*Class 3 Operations where loss of position keeping capability may cause fatal accidents, or severe pollution or damage with major economic consequences.

Based on this the type of ship is specified for each operation:
*Class 1 DP units with equipment class 1 should be used during operations where loss of position is not considered to endanger human lives, cause significant damage or cause more than minimal pollution.
*Class 2 DP units with equipment class 2 should be used during operations where loss of position could cause personnel injury, pollution or damage with great economic consequences.
*Class 3 DP units with equipment class 3 should be used during operations where loss of position could cause fatal accidents, severe pollution or damage with major economic consequences.

===Redundancy===
Redundancy is the ability to withstand, while on DP mode, the loss of equipment which is online, without losing position and/or heading. A single failure can be, amongst others:
*Thruster failure
*Generator failure
*Power bus failure (when generators are combined on one power bus)
*Control computer failure
*Position reference system failure
*Reference system failure

For certain operations redundancy is not required. For instance, if a survey ship loses its DP capability, there is normally no risk of damage or injuries. These operations will normally be done in Class 1.

For other operations, such as diving and heavy lifting, there is a risk of damage or injuries. Depending on the risk, the operation is done in Class 2 or 3. This means at least three Position reference systems should be selected. This allows the principle of voting logic, so the failing PRS can be found. For this reason, there are also three DP control computers, three gyrocompasses, three MRU’s and three wind sensors on Class 3 ships. If a single fault occurs that jeopardizes the redundancy, i.e., failing of a thruster, generator or a PRS, and this cannot be resolved immediately, the operation should be abandoned as quickly as possible.

To have sufficient redundancy, enough generators and thrusters should be on-line so the failure of one does not result in a loss of position. This is left to the judgment of the DP operator. For Class 2 and Class 3 a Consequence Analysis should be incorporated in the system to assist the DPO in this process.

The redundancy of a DP ship should be judged by a failure mode and effects analysis (FMEA) study and proved by FMEA trials. Besides that, annual trials are done and normally DP function tests are completed prior to each project.

===DP operator===
The DP operator (DPO) judges whether there is enough redundancy available at any given moment of the operation. IMO issued MSC/Circ.738 (Guidelines for dynamic positioning system (DP) operator training) on 24-06-1996. This refers to IMCA (International Marine Contractors Association) M 117 as acceptable standard.

===IMCA===
The International Marine Contractors Association was formed in April 1995 from the amalgamation of AODC (originally the International Association of Offshore Diving Contractors), founded in 1972, and DPVOA (the Dynamic Positioning Vessel Owners Association), founded in 1990. It represents offshore, marine and underwater engineering contractors.

==Role of diving support vessels==
&lt;!--IAC0303 Discuss the role of dive support vessels (DSV’s)--&gt;

==ROV support in diving operations==
&lt;!--IAC0304 Discuss the principles of ROV support in diving operations--&gt;

{{CourseCat}}</text>
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  <page>
    <title>Scientific Reward System</title>
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      <contributor>
        <username>Michael Ten</username>
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      <comment>added == Discussion Questions, Essay Ideas, and AI Prompt Ideas ==</comment>
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      <text bytes="3575" sha1="1vdxgdfa5rvy2moaz08j0jeu9meo389" xml:space="preserve">This learning resource is about the scientific reward system. To learn about some systemic drivers of scientific innovation beside the intrinsic motivation of scientist to solve problems and explore the unknown structures e.g. with an experimental design.

* Number scientific publications (impact factor of journals and publication in peer-reviewed journals)
* Number grants and amount of funding
* number of awards provided by institutions, organisations or governments in recognition of technical, social, cultural or scientific advances (e.g. the [[w:Nobel prize|Nobel Prize]]).

== Learning Task ==
This learning task is for scientists that want to step back and look at drivers for their own scientific innovation: 
* How does the reward system influence your decisions to create proposal and form teams with other scientists?
* Compare interdisciplary teams (e.g. Medicine, Computer Science, Geographers, Physisist, Mathematics, ...)  with teams of single discipline team applying for a grant in terms of workload and success rate for the proposal?
* How is the current scientifc reward system encouraging for the scientist and what are the challenges and obstacles in the scientific reward system?
* ''&quot;If you want to walk fast walk alone, if you want to walk far walk together!&quot;''. Would you agree or disagree with that statement and do you find evidence in the scientific reward system that encouraged scientific collaboration and how is that done?
* Write a short summary for yourself, about your future scientifc work!
* '''(Optimisation)''' Look at the concept of [[Wikipedia:Least_publishable_unit|Minimum or Least Publishable Units]]&lt;ref&gt;Refinetti, R. (1990). In defense of the least publishable unit. The FASEB Journal, 4(1), 128-129.&lt;/ref&gt;&lt;ref&gt;Dupps, W. J., &amp; Randleman, J. B. (2012). The perils of the least publishable unit. Journal of refractive surgery, 28(9), 601-602.&lt;/ref&gt; as an approach 
** to maximise the reward for scientific innovation,
** to decompose knowledge in smaller fraction, that can be reused and cited according to the fraction of the innovation.
** workload to aggregate units of decomposed scientific results into main result discovered by the scientist.
* '''(Open Badges for Scientific Advancements)''' Assume Organisations like [[w:WHO|WHO]] would issue [[Open Badges]] to acknowledge scientific results that provide important advancements in the Health Domain. That might be applied for [[Sustainable Development Goals]] in general. Why will this form of acknowledge has some limitations to replace the Scientific Reward System mentioned above.

== Discussion Questions, Essay Ideas, and AI Prompt Ideas ==
{{Template:AI-generated-section}}
=== Discussion Questions ===
# How does the pressure to accumulate traditional metrics (such as high-impact citations and grant volume) disincentivize long-term, high-risk interdisciplinary research?
# Why do institutional hiring and tenure boards remain resistant to incorporating non-traditional validation mechanics into career advancement?
# In an era where AI agents can autonomously generate hypotheses and execute routine analysis, how should scientific reward systems adapt to value human intellectual effort and creativity?

=== AI Prompt Ideas ===
# ''&quot;Analyze the structural incentives of Decentralized Science (DeSci) mechanics versus legacy NIH or ERC grant funding.&quot;''
# ''&quot;Draft a policy framework that uses smart contracts to attribute micro-contributions across human-AI collaborative research teams, ensuring reasonable and fair reward distribution.&quot;''

== References ==</text>
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  <page>
    <title>Wikimedia Deutschland/Open Science Fellows Program/mentors</title>
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      <minor />
      <comment>Attempting to solve lints - Please ignore the notification this edit generated.</comment>
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{{:Wikimedia Deutschland/Open Science Fellows Program/Navigation}}
{| class=&quot;plainlinks&quot;  border=0 cellspacing=12 cellpadding=2 style=&quot;width:100%; height:100%; font-size: 95%; background-color:#dce4e8;{{Text color default}};&quot;
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&lt;div style=&quot;min-height:200px; border:5px solid #FFFFFF; background-color:#FFFFFF;{{Text color default}}; box-shadow:0.2em 0.3em 0.7em #9C9B9B; margin-bottom:.6em; padding:1.0em;&quot;&gt;
{| class=&quot;toptextcells&quot; style=&quot;margin-top:40px;&quot;
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|id =&quot;zwei&quot; style=&quot;font-size:200%;font-family:georgia; font-weight:bold;&quot;| Mentors (2016 - 2021)
|-
|
&lt;gallery mode=&quot;packed-overlay&quot; heights=&quot;250px&quot; class=&quot;center centered&quot; perrow=&quot;2&quot;&gt;
File:Kerstin Schoch.jpg | Kerstin Schoch&lt;br /&gt; (Hochschule für Künste im Sozialen, Ottersberg / Universität Witten/Herdecke)|link=Wikiversity:Fellow-Programm_Freies_Wissen/MentorInnen/Kerstin_Schoch
File:Rima-Maria_Rahal.jpg |Dr. Rima-Maria Rahal&lt;br /&gt; Max Planck Institute for Research on Collective Goods, Bonn|link=Wikiversity:Fellow-Programm_Freies_Wissen/MentorInnen/Rima_Maria_Rahal
File:Avatar_Anita_Runge.png | Dr. Anita Runge &lt;br /&gt; Ehemalige Geschäftsführerin des Margherita-von-Brentano-Zentrums an der Freien Universität Berlin, Publikationsförderung|link=Wikiversity:Fellow-Programm_Freies_Wissen/MentorInnen/Anita_Runge
File:Benedikt Fecher.jpg |Dr. Benedikt Fecher&lt;br /&gt; Alexander von Humboldt Institut für Internet und Gesellschaft|link=Wikiversity:Fellow-Programm_Freies_Wissen/MentorInnen/Benedikt_Fecher
File:Jakob Voß.jpg |Dr. Jakob Voß&lt;br /&gt; Verbundzentrale des Gemeinsamen Bibliotheksverbundes (VZG)|link=Wikiversity:Fellow-Programm_Freies_Wissen/MentorInnen/Jakob_Voss
File:Isabel Steinhardt.jpg |Dr. Isabel Steinhardt&lt;br /&gt; International Centre for Higher Education Research, INCHER-Kassel|link=Wikiversity:Fellow-Programm_Freies_Wissen/MentorInnen/Isabel_Steinhardt
File:Maximilian Heimstädt.jpg |Dr. Maximilian Heimstädt&lt;br /&gt; Weizenbaum-Institut|link=Wikiversity:Fellow-Programm_Freies_Wissen/MentorInnen/Maximilian_Heimstädt
File:Johanna Havemann.jpg |Dr. Johanna Havemann&lt;br /&gt; Access 2 Perspectives|link=Wikiversity:Fellow-Programm_Freies_Wissen/MentorInnen/Johanna_Havemann
File:Portraet Heck Tamara.jpg|Dr. Tamara Heck&lt;br /&gt; Deutsche Institut für Internationale Pädagogische Forschung (DIPF)|link=Wikiversity:Fellow-Programm_Freies_Wissen/MentorInnen/Tamara_Heck 
File:Gregor Hagedorn.jpg |Dr. Gregor Hagedorn&lt;br /&gt; Museum für Naturkunde Berlin|link= https://www.museumfuernaturkunde.berlin/en/taxonomy/term/234/gregor.hagedorn
File:Ina Blümel.jpg | Dr. Ina Blümel&lt;br /&gt; Leibniz Information Centre for Science and Technology (TIB).|link=https://twitter.com/inablu?lang=de 
File:Daniel Mietchen.jpg |Dr. Daniel Mietchen&lt;br /&gt; University of Virginia|link=https://twitter.com/evomri?lang=de
File:Claudia Müller-Birn 2.jpg |Prof. Dr. Claudia Müller-Birn&lt;br /&gt; Freie Universität Berlin|link=https://www.mi.fu-berlin.de/en/inf/groups/hcc/members/professor/mueller-birn.html
File:Peter Kraker 1.jpg |Dr. Peter Kraker&lt;br /&gt; Open Knowledge Maps|link=https://twitter.com/peterkraker?lang=de
File:Isabella Peters.jpg |Prof. Dr. Isabella Peters&lt;br /&gt; ZBW Leibniz-Informationszentrum Wirtschaft und Christian-Albrechts-Universität zu Kiel|link=Wikiversity:Fellow-Programm_Freies_Wissen/MentorInnen/Isabella_Peters
File:Katja Mayer 1.jpg |Dr. Katja Mayer&lt;br /&gt; Universität Wien|link=Wikiversity:Fellow-Programm_Freies_Wissen/MentorInnen/Katja_Mayer
File:Sandra_Hofhues 2.jpg |Jun.-Prof. Dr. Sandra Hofhues&lt;br /&gt; Universität zu Köln|link=Wikiversity:Fellow-Programm_Freies_Wissen/MentorInnen/Sandra_Hofhues 
File:Sascha Friesike.jpg |Prof. Dr. Sascha Friesike &lt;br /&gt; Berlin University of the Arts/Weizenbaum Institute for the Networked Society|link=Wikiversity:https://www.friesike.de/
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  <page>
    <title>Animal Phyla/Arthropoda</title>
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      <comment>/* The Fossil Record */</comment>
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      <text bytes="3087" sha1="nl6j5j12d6g8046zxnx5vefzc2afe4x" xml:space="preserve">[[Image:Chelicerae_%26_pedipalps_%288689230685%29.jpg|thumb|300px|Right|A scorpion, an example of an Arthropod]]
*Arthropoda
*Name Meaning: Jointed foot
*English Common Name: Arthropods
*Major distinguishing characteristics: Chitin exoskeleton
*Approximate number of species described: 1,134,000+

==Natural History==

Counted by number and diversity of species, arthropods are the most successful Phylum of animals. Over half known species are arthropods.

Arthropods live in most habitats on Earth. They are present in the deepest ocean trenches and have been found high in the atmosphere.
 
==Taxonomy==

The Phylum Arthropoda is divided into five Subphyla (four extant, one extinct).
The Subphyla are divided into 16 Classes. There are an additional 6 extinct Classes that are so far unable to be placed within Subphyla.

*Subphylum Trilobitomorpha (extinct)
**Trilobita (trilobites, extinct)
*Subphylum Chelicerata
**Arachnida (spiders, scorpions, ticks, etc.)
**Merostomata (horseshoe crabs, eurypterids) - eurypterids are extinct
**Pycnogonida (sea spiders)
*Subphylum Myriapoda 
**Chilopoda (centipedes)
**Diplopoda (millipedes)
**Pauropoda
**Symphyla (resemble centipedes)
*Subphylum Crustacea 
**Branchiopoda (brine shrimp)
**Remipedia (blind crustaceans)
**Cephalocarida (horseshoe shrimp)
**Maxillopoda (barnacles, copepods, fish lice)
**Ostracoda (seed shrimp)
**Malacostraca (lobsters, crabs, shrimp)
*Subphylum Hexapoda
**Entognatha (springtails)
**Insecta (insects)

It's uncertain how these extinct groups fit in with the rest of the Arthropoda, but they are arthropods.
*Camptophyllia
*Marrellomorpha
*Acanthomeridion
*Thelxiope
*Euthycarcinoidea
*Carnarvonia

==Anatomy==

Being a large and diverse group, the anatomy of arthropods is also somewhat diverse.

Arthropods have an exoskeleton primarily made of chiton, a fibrous material which is strong, yet somewhat flexible. Their bodies are segmented, with some specialization of segments.

Though they have hearts to move fluids in the body around, Arthropods have open circulatory systems. Their blood flows freely among their tissues, though some have some open ended arteries.

[[Bee Anatomy]]

==The Fossil Record==

Arthropods appear in the fossil record as early as the Vendian/Ediacaran, 543 million years ago. Their diversification was rapid during the Cambrian, and there are several represented in the Burgess Shale.

There are several extinct groups, the most well known being the trilobites which evolved by about 521 million years ago and became extinct about 252 million years ago at the end of the Permian.

==Quiz==

* [[/Arthropoda Quiz/]]
==References and Further Reading==
*[https://en.wikipedia.org/wiki/Arthropod Arthropod] at Wikipedia
*[http://www.ucmp.berkeley.edu/arthropoda/arthropoda.html Introduction to the Arthropoda] at University of California Museum of Paleontology
*[http://tolweb.org/Arthropoda Arthropoda] at Tree of Life
*[http://eol.org/pages/164/overview Arthropoda] at Encyclopedia of Life]

[[Category:Animals]]
[[Category:Taxonomy]]
[[Category:Zoology]]
[[Category:Biology]]</text>
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  <page>
    <title>OpenStax</title>
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      <text bytes="3863" sha1="aj12kxf0ntp4a10maensa4n4ekg5rpt" xml:space="preserve">'''OpenStax''' (formerly OpenStax College) is a nonprofit ed-tech initiative based at Rice University. Since 2012, OpenStax has created peer-reviewed, openly licensed textbooks, which are available as free downloadable PDFs, web versions, audiobooks&lt;ref&gt;{{Cite web|url=https://openstax.org/blog/guest-post-how-audio-technology-is-creating-more-inclusive-learning|title=OpenStax {{!}} How audio technology is creating more inclusive learning|website=openstax.org|language=en-US|access-date=2025-10-20}}&lt;/ref&gt; and for a low cost in print. All textbook content is licensed under Creative Commons Attribution Licenses; specifically, the books are available under the Creative Commons Attribution-NonCommercial-ShareAlike License v4.0, which means that instructors are free to use, adapt, and remix the content, as long as they attribute OpenStax.&lt;ref&gt;[[Wikipedia: OpenStax]]&lt;/ref&gt;

The following Wikiversity resources devoted to OpenStax textbooks.  These resources also included materials available at [https://openstax.org/ '''openstax.org''']. Although some versions found on Wikiversity are out-of-date, some might find them more convenient to access.

*[[OpenStax Additive Manufacturing Essentials]]
*[[OpenStax American Government 3e]]
*[[OpenStax American Government 4e]]
*[[OpenStax University Physics|OpenStax University Physics (click to visit)]]

*[[OpenStax College Physics|OpenStax College Physics (click to visit)]]

*[[OpenStax Astronomy|OpenStax Astronomy (click to visit)]]
*[[OpenStax Astronomy 2e|OpenStax Astronomy 2e (click to visit)]]
*[[OpenStax Anatomy and Physiology 2e|OpenStax Anatomy &amp; Physiology 2e]]
*[[OpenStax Biology 2e]]
*[[OpenStax Business Ethics]]
*[[OpenStax Chemistry 2e]]
*[[OpenStax Clinical Nursing Skills]]
*[[OpenStax College Success]]
*[[OpenStax College Success Concise]]
*[[OpenStax Concepts of Biology]]
*[[OpenStax Entrepreneurship]]
*[[OpenStax Fundamentals of Nursing]]
*[[OpenStax Introduction to Anthropology]]
*[[OpenStax Introduction to Behavioral Neuroscience]]
*[[OpenStax Introduction to Business]]
*[[OpenStax Introduction to Business 2e]]
*[[OpenStax Introduction to Philosophy]]
*[[OpenStax Introduction to Political Science]]
*[[OpenStax Introduction to Sociology 3e]]
*[[OpenStax Lifespan Development]]
*[[OpenStax Maternal Newborn Nursing]]
*[[OpenStax Medical Surgical Nursing]]
*[[OpenStax Microbiology]]
*[[OpenStax Nutrition for Nurses]]
*[[OpenStax Organizational Behavior]]
*[[OpenStax Pharmacology for Nurses]]
*[[OpenStax Population Health for Nurses]]
*[[OpenStax Principles of Economics 3e]]
*[[OpenStax Principles of Finance 2e]]
*[[OpenStax Principles of Macroeconomics 3e]]
*[[OpenStax Principles of Marketing]]
*[[OpenStax Principles of Microeconomics 3e]]
*[[OpenStax Psychiatric Mental Health Nursing]]
*[[OpenStax Psychology 2e]]
*[[OpenStax US History]]
*[[OpenStax world history volume 1 to 1500|OpenStax World History, Volume 1: to 1500]]
*[[OpenStax World History Volume 2 from 1400]]

*'''OpenStax Calculus: ''' No resources have been developed, but (out-of-date) pdf versions of the three volume textbook are posted on Wikiversity at: '''[[:File:CalculusVolume1-OP.pdf|V1]]''' | '''[[:File:CalculusVolume2-OP.pdf|V2]]''' | '''[[:File:CalculusVolume3-LR.pdf|V3]]''' 

== See Also ==
* [[Wikipedia: OpenStax]]

* [https://openstax.org/ OpenStax.org]
* [https://audileo.com/ Official OpenStax Audio Textbooks]

*[[:Category:openstax textbook]]
*[https://www.facebook.com/openstax/ OpenStax Facebook page]
* [https://www.ted.com/talks/richard_baraniuk_the_birth_of_the_open_source_learning_revolution TED Talk dated 2006-02] Founder Richard Baraniuk discussing Connexions
*[[Quizbank]]
* [https://www.youtube.com/watch?v=Xog2X2SnjvQ YouTube: Importing OpenStax content into Pressbooks]

== References ==
{{reflist}}

{{subpages/List}}

[[category:openstax file]] [[Category:Quizbank]]</text>
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      <text bytes="3902" sha1="s8phuyk6qmm4p9qhhyhqiutua16uby0" xml:space="preserve">'''OpenStax''' (formerly OpenStax College) is a nonprofit ed-tech initiative based at Rice University. Since 2012, OpenStax has created peer-reviewed, openly licensed textbooks, which are available as free downloadable PDFs, web versions, audiobooks&lt;ref&gt;{{Cite web|url=https://openstax.org/blog/guest-post-how-audio-technology-is-creating-more-inclusive-learning|title=OpenStax {{!}} How audio technology is creating more inclusive learning|website=openstax.org|language=en-US|access-date=2025-10-20}}&lt;/ref&gt; and for a low cost in print. All textbook content is licensed under Creative Commons Attribution Licenses; specifically, the books are available under the Creative Commons Attribution-NonCommercial-ShareAlike License v4.0, which means that instructors are free to use, adapt, and remix the content, as long as they attribute OpenStax.&lt;ref&gt;[[Wikipedia: OpenStax]]&lt;/ref&gt;

The following Wikiversity resources devoted to OpenStax textbooks.  These resources also included materials available at [https://openstax.org/ '''openstax.org''']. Although some versions found on Wikiversity are out-of-date, some might find them more convenient to access.

*[[OpenStax Additive Manufacturing Essentials]]
*[[OpenStax American Government 3e]]
*[[OpenStax American Government 4e]]
*[[OpenStax University Physics|OpenStax University Physics (click to visit)]]

*[[OpenStax College Physics|OpenStax College Physics (click to visit)]]

*[[OpenStax Astronomy|OpenStax Astronomy (click to visit)]]
*[[OpenStax Astronomy 2e|OpenStax Astronomy 2e (click to visit)]]
*[[OpenStax Anatomy and Physiology 2e|OpenStax Anatomy &amp; Physiology 2e]]
*[[OpenStax Biology 2e]]
*[[OpenStax Business Ethics]]
*[[OpenStax Chemistry 2e]]
*[[OpenStax Clinical Nursing Skills]]
*[[OpenStax College Success]]
*[[OpenStax College Success Concise]]
*[[OpenStax Concepts of Biology]]
*[[OpenStax Entrepreneurship]]
*[[OpenStax Fundamentals of Nursing]]
*[[OpenStax Introduction to Anthropology]]
*[[OpenStax Introduction to Behavioral Neuroscience]]
*[[OpenStax Introduction to Business]]
*[[OpenStax Introduction to Business 2e]]
*[[OpenStax Introduction to Philosophy]]
*[[OpenStax Introduction to Political Science]]
*[[OpenStax Introduction to Sociology 3e]]
*[[OpenStax Lifespan Development]]
*[[OpenStax Maternal Newborn Nursing]]
*[[OpenStax Medical Surgical Nursing]]
*[[OpenStax Microbiology]]
*[[OpenStax Nutrition for Nurses]]
*[[OpenStax Organizational Behavior]]
*[[OpenStax Pharmacology for Nurses]]
*[[OpenStax Population Health for Nurses]]
*[[OpenStax Principles of Economics 3e]]
*[[OpenStax Principles of Finance 2e]]
*[[OpenStax Principles of Macroeconomics 3e]]
*[[OpenStax Principles of Management]]
*[[OpenStax Principles of Marketing]]
*[[OpenStax Principles of Microeconomics 3e]]
*[[OpenStax Psychiatric Mental Health Nursing]]
*[[OpenStax Psychology 2e]]
*[[OpenStax US History]]
*[[OpenStax world history volume 1 to 1500|OpenStax World History, Volume 1: to 1500]]
*[[OpenStax World History Volume 2 from 1400]]

*'''OpenStax Calculus: ''' No resources have been developed, but (out-of-date) pdf versions of the three volume textbook are posted on Wikiversity at: '''[[:File:CalculusVolume1-OP.pdf|V1]]''' | '''[[:File:CalculusVolume2-OP.pdf|V2]]''' | '''[[:File:CalculusVolume3-LR.pdf|V3]]''' 

== See Also ==
* [[Wikipedia: OpenStax]]

* [https://openstax.org/ OpenStax.org]
* [https://audileo.com/ Official OpenStax Audio Textbooks]

*[[:Category:openstax textbook]]
*[https://www.facebook.com/openstax/ OpenStax Facebook page]
* [https://www.ted.com/talks/richard_baraniuk_the_birth_of_the_open_source_learning_revolution TED Talk dated 2006-02] Founder Richard Baraniuk discussing Connexions
*[[Quizbank]]
* [https://www.youtube.com/watch?v=Xog2X2SnjvQ YouTube: Importing OpenStax content into Pressbooks]

== References ==
{{reflist}}

{{subpages/List}}

[[category:openstax file]] [[Category:Quizbank]]</text>
      <sha1>s8phuyk6qmm4p9qhhyhqiutua16uby0</sha1>
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      <text bytes="3945" sha1="98mwpc42vzm9qs0rsvs52xjtguret5u" xml:space="preserve">'''OpenStax''' (formerly OpenStax College) is a nonprofit ed-tech initiative based at Rice University. Since 2012, OpenStax has created peer-reviewed, openly licensed textbooks, which are available as free downloadable PDFs, web versions, audiobooks&lt;ref&gt;{{Cite web|url=https://openstax.org/blog/guest-post-how-audio-technology-is-creating-more-inclusive-learning|title=OpenStax {{!}} How audio technology is creating more inclusive learning|website=openstax.org|language=en-US|access-date=2025-10-20}}&lt;/ref&gt; and for a low cost in print. All textbook content is licensed under Creative Commons Attribution Licenses; specifically, the books are available under the Creative Commons Attribution-NonCommercial-ShareAlike License v4.0, which means that instructors are free to use, adapt, and remix the content, as long as they attribute OpenStax.&lt;ref&gt;[[Wikipedia: OpenStax]]&lt;/ref&gt;

The following Wikiversity resources devoted to OpenStax textbooks.  These resources also included materials available at [https://openstax.org/ '''openstax.org''']. Although some versions found on Wikiversity are out-of-date, some might find them more convenient to access.

*[[OpenStax Additive Manufacturing Essentials]]
*[[OpenStax American Government 3e]]
*[[OpenStax American Government 4e]]
*[[OpenStax University Physics|OpenStax University Physics (click to visit)]]

*[[OpenStax College Physics|OpenStax College Physics (click to visit)]]

*[[OpenStax Astronomy|OpenStax Astronomy (click to visit)]]
*[[OpenStax Astronomy 2e|OpenStax Astronomy 2e (click to visit)]]
*[[OpenStax Anatomy and Physiology 2e|OpenStax Anatomy &amp; Physiology 2e]]
*[[OpenStax Biology 2e]]
*[[OpenStax Business Ethics]]
*[[OpenStax Business Law I Essentials 2e]]
*[[OpenStax Chemistry 2e]]
*[[OpenStax Clinical Nursing Skills]]
*[[OpenStax College Success]]
*[[OpenStax College Success Concise]]
*[[OpenStax Concepts of Biology]]
*[[OpenStax Entrepreneurship]]
*[[OpenStax Fundamentals of Nursing]]
*[[OpenStax Introduction to Anthropology]]
*[[OpenStax Introduction to Behavioral Neuroscience]]
*[[OpenStax Introduction to Business]]
*[[OpenStax Introduction to Business 2e]]
*[[OpenStax Introduction to Philosophy]]
*[[OpenStax Introduction to Political Science]]
*[[OpenStax Introduction to Sociology 3e]]
*[[OpenStax Lifespan Development]]
*[[OpenStax Maternal Newborn Nursing]]
*[[OpenStax Medical Surgical Nursing]]
*[[OpenStax Microbiology]]
*[[OpenStax Nutrition for Nurses]]
*[[OpenStax Organizational Behavior]]
*[[OpenStax Pharmacology for Nurses]]
*[[OpenStax Population Health for Nurses]]
*[[OpenStax Principles of Economics 3e]]
*[[OpenStax Principles of Finance 2e]]
*[[OpenStax Principles of Macroeconomics 3e]]
*[[OpenStax Principles of Management]]
*[[OpenStax Principles of Marketing]]
*[[OpenStax Principles of Microeconomics 3e]]
*[[OpenStax Psychiatric Mental Health Nursing]]
*[[OpenStax Psychology 2e]]
*[[OpenStax US History]]
*[[OpenStax world history volume 1 to 1500|OpenStax World History, Volume 1: to 1500]]
*[[OpenStax World History Volume 2 from 1400]]

*'''OpenStax Calculus: ''' No resources have been developed, but (out-of-date) pdf versions of the three volume textbook are posted on Wikiversity at: '''[[:File:CalculusVolume1-OP.pdf|V1]]''' | '''[[:File:CalculusVolume2-OP.pdf|V2]]''' | '''[[:File:CalculusVolume3-LR.pdf|V3]]''' 

== See Also ==
* [[Wikipedia: OpenStax]]

* [https://openstax.org/ OpenStax.org]
* [https://audileo.com/ Official OpenStax Audio Textbooks]

*[[:Category:openstax textbook]]
*[https://www.facebook.com/openstax/ OpenStax Facebook page]
* [https://www.ted.com/talks/richard_baraniuk_the_birth_of_the_open_source_learning_revolution TED Talk dated 2006-02] Founder Richard Baraniuk discussing Connexions
*[[Quizbank]]
* [https://www.youtube.com/watch?v=Xog2X2SnjvQ YouTube: Importing OpenStax content into Pressbooks]

== References ==
{{reflist}}

{{subpages/List}}

[[category:openstax file]] [[Category:Quizbank]]</text>
      <sha1>98mwpc42vzm9qs0rsvs52xjtguret5u</sha1>
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      <text bytes="3998" sha1="ebd3lcue3woxjpvglu94zkzx33ejw1r" xml:space="preserve">'''OpenStax''' (formerly OpenStax College) is a nonprofit ed-tech initiative based at Rice University. Since 2012, OpenStax has created peer-reviewed, openly licensed textbooks, which are available as free downloadable PDFs, web versions, audiobooks&lt;ref&gt;{{Cite web|url=https://openstax.org/blog/guest-post-how-audio-technology-is-creating-more-inclusive-learning|title=OpenStax {{!}} How audio technology is creating more inclusive learning|website=openstax.org|language=en-US|access-date=2025-10-20}}&lt;/ref&gt; and for a low cost in print. All textbook content is licensed under Creative Commons Attribution Licenses; specifically, the books are available under the Creative Commons Attribution-NonCommercial-ShareAlike License v4.0, which means that instructors are free to use, adapt, and remix the content, as long as they attribute OpenStax.&lt;ref&gt;[[Wikipedia: OpenStax]]&lt;/ref&gt;

The following Wikiversity resources devoted to OpenStax textbooks.  These resources also included materials available at [https://openstax.org/ '''openstax.org''']. Although some versions found on Wikiversity are out-of-date, some might find them more convenient to access.

*[[OpenStax Additive Manufacturing Essentials]]
*[[OpenStax American Government 3e]]
*[[OpenStax American Government 4e]]
*[[OpenStax University Physics|OpenStax University Physics (click to visit)]]

*[[OpenStax College Physics|OpenStax College Physics (click to visit)]]

*[[OpenStax Astronomy|OpenStax Astronomy (click to visit)]]
*[[OpenStax Astronomy 2e|OpenStax Astronomy 2e (click to visit)]]
*[[OpenStax Anatomy and Physiology 2e|OpenStax Anatomy &amp; Physiology 2e]]
*[[OpenStax Biology 2e]]
*[[OpenStax Business Ethics]]
*[[OpenStax Business Law I Essentials 2e]]
*[[OpenStax Chemistry 2e]]
*[[OpenStax Clinical Nursing Skills]]
*[[OpenStax College Success]]
*[[OpenStax College Success Concise]]
*[[OpenStax Concepts of Biology]]
*[[OpenStax Entrepreneurship]]
*[[OpenStax Fundamentals of Nursing]]
*[[OpenStax Introduction to Anthropology]]
*[[OpenStax Introduction to Behavioral Neuroscience]]
*[[OpenStax Introduction to Business]]
*[[OpenStax Introduction to Business 2e]]
*[[OpenStax Introduction to Philosophy]]
*[[OpenStax Introduction to Political Science]]
*[[OpenStax Introduction to Sociology 3e]]
*[[OpenStax Lifespan Development]]
*[[OpenStax Maternal Newborn Nursing]]
*[[OpenStax Medical Surgical Nursing]]
*[[OpenStax Microbiology]]
*[[OpenStax Nutrition for Nurses]]
*[[OpenStax Organizational Behavior]]
*[[OpenStax Pharmacology for Nurses]]
*[[OpenStax Population Health for Nurses]]
*[[OpenStax Principles of Economics 3e]]
*[[OpenStax Principles of Finance 2e]]
*[[OpenStax Principles of Macroeconomics 3e]]
*[[OpenStax Principles of Management]]
*[[OpenStax Principles of Marketing]]
*[[OpenStax Principles of Microeconomics 3e]]
*[[OpenStax Psychiatric Mental Health Nursing]]
*[[OpenStax Psychology 2e]]
*[[OpenStax US History]]
*[[OpenStax world history volume 1 to 1500|OpenStax World History, Volume 1: to 1500]]
*[[OpenStax World History Volume 2 from 1400]]

*'''OpenStax Calculus: ''' No resources have been developed, but (out-of-date) pdf versions of the three volume textbook are posted on Wikiversity at: '''[[:File:CalculusVolume1-OP.pdf|V1]]''' | '''[[:File:CalculusVolume2-OP.pdf|V2]]''' | '''[[:File:CalculusVolume3-LR.pdf|V3]]''' 

== See Also ==
* [[Wikipedia: OpenStax]]

* [https://openstax.org/ OpenStax.org]
* [https://audileo.com/ Official OpenStax Audio Textbooks]

*[[:Category:openstax textbook]]
*[https://www.facebook.com/openstax/ OpenStax Facebook page]
* [https://www.ted.com/talks/richard_baraniuk_the_birth_of_the_open_source_learning_revolution TED Talk dated 2006-02] Founder Richard Baraniuk discussing Connexions
*[[Quizbank]]
* [https://www.youtube.com/watch?v=Xog2X2SnjvQ YouTube: Importing OpenStax content into Pressbooks]

== References ==
{{reflist}}

{{subpages/List}}

[[category:openstax file]] [[Category:Quizbank]]
[[Category:OpenStax]]
[[Category:Openstax textbook]]</text>
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&lt;h1 style=&quot;color:#000000&quot;&gt;Training education actors on Wikimedia education projects&lt;/h1&gt;
&lt;/div&gt;
&lt;br&gt;
__TOC__


==Workshops and training programs for education actors==
In this lesson we will explore the main characteristics of workshops and training programs. We will go through recommended best practices and the stages of planning and developing these events that can best respond to the needs and opportunities of our local education contexts.

As you go through the contents of this module keep in mind that language and context can influence the way that these events (workshops, training programs, training sessions) are understood. To start, reflect on the following questions: 
* Have you organized or participated in events as part of an education initiative? What kind of events were they?
* How did you decide on the objectives and development of these events?

=== Incorporating effective teacher development principles in our work === 

Remember the reading from Module 2 on professional development for teachers, &quot;[https://www.researchgate.net/publication/237327162_Professional_Learning_in_the_Learning_Profession_A_Status_Report_on_Teacher_Development_in_the_United_States_and_Abroad Effective Teacher Development: What does the research show?&quot;]. Here are some of the main ideas it presented:

* Professional development should be intensive, ongoing, and connected to practice. 
* Professional development should focus on student learning and address the teaching of specific curriculum content. 
* Professional development should build strong working relationships among teachers. 

Additionally, in her article [https://www.globalpartnership.org/blog/six-strategies-improve-teacher-training-workshops &quot;Six strategies to improve teacher training workshops&quot;], education specialist Mary Burns&lt;ref&gt;{{Cite web|url=https://www.globalpartnership.org/users/mburns|title=Mary Burns {{!}} Global Partnership for Education|website=www.globalpartnership.org|language=en|access-date=2020-06-25}}&lt;/ref&gt; states that: &lt;blockquote&gt;&quot;Professional development—whether observation and feedback, coaching or workshops—only works when it is ongoing and continuous versus sporadic and episodic.  One of the most successful models with which I’ve been involved occurred over three years where every month we held a Saturday workshop followed by five days of in-school coaching. Eventually, in year three, when teachers did not need such intensive support, we shifted to workshops every two months and coaching even less (teachers no longer needed me; they had each other).  As teachers become more comfortable with new content and approaches, the role of external PD expert will attenuate. Ongoing workshops that actualize the suggestions outlined in this post can do much to address existing weaknesses of workshops. They can help teachers, not simply learn new information, but wrestle with the affective, behavioral, and cognitive dimensions of that information. They can provide the time, space, support and social context for professional learning and relationship building around the same set of topics with the same cohort of people over an extended period. They can help teachers design and implement new classroom practices and provide teachers with communities to support those practices so they are more “ready” to apply them in their classes. They can promote the risk-taking, shared practice, honest reflection and self-examination so necessary to help teachers begin to transfer learning from the “training room” to the “classroom.”&quot; &lt;/blockquote&gt;Is it possible to incorporate these reflections and recommendations into the trainings we develop as part of our Wikimedia education initiatives? Why or why not? Document your answers in your [[Wikimedia Education Greenhouse/Starter Guide#Will I receive any kind of learning recognition if I complete the course?|Course Portfolio]] or share your thoughts in the [[Talk:Wikimedia Education Greenhouse/Unit 1 - Module 3|Discuss]] section of this page as well! 

=== Examples of training events ===
Let's check some fictional scenarios of workshops and training programs for education actors. As you go through these examples, reflect back on the previous readings and pay attention to the following:
* What went well?
* What went wrong?
* How could this activity be improved in a future iteration?

{{Robelbox|theme={{{theme|9}}}|title=Example 1}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
A school principal contacted the local Wikimedia user group and invited them to give a workshop about Wikipedia in the school to 40 students. The Wikimedia volunteers prepared a 1-hour workshop where their goal was to teach teachers and students the different parts of a Wikipedia article, how to create an account, and where to ask for help from the community. When the Wikimedians arrived to give the workshop, they realized the principal had not secured a computer lab, but instead all the students had been asked to wait in the auditorium with no access to laptops nor cellphones. The teachers took that hour to enjoy a break and did not participate in the event. The Wikimedians did their best to keep their presentation dynamic and interesting.  
  &lt;/div&gt;
  {{Robelbox/close}}
{{Robelbox|theme={{{theme|10}}}|title=Example 2}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
A group of Wikimedians organized a professional development program for 10 teachers in partnership with a local think-tank. The course consisted of 15 hours of training divided in 5 sessions every Saturday. Every session focused on a different Wikimedia project and its use as a pedagogical tool. The program developed smoothly and the teachers seemed to enjoy the sessions and were excited to apply their newly acquired knowledge and skills in their classrooms. After the program was over, the Wikimedians interviewed some teachers to get their impressions about the experience but there were no follow-up strategies. A month later, it was not possible to know if the participating teachers were using any of the Wikimedia projects in their classrooms.  
  &lt;/div&gt;
  {{Robelbox/close}}
{{Robelbox|theme={{{theme|13}}}|title=Example 3}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
Representatives of a school district contacted a local Wikimedian who is also a teacher in a university to give a 3-hour workshop about Wikisource. They agree to invite 3 teachers of 10 different secondary schools to receive the workshop and learn how to bring classic texts of their city library to Wikisource while practicing typing in their mother tongue. It is expected that these teachers will in turn teach their students how to do the same. The Wikimedian leading the event prepares in advance: a detailed and hands-on presentation, surveys applied before and after the event to measure learning goals, a laptop ready for each teacher, and the teachers have created their Wikimedia accounts in advance. The day of the workshop, teachers get easily distracted while waiting for support during the practical exercises because there is only one Wikimedian conducting the workshop. Because the Wikimedian had to give one-on-one guidance to many teachers during the workshop some activities are not finalized and the teachers are asked to return for a second edition.   
  &lt;/div&gt;
  {{Robelbox/close}}

We would like to hear your reflections about these examples! Share them in the [[Talk:Wikimedia Education Greenhouse/Unit 1 - Module 3|Discuss]] section of this page.

==Planning and developing workshops and training programs ==
On this section of the module we will look at some case scenarios and analyze challenges, best practices, and impact of workshops and training programs.

=== How do you plan Wikimedia education events with education actors? ===
In the presentation below you can find an approach based on &quot;backwards planning&quot;. As you review the information in the slides, reflect on the following questions: 
* How similar or different are these suggested steps to your regular planning process?
* Are these suggested steps helpful?
* What suggestions could you immediately integrate into your planning process?
* What suggestions would be challenging to integrate?
[[File:Planning for learning with Wikimedia projects slides.pdf|center|thumb|450x450px|&lt;small&gt;NSaad (WMF) / CC BY-SA&lt;/small&gt;]]
'''Quiz: According to the backwards planning approach you just analyzed, which step should be taken first?'''
# Determine what evidence you need to collect
# Identify desired results
# Plan the learning activities

=== Delivering professional development events === 
You are going to read the article &quot;[https://www.edutopia.org/blog/10-tips-delivering-awesome-professional-development-elena-aguilar 10 Tips for Delivering Awesome Professional Development]&quot; by Elena Aguilar. As you go through the article identify:  

* the most innovative tip on the list  
* the most challenging tip to implement in your context, and  
* the tip that is easiest to implement in your context.  

Share your reflections about this reading using the [[Talk:Wikimedia Education Greenhouse/Unit 1 - Module 3|Discuss]] section of this page. 

== What works in your education context? ==
Let's reflect on our experiences organizing (or participating in) workshops or training programs for Wikimedia education initiatives. 

Think about the most successful Wikimedia education event you have organized (or observed/participated in) in your local community. Use the [[Talk:Wikimedia Education Greenhouse/Unit 1 - Module 3|Discuss]] section of this page to share your answers or document them in your [[Wikimedia Education Greenhouse/Starter Guide#Will I receive any kind of learning recognition if I complete the course?|Course Portfolio]].
* What kind of event was it? Who was the audience?
* What were the goals of this event?
* What was done in advance to prepare for the event?
* What were some key skills that facilitators of the event had?
* How did the organizers know that the goals were achieved?
* Were there any follow-up steps after the activity was over?

== Lessons and resources from our community == 
In this section we will explore best practices for the design, delivery and assessment of workshops and training programs for an audience of education actors.

=== Wikimedia Argentina ===
[[File:Actividad Huergo I.jpg|thumb|190x190px|&lt;small&gt;Luisina Ferrante (WMAR)/CC BY-SA&lt;/small&gt;]]
When it comes to developing workshops with education actors, the team from Wikimedia Argentina offers the following suggestions:

'''Organizing your workshop:'''

* It's always important to keep in mind the technical requirements: internet access, projector, computers. It's not necessary for every participant to have a computer, team work is possible (specially at schools).
* If you are giving a general presentation about Wikipedia or any of the other Wikimedia projects, 90 to 120 minutes is enough. If you want to edit you need at least 3 hours or break the workshop in two parts.
* If you are editing, it's important to keep in mind what happens after the workshop. It's necessary to follow up on what the participants did, if it was deleted/changed and why, etc. Always ask the participants to share their usernames so we can follow up on their work.

'''Communicating your event:'''

* Use the communication channels that teachers use. In our case, social media works really well to spread the word about our activities.
* Partner with education allies that allow you to expand your initiatives on the local level. For example: online education platforms, civil society organizations that work in education, universities, etc.

'''General tips:'''

* Think of projects that respond to the schedules, interests, and seasons of the schools in your country.
* It's important to have teachers in the organizing teams of your education initiatives. They know the education system or have general ideas about education in different contexts. This way it's easier to engage with other teachers and think of initiatives that interest them.
* Teachers are key to partner with education institutions. While it's true that many education institutions require formal approval of the administrative level, it's very important that the teachers who will carry out the activities bring them forward and are interested in working with you. 
* It's recommended to always do a first workshop with the teacher in charge of a class, to get to know them and to provide them with a first encounter with Wikipedia. Later they can think about ways of bringing Wikipedia into their classrooms themselves. By workshop we mean providing an understanding of the Wiki philosophy and also the basic editing norms. 
* If you are going to work editing contents in high schools it's recommendable not to let the students freely choose the topics or articles to edit. It's important to work with the teachers and focus on a topic they are already working on. First, focus on improvement and updating of existing content. To work on creating new content we suggest it happens on a second stage of the project.
* We put a lot of emphasis on what we can and we can't edit on Wikipedia. For example, articles about schools. This is a subject that education actors are always interested in and we tend to dedicate some time in the workshop to present solid arguments about why we do not suggest or encourage the creation of a school's institutional profile on Wikipedia.

'''Published resources:'''

[[c:File:Construyendo_nuevos_horizontes.pdf|Construyendo nuevos horizontes]] (Spanish)

[https://commons.wikimedia.org/w/index.php?title=File:Sumando_conocimiento_al_mundo_1920x1080.pdf&amp;page=0 Sumando conocimiento al mundo] (Spanish)

=== Wikimedia Serbia ===
[[File:14th birthday of Wikimedia Serbia 02.jpg|thumb|190x190px|&lt;small&gt;Dungodung/CC BY-SA 4.0&lt;/small&gt;]]
On their [https://upload.wikimedia.org/wikipedia/commons/4/40/WMRS_EDU_Brochure.pdf Education Program brochure], the education program managers of [[metawiki:Wikimedia_Serbia|Wikimedia Serbia]] share the following reflection:

&quot;It is possible to realize a program in numerous ways with respecting its principles. It depends on the educational priorities, interests, and needs of the students and teachers. We especially support the development of other Wiki projects, such as Wikibooks or Wiktionary. Working on networking the teachers and professors involved in the program is equally as important. They are the ones who know best about how a program like this could thrive in their classrooms, so the experience and the suggestions of their colleagues mean a lot to them. This is why we made a portal called Seminars&lt;ref&gt;{{Cite web|url=http://seminari.wikimedia.rs/index.php/%D0%93%D0%BB%D0%B0%D0%B2%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B0|title=Семинари|website=seminari.wikimedia.rs|access-date=2020-06-25}}&lt;/ref&gt;, where the participants can find all the necessary material, but also discuss relevant questions or just share their experience with the colleagues.&quot;

Additionally, here are their top tips for Wikimedians organizing workshops and training programs for education actors:

* If the group has not met with our projects before, definitely pay attention to the essence and ignore the details. The first workshop should focus on the most important things, it should be concise and clear. Interactive activities are supported and encouraged. In practice, it often happens that facilitators go too much into detail (especially when explaining how to edit Wikipedia in code) which deters the target group from our goal.
* Always ask for help. If you do not have enough experience and you work with a group with whom you can not achieve your goal on your own, it is necessary to ask for the help of our volunteers in order to make the workshop successful.
* Consider how you will follow the work of the group after the workshop. I always recommend the use of tools such as Dashboard, but new suggestions are welcome. The group needs to be aware of it as well as their rights and commitments. They need to know what is expected of them.

'''Resources:'''

[[c:File:WMRS_EDU_Brochure.pdf|Education program of Wikimedia Serbia]] (English) 

[[c:File:Приручник_за_Вики_амбасадоре.pdf|Manual for Wiki Ambassadors]] (Serbian)

=== Wikimedia Israel ===
[[File:נוער שוחר מדע 2019.jpg|thumb|200x200px|&lt;small&gt;Bks-WMIL/CC BY-SA&lt;/small&gt;]]
On their [[commons:Category:Wikimedia Israel Activities in Education|Commons category]], Wikimedia Israel has diverse resources you can use as inspiration to include in your workshops or training programs with education actors. 

Here are some key ideas they recommend communicating to teachers when you are are developing Wikimedia projects in a higher education setting:

* Wikipedia is not just a site, it is also a community: it's stunning to note how very little people know about how Wikipedia operates and how the information got there, despite the fact that they use it daily (aware or unaware, as the content is often reused).
* Unlike regular essays or seminar papers whose target audience is the academic instructor, a Wikipedia assignment is written for the general public to read. This means it needs to be written in a language that anybody can understand, without prior knowledge. To achieve this, students need to distill the important information about the topic and re-write it in their own words. This process requires a deeper assimilation and &quot;owning&quot; of the information, rather than reiterating what one has read in the academic literature.
* Wikipedia will never replace academic literature. It's not meant to. It's meant to allow people who do not have the privilege of an academic education to learn and access that knowledge - and by doing a Wikipedia assignment we are helping in that.

And here are some additional ideas for workshop management:

* Divide the event between a frontal lecture and then a workshop where teachers are invited to practice what they learned about Wikipedia (for example, &quot;recent changes&quot;, &quot;talk pages&quot;, ...).
* Meeting with a Wikipedian was a meaningful experience for teachers, especially when he spoke about topics' notability, or dispute's resolution in Wikipedia. 
* Much can be learned from a good article, but when you speak to teachers, perhaps even more can be learned from others' mistakes by a critical reading of a draft entry.

'''Published Resources:'''

[[c:File:ויקיפדיה_בכיתה_-_עלון_למורים.pdf|Wikipedia in the Classroom:]] the guide introduces the skills acquired in the project, and suggests various wiki-activities (e.g. Analytical tasks: comparing articles between languages/Wikipedia with other knowledge resources, discussion pages; Gnome-edits; writing new articles, improving existing ones). Currently developing an updated version of this guideline in Arabic, through which the teachers will be introduced to Wiki Warsha (the instructional website). More to be found on the following  [https://wikimedia.org.il/%d7%94%d7%93%d7%a8%d7%9b%d7%94-%d7%90%d7%99%d7%9a-%d7%99%d7%93%d7%a2-%d7%97%d7%95%d7%a4%d7%a9%d7%99-%d7%a0%d7%95%d7%9c%d7%93/%d7%9b%d7%9c%d7%99%d7%9d-%d7%9c%d7%9e%d7%95%d7%a8%d7%99%d7%9d-%d7%95%d7%9c%d7%9e%d7%a8%d7%a6%d7%99%d7%9d/ webpage.]

Videos in collaboration with The Center for Educational Technology and MoE (Hebrew): [https://video.cet.ac.il/VideoPlayerHTML5.aspx?xmlConfigPath=mafilim/2014/hishtalmut/wikipedia_nimrodrapoport_1_mdi.xml What could be learned from reading Wikipedia?], [https://video.cet.ac.il/VideoPlayerHTML5.aspx?xmlConfigPath=mafilim/2014/hishtalmut/dafhabait_wikipedia_nimrodrapoport_1_mdi.xml Learn about Wikipedia homepage]

Information [https://drive.google.com/file/d/0B88DaZg3rm6rRy1mZFd1WXNwaE0/view Leaflet] about Wikipedia and Wikimedia projects (Hebrew)

== Course Portfolio Assignment: One challenge, one lesson, one question ==

On the previous module we reflected about our local education systems and actors, and how to best collaborate with them. Understanding the needs, challenges and opportunities of our local education allies is key to design Wikimedia education initiatives that are impactful and meaningful. On this module we reflected on recommendations and best practices for workshops and training programs with local education actors.

After reviewing the resources and tips from some members of our global community, let's continue reflecting on our experiences. When you conduct or participate in Wikimedia education events in your community:
* What is the main challenge you face?
* What is an important lesson for success you have learned?
Document your answers to these questions in your [[Wikimedia Education Greenhouse/Starter Guide#Will I receive any kind of learning recognition if I complete the course?|Course Portfolio]] or share them in the [[Talk:Wikimedia Education Greenhouse/Unit 1 - Module 3|Discuss]] section of this page.

== Additional resources and activities ==
[[File:Fátima Iturríos.jpg|thumb|200x200px|&lt;small&gt;Fátima Iturríos (Wotancito / CC BY-SA)&lt;/small&gt;]]
* Reflect on past experiences organizing Wikimedia education projects? What kind of training opportunities did you provide? Who has been the main audience of the events you have organized as part of your education projects? What are some key learnings you have gathered from these experiences that can help you improve future iterations? If you haven't organized a Wikimedia education project yet, think of the opportunities you have had as a participant or observing these kind of initiatives.
* On the episode [https://www.cultofpedagogy.com/improve-nonverbal-communication/ &quot;How your nonverbals impact your teaching&quot;] Jennifer Gonzalez and Jack Shrawder discuss how posture, voice, eye contact, etc. affect your effectiveness in a classroom setting. These are other factors to consider when conducting impactful professional development events.
*[https://drive.google.com/file/d/17-Bw6WCr9SHhk1WHgcQkdx_Vg88gY3nN/view?usp=sharing This guide] provides practical activities that support participation and engagement.
*[https://graduateschool.nd.edu/assets/65180/effective_practices_of_workshop_design.pdf This compilation] offers additional effective practices for workshops.
* The Mozilla Science community offers [http://mozillascience.github.io/open-science-leadership-workshop/facilitator_tips_&amp;_tricks.html these facilitator tips and tricks], pay particular attention to the &quot;During the event&quot; section.

== References ==
{{Reflist}}
&lt;br&gt;
&lt;div style=&quot;float:{{dir|{{CURRENTCONTENTLANGUAGE}}|right|left}}&quot;&gt;[[File:Arrow l.svg|15px|link=]] [[Wikimedia Education Greenhouse/Unit 1 - Module 2|Go back to Unit 1 - Module 2]]  &lt;/div&gt;
&lt;div style=&quot;float:{{dir|{{CURRENTCONTENTLANGUAGE}}|right|right}}&quot;&gt; [[Wikimedia Education Greenhouse/Unit 1 - Module 4|Go to Unit 1 - Module 4]] [[File:Arrow r.svg|15px|link=]]  &lt;/div&gt;</text>
      <sha1>l879cvbc7wscnq57tgqpdv61b2hcldy</sha1>
    </revision>
  </page>
  <page>
    <title>Universal Bibliography/Countries</title>
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      <timestamp>2026-09-06T16:16:08Z</timestamp>
      <contributor>
        <username>James500</username>
        <id>297601</id>
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      <text bytes="39977" sha1="a1sj3l9aejav07io7zd8zildmnx0ssv" xml:space="preserve">{{Bibliography}}

See also [[Universal Bibliography/Geography|Geography]].

See [[w:Category:Bibliographies of countries or regions]] and [[w:Category:Works about countries]].

This part of the [[Universal Bibliography]] is a bibliography of countries (including former countries).

==Countries==
*Bateman and Egan (eds). The Encyclopedia of World Geography: A Country by Country Guide. 1993. Revised 1997.
*Peter Stalker. Handbook of the World. 2000. A Guide to Countries of the World. (Oxford Guide to Countries of the World. 2nd Ed: 2004, 2nd Revised Ed: 2007 [https://books.google.co.uk/books?id=GtztAAAAMAAJ], 3rd Ed: 2010 [https://books.google.co.uk/books?id=gvKvfxkbZ1AC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Countries of the World and Their Leaders Yearbook. Gale. [https://books.google.co.uk/books?id=5etKAAAAYAAJ] [https://books.google.co.uk/books?id=p41OAAAAIAAJ]
*Hutchinson Guide to Countries of the World [https://books.google.co.uk/books?id=GgpjUe4kN_IC]
*The World Guide: Global Reference, Country by Country. 11th Ed: 2007 [https://books.google.co.uk/books?id=EoWoLgAACAAJ]
*Spence. The World Today: A Nation-by-Nation Guide. Cassell. 1994. 1999. [https://books.google.com/books?id=Ub8qOQAACAAJ]
*Worldmark Encyclopedia of the Nations [https://books.google.co.uk/books?id=I0oYAQAAMAAJ]
*Kurian. Encyclopedia of the World's Nations. Facts on File. Reviews: [https://books.google.co.uk/books?id=Y1EnAQAAIAAJ] [https://books.google.co.uk/books?id=lz0RAQAAMAAJ]
*Michael O'Mara. Facts about the World's Nations. 1999. [https://books.google.co.uk/books?id=mygYAAAAIAAJ]
*Status of the World's Nations. 1965 [https://books.google.co.uk/books?id=sftEyRbAXMUC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. 1973 [https://books.google.co.uk/books?id=kw2U_Cg2gKYC&amp;pg=PP3#v=onepage&amp;q&amp;f=false].
*[[s:Author:John Alexander Hammerton|Hammerton, John Alexander]] (ed). Countries of the World. Published at the Fleetway House. 6 vols. [https://books.google.co.uk/books?id=e6IaAQAAMAAJ] [https://books.google.co.uk/books?id=K5oaAQAAMAAJ]
*[[s:Author:Robert Brown (1842-1895)|Brown, Robert]]. The Countries of the World. [https://books.google.co.uk/books?id=nO0DAAAAQAAJ&amp;pg=PP13#v=onepage&amp;q&amp;f=false]
*A Morely Dell. The Countries of the World. (Harrap's New Geographical Series). 1932. (School certificate). Reviews: [https://books.google.co.uk/books?id=oSS9PB_Jf7AC] [https://books.google.co.uk/books?id=BicVAAAAIAAJ] [https://books.google.co.uk/books?id=5qBOAAAAIAAJ] [https://books.google.co.uk/books?id=YbwcAQAAIAAJ] [https://books.google.co.uk/books?id=sc1AAAAAIAAJ]

General series:
*National Geographic Countries of the World [https://books.google.co.uk/books?id=IT2wfzVIPykC]
*Countries of the World. Evans Brothers. (GCSE) [https://books.google.co.uk/books?id=a3sZvWc7E1EC&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*One Europe. Longman. [https://search.worldcat.org/en/title/west-germany-adapted-by-lj-russon-from-the-original-german-by-sylvia-lof-ingrid-mallberg-dietrich-rosenthal/oclc/561591761]
*Collier's Nations of the World. The Nations of the World: An Historical Series. [https://books.google.co.uk/books?id=VJY-AAAAYAAJ&amp;pg=PP8#v=onepage&amp;q&amp;f=false]
*Collier's History of Nations. The History of Nations. [https://books.google.co.uk/books?id=fmSUfTY5E80C]
*The Story of the Nations. T Fisher Unwin.
*The World and Its Peoples. (The Illustrated Library of the World and Its Peoples). Greystone Press, New York.
*World and Its Peoples. Marshall Cavendish. [https://books.google.co.uk/books?id=oms5xjI7ba0C&amp;pg=PA141#v=onepage&amp;q&amp;f=false]

==England==
===Counties===
See [[s:Portal:Counties]]

* Harrison, &quot;County Bibliography&quot; (1886) 3 Library Chronicle [https://books.google.co.uk/books?id=Wz9FAAAAYAAJ&amp;pg=PA49#v=onepage&amp;q&amp;f=false 49]

General series
*Victoria County History
*Oxford County Histories
*Pinnock's County Histories
*Shire County Guides. Shire Publications.
*Cambridge County Geographies
*Pike's New Century Series
*[[s:Page:County Churches of Cornwall.djvu/6|County Churches]]. G Allen.

Avon
*Moore. Avon Local History Handbook. Phillimore. 1979. [https://books.google.co.uk/books?id=h0kjAAAAMAAJ] Bibliography, p 102

Bedfordshire
*Conisbee, Lewis Ralph. A Bedfordshire Bibliography. Bedfordshire Historical Record Society. Bedford. 1962. Supplements 1967, 1971, 1978. Third supplement by Threadgill. Review: 6 Archives 52 [https://books.google.co.uk/books?id=oOMZAAAAYAAJ]. See also [https://books.google.co.uk/books?id=MjspAAAAYAAJ] [https://books.google.co.uk/books?id=PejgAAAAMAAJ]
*Godber. History of Bedfordshire. 1969. 1984. [https://books.google.co.uk/books?id=jdvwPQAACAAJ]
*Pinnock. The History and Topography of Bedfordshire [https://books.google.co.uk/books?id=9bJYAAAAcAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*Parry. Select Illustrations, Historical and Topographical, of Bedfordshire [https://books.google.co.uk/books?id=UTUJAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Blyth. The History of Bedford and Visitor's Guide. 1873 [https://books.google.co.uk/books?id=IuIGAAAAQAAJ&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
*Cambridge County Geographies [https://books.google.co.uk/books?id=kTc8AAAAIAAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Buckinghamshire
*Reed. A History of Buckinghamshire. 1993 [https://books.google.co.uk/books?id=BtkWAQAAIAAJ]

Cambridgeshire
*Carter. History of the County of Cambridge [https://books.google.co.uk/books?id=jXpbAAAAQAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*Babington. Ancient Cambridgeshire [https://books.google.co.uk/books?id=DPrCAwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Devon
*Ravenhill and Rowe. Devon Maps and Map-makers [https://books.google.co.uk/books?id=tjf2yAEACAAJ]
*Wright. A Plea for a Devonshire Bibliography. 1885 [https://books.google.co.uk/books?id=8ZUDAAAAQAAJ]

Derbyshire
*Woore. A Catalogue of Local Maps of Derbyshire, C.1528-1800. 2012. [https://books.google.co.uk/books?id=oWmCMwEACAAJ]
*O'Neal. A Bibliography of Derbyshire Lead Mining. 1961

Essex
*Cunnington. Catalogue of Books, Maps and Manuscripts, relating to or connected with the County of Essex. 1902 [https://books.google.co.uk/books?id=oIcqpibGE4MC]
*&quot;The Bibliography of Essex&quot; (1882) 1 Antiquarian Magazine &amp; Bibliographer [https://books.google.co.uk/books?id=dEkEAAAAQAAJ&amp;pg=PA72#v=onepage&amp;q&amp;f=false 72]. See also [https://books.google.co.uk/books?id=dEkEAAAAQAAJ&amp;pg=PA283#v=onepage&amp;q&amp;f=false p 283].
*&quot;The Bibliography of Essex&quot; (1891) 5 The Essex Naturalist 30 [https://books.google.co.uk/books?id=iIo1AQAAMAAJ]
*Moon. Essex Literature. 1900. Review: 61 Literary World 438 [https://books.google.co.uk/books?id=2T0ZAAAAYAAJ] See also [https://books.google.co.uk/books?id=1Y4UAQAAIAAJ] [https://books.google.co.uk/books?id=C_pEAAAAMAAJ]
*Fenn and Lowery, &quot;An Essex Bibliography&quot;, Journal of the South West Essex Technical College, vols 2 &amp; 3
*Victoria County History bibliography. 1959 [https://books.google.co.uk/books?id=F2EJAQAAIAAJ]
*O'Leary, John Gerard. A Supplement to the Essex Bibliography. Dagenham. 1962.
*A Bibliography of Essex Archaeology &amp; History
*Essex and Dagenham: A Catalogue of Books, Pamphlets and Maps. Dagenham. 1961
*Essex Archaeology and History: The Transactions of the Essex Society for Archaeological and History [https://books.google.co.uk/books?id=CtFAAAAAYAAJ]
*Essex Naturalist: Being the Journal of the Essex Field Club
*Wright. The History and Topography of the County of Essex [https://books.google.co.uk/books?id=SgQVAAAAQAAJ&amp;pg=PP9#v=onepage&amp;q&amp;f=false]
*Ogborne, The History of Essex [https://books.google.co.uk/books?id=IeVSAAAAcAAJ&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
*Suckling. Memorials of the Antiquities and Architecture, Family History and Heraldry of the County of Essex [https://books.google.co.uk/books?id=bcw_AAAAcAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Hunter, The Essex Landscape: A Study of Its Form and History [https://books.google.co.uk/books?id=w9kWAQAAIAAJ]
*Cambridge County Geography [https://books.google.co.uk/books?id=GPHa_X_0qo0C&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*Sokoll. Essex  Pauper Letters, 1731-1837 [https://books.google.co.uk/books?id=rCLia7XlqtMC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Morant. The History and Antiquities of Colchester in the County of Essex [https://books.google.co.uk/books?id=DDgtAAAAYAAJ&amp;pg=PP9#v=onepage&amp;q&amp;f=false]
*Wallen. The History and Antiquities of the Round Church at Little Maplestead, Essex [https://books.google.co.uk/books?id=FPYVAAAAYAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]

Kent
*Smith. Bibliotheca Cantiana. 1837. [https://books.google.co.uk/books?id=1dJDAAAAYAAJ&amp;pg=PP11#v=onepage&amp;q&amp;f=false]

Leicestershire
*Kirkby, C V (compiler). Catalogue of the books, pamphlets, &amp;c., relating to Leicestershire in the Central Reference Library. Leicester Free Public Libraries. 1893. Reviews: [https://books.google.co.uk/books?id=3boqAQAAIAAJ&amp;pg=PA84#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=UcHnAAAAMAAJ&amp;pg=PA728#v=onepage&amp;q&amp;f=false]
*Leicestershire and Rutland Bibliography, 1963-65 (1966) [https://books.google.co.uk/books?id=-OhVAAAAYAAJ 40] Leicestershire Archaeological and Historical Society: Transactions (1964/5) 92. Available as pdf from University of Leicester.
*Leicestershire and Rutland Bibliography, 1961-63. Available as pdf from University of Leicester.
*Leicestershire and Rutland Bibliography, 1960-61. Available as pdf from University of Leicester.
*A Bibliography of the Small Towns in Leicestershire and Rutland, 1600–1850. (Dissertation). [https://repository.lboro.ac.uk/articles/educational_resource/A_bibliography_of_the_small_towns_in_Leicestershire_and_Rutland_1600_1850/9414200]
*Loughborough's Heritage: A Bibliography of the Holdings of Leicestershire Libraries and Information Service and Record Office. [https://books.google.co.uk/books?id=Bwx2zgEACAAJ]
*Keith Ambrose and Frank Williams, &quot;Bibliography of the Geology of Leicestershire and Rutland: Part 2: 1971-2003&quot; (2004) [https://books.google.co.uk/books?id=U-tQAQAAIAAJ 16] The Mercian Geologist 5. Available as pdf from East Midlands Geological Society.
*Parsons and Brandwood. A Bibliography of Leicestershire Churches. 1978.
*Education in Leicestershire: A Bibliography. [https://books.google.co.uk/books?id=X6EfzQEACAAJ]

Sussex
*Brent, Fletcher and McCann. Sussex in the 16th and 17th Centuries: A Bibliography. 2nd Ed [https://books.google.co.uk/books?id=I7UtAAAAYAAJ]
*Farrant. Sussex in the 18th and 19th Centuries: A Bibliography. 1st Ed: 1973, 2nd Ed: 1977 [https://books.google.co.uk/books?id=MLUtAAAAYAAJ], 3rd Ed: 1979

==France==
Bibliography:
*Bibliographie de la France. Commentary: Encyclopedia of Library and Information Science, vol 37, supplement 2, [https://books.google.co.uk/books?id=10rgjNvOV8oC&amp;pg=PA145#v=onepage&amp;q&amp;f=false p 145]; The Bookseller, 6 January 1881, [https://books.google.co.uk/books?id=4dsiAQAAMAAJ&amp;pg=PA10#v=onepage&amp;q&amp;f=false p 10]; Stein, Manuel de bibliographie générale, [https://books.google.co.uk/books?id=lJYPyKjV1qYC&amp;pg=PA23#v=onepage&amp;q&amp;f=false p 23]. 
*Girault de Saint-Fargeau. Bibliographie historique et topographique de la France. 1845 [https://books.google.co.uk/books?id=kClB9CQNZoMC&amp;pg=PP9#v=onepage&amp;q&amp;f=false]
*Catalogue d'une collection d'ouvrages sur l'histoire des provinces de la France. 1842 [https://books.google.co.uk/books?id=qQBX5WZouzAC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Landscape:
*Beaujeu-Garnier. France. (The World's Landscapes). 1975. [https://books.google.com/books?id=nwxDAQAAIAAJ]

Agenais:
*Andrieu. Bibliographie générale de l’Agenais et des parties du Condomois et du Bazadais. 1886 to 1891. Reprinted 1969.

Alsace:
*Ristelhuber. Bibliographie alsacienne. 1869 to 1873 [https://books.google.co.uk/books?id=0mhLAQAAMAAJ&amp;pg=PP13#v=onepage&amp;q&amp;f=false]
*Bibliographie alsacienne: Revue critique des publications concernant l'Alsace. 1918 to 1936
*Ritter. Répertoire bibliographique des livres imprimés en Alsace aux XVe et XVIe siècles [https://books.google.co.uk/books?id=DewaAQAAMAAJ]

Angoumois:
*Castaigne. Essai d'une bibliothèque historique de l'Angoumois, ou Catalogue raisonné des principaux ouvrages qui traitent des différentes branches de l'histoire de cette province. 1847 [https://books.google.co.uk/books?id=R-UanmmlvAEC&amp;pg=PP7#v=onepage&amp;q&amp;f=false]

Anjou:
*Braguier and Braguier. Archéologie en Anjou: bibliographie. 1984 [https://books.google.co.uk/books?id=LvsmAQAAIAAJ]

Auvergne:
*Gonot. Catalogue des ouvrages imprimés et manuscrits concernant l'Auvergne, extrait du catalogue général de la Bibliotlèque de Clermont-Fd (Puy-de-Dome). 1849. [https://books.google.co.uk/books?id=yCFtbObRCbUC&amp;pg=PP13#v=onepage&amp;q&amp;f=false]
*Catalogue des livres et estampes concernant l'ancienne Province d'Auvergne (Puy-de-Dôme, Cantal, Haute-Loire) réunis par feu M. G. Desbouis. 1865. [https://books.google.co.uk/books?id=Ui4S8_D0N74C&amp;pg=PP7#v=onepage&amp;q&amp;f=false]

Béarn
*&quot;Bibliographie Béarnaise&quot;, Revue de Pau et du Béarn [https://books.google.co.uk/books?id=FuZnAAAAMAAJ] Commentary: [https://books.google.co.uk/books?id=FQYqvPo9D9IC&amp;pg=PA158#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=RL9VAAAAYAAJ]

Brittany
*Sacher. Bibliographie de la Bretagne, ou Catalogue général des ouvrages historiques, littéraires et scientifiques parus sur la Bretagne, avec la liste des revues publiées en cette province, les prix approximatifs des volumes rares, etc. 1881 [https://archive.org/details/bibliographiede00sach]

Burgundy:
*Milsand. Bibliographie bourguignonne; ou, Catalogue méthodique d'ouvrages relatifs à la Bourgogne: Sciences - Arts - Histoire. 1885 [https://archive.org/details/bibliographiebo00milsgoog] [https://archive.org/details/bibliographiebo00sciegoog] [https://books.google.co.uk/books?id=CxIIAAAAQAAJ]
*Catalogue des manuscrits de la Bibliothèque royale des ducs de Bourgogne. 1842 [https://books.google.co.uk/books?id=FX5MAAAAcAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*The Companion Guide to Burgundy [https://books.google.co.uk/books?id=NraRP0AkDT0C&amp;pg=PP3#v=onepage&amp;q&amp;f=false]
*Lecat. The Golden Book of Burgundy. (The Golden Book) [https://books.google.co.uk/books?id=FyzR9qU1Zl4C&amp;lpg=PP1&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Gwynn. Burgundy: With Chapters on the Jura and Savoy. (Kitbag Travel Books). 1935 [https://books.google.co.uk/books?id=ny1LAAAAMAAJ]
*Bazin. Wonderful Burgundy. 1988. 1997 [https://books.google.co.uk/books?id=Yt1CRdICWCUC]
*Bailey. Burgundy. (Insight Guides). 1993 [https://books.google.co.uk/books?id=Q69a1dMW2NQC]
*Dunlop. Burgundy. Hamilton.1990 [https://books.google.co.uk/books?id=S_1OAAAAMAAJ]

Champagne:
*Lhermitte. Ouvrages sur la Champagne: contribution à la bibliographie champenoise. 1992. [https://books.google.co.uk/books?id=jbPfAAAAMAAJ]

Dauphiné:
*Mélanges biographiques et bibliographiques relatifs à l'histoire littéraire du Dauphiné par Colomb de Batines et Ollivier Jules. 1837 [https://books.google.co.uk/books?id=2F5MAAAAcAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

Lorraine:
*Bibliographie lorraine. Académie nationale de Metz [https://books.google.co.uk/books?id=n-DfAAAAMAAJ]

Maine:
*Desportes. Bibliographie du Maine, précédée de la description topographique et hydrographique du diocése du Mans, Sarthe et Mayenne. 1844. [https://books.google.co.uk/books?id=hSk-AAAAYAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

Normandy:
*Frère. Manuel du bibliographe Normand ou dictionnaire bibliographique et historique. 1858 to 1860. [https://books.google.co.uk/books?id=dp6geJClg1YC&amp;pg=PP13#v=onepage&amp;q&amp;f=false vol 1]

==Japan==
Bibliography and literature
*Hideo Kaneko. &quot;Japanese Literature and Bibliography&quot;. Kent, Lancour and Daily (eds). Encyclopedia of Library and Information Science. Marcel Dekker. 1977. vol 21. pp [https://books.google.co.uk/books?id=H1pNvzr_n98C&amp;pg=PA131#v=onepage&amp;q&amp;f=false 131] to 176.

Bibliography
*Jozef Rogala. A Collector's Guide to Books on Japan in English: An Annotated List of Over 2500 Titles with Subject Index. 2001. [https://books.google.co.uk/books?id=7KI9ao-w2FEC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Ria Koopmans-de Bruijn. Area Bibliography of Japan. (Scarecrow Area Bibliographies). Scarecrow Press. 1998. [https://books.google.co.uk/books?id=Hlx2OMjgUi0C&amp;pg=PR1#v=onepage&amp;q&amp;f=false]
*Frank Joseph Shulman. Japan. (World Bibliographical Series, vol 103). Clio Press. 1989. [https://books.google.co.uk/books?id=LsoUAQAAIAAJ]
*Eibun Nihon Kankei Tosho Mokuroku, 1945-1981. (Japanese: 英文日本関係図書目録, 1945-1981). (English: Catalogue of Books in English on Japan, 1945-1981). Japan Foundation. Tokyo. 1986.
*Japan: analytical bibliography: with supplementary research aids: and selected data on Okinawa . . . Department of the Army. Washington. 1972. [https://books.google.co.uk/books?id=h4d4nYxrxtMC&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Books on Japan in Western Languages. The International Christian University Library. 1971. [https://books.google.co.uk/books?id=F2bQAAAAMAAJ]
*Books on Japan: A List of Acquisitions, 1955-1970. International House of Japan Library. 1971. [https://books.google.co.uk/books?id=F8sWAQAAIAAJ]
*Fukuda. Union Catalog of Books on Japan in Western Languages. 1968. [https://books.google.co.uk/books?id=HKYyAQAAIAAJ]
*A Classified List of Books in Western Languages Relating to Japan. University of Tokyo Press. 1965. [https://books.google.co.uk/books?id=U8MUAQAAIAAJ]
*Katsuji Yabuki (ed). Japan Bibliographic Annual. Published by the Hokuseido Press for the Japan Writers Society. 1956 and 1957.
**Japan Bibliographic Annual 1956. [https://books.google.co.uk/books?id=9XLQAAAAMAAJ]
**Japan Bibliographic Annual 1957. [https://books.google.co.uk/books?id=vesSAAAAIAAJ]. Reviews: (1957) 13 Monumenta Nipponica 166 (April-July) [https://books.google.co.uk/books?id=8S1yb-iwrOwC] (1957) 25 The Oriental Economist 212 (April) [https://books.google.co.uk/books?id=QELoAAAAMAAJ]
*Haring. Books on Japan: A Reference List. 1955. [https://books.google.co.uk/books?id=RbDoAAAAMAAJ]
*Borton. A Selected List of Books and Articles on Japan in English, French, and German. 1940: [https://books.google.co.uk/books?id=YYIsAAAAYAAJ]. Revised and enlarged. Harvard University Press. 1954: [https://books.google.co.uk/books?id=F8O2VwJUPUkC].
**A Selected List of Books on Japan in Western Languages (1945-1960). (Studies on Asia Abroad, vol 1). The Information Centre of Asian Studies, The Toyo Bunko. 1964. [https://books.google.co.uk/books?id=i1_QAAAAMAAJ]
*Oskar Nachod. Bibliography of the Japanese Empire 1906-1926. 1928. [https://archive.org/details/bibliographyofja0001oska/page/n8/mode/1up vol 1]. [https://archive.org/details/bibliographyofja0002oska/page/n6/mode/1up vol 2].
*Fr. von Wenckstern. A Bibliography of the Japanese Empire: being a Classified List of All Books, Essays and Maps in European Languages relating to Dai Nihon (Great Japan) published in Europe, America and in the East from 1859-93 . . . 1895. vol 1. [https://books.google.co.uk/books?id=dcVAAAAAYAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=v7lO4ddqDywC&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
**Volume 2, from 1894 to the middle of 1906. 1907. [https://archive.org/details/bibliographyofja0002frvo/page/n6/mode/1up]
*Hyman Kublin. What Shall I Read on Japan? An Introductory Guide. Japan Society, New York. 1971. [https://books.google.co.uk/books?id=yRRUAAAAYAAJ]

Japanese studies
*An Introductory Bibliography for Japanese Studies. The Japan Foundation. [https://books.google.co.uk/books?id=53O6AAAAIAAJ]
*Richard Perren. Japanese Studies from Pre-History to 1990: A Bibliographical Guide. 1992. [https://books.google.co.uk/books?id=CN9RAQAAIAAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. &quot;Bibliographies&quot; at pp 1 to 3.
*K.B.S. Bibliography of Standard Reference Books for Japanese Studies, with Descriptive Notes. University of Tokyo Press. [https://books.google.co.uk/books?id=95wbAAAAMAAJ]
*[[w:en:Monumenta Nipponica|Monumenta Nipponica]]
*[[w:en:Japan Forum|Japan Forum]]. British Association for Japanese Studies. [https://www.tandfonline.com/journals/rjfo20]
*Japanese Studies. Japanese Studies Association of Australia. ISSN 1037-1397. [https://www.tandfonline.com/journals/cjst20]
*[[w:en:The Journal of Japanese Studies|The Journal of Japanese Studies]]. University of California Press.
*Nichibunken Newsletter. [[w:en:International Research Center for Japanese Studies|International Research Center for Japanese Studies]]. [https://books.google.co.uk/books?id=5TnjAAAAMAAJ] [https://www.nichibun.ac.jp/en/publications/data/news/] [https://newsletter.nichibun.ac.jp/en/]

History and culture
*John W Dower. Japanese History &amp; Culture from Ancient to Modern Times: Seven Basic Bibliographies. 1986. [https://books.google.co.uk/books?id=NX67AAAAIAAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. &quot;Bibliographies &amp; Research Guides&quot; at chapter 6.

Research guides
*Mindy L Kotler. Information Gathering on Japan: A Primer. Search Associates. 1988. ISBN 9780962546006. Catalogue: [https://search.worldcat.org/zh-cn/title/Information-gathering-on-Japan-Joho-:-a-primer/oclc/20530148]. Review: (1989) [https://books.google.co.uk/books?id=NZLiAAAAMAAJ 27] Choice 82

Encyclopedias

See also [[w:ja:Japanese encyclopedias]]
*Louis-Frédéric. Japan Encyclopedia. 2002. [https://books.google.co.uk/books?id=p2QnPijAEmEC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Japan: An Illustrated Encyclopedia. Kodansha. 1993.
**Japan: Profile of a Nation. Kodansha. 1995. Revised Edition. 1999.
*[[w:Kodansha Encyclopedia of Japan|Kodansha Encyclopedia of Japan]]. 1983. Supplement. 1986. [https://books.google.co.uk/books?id=WvApAQAAMAAJ]
*Dorothy Perkins. Encyclopedia of Japan: Japanese History and Culture, from Abacus to Zori. Facts on File. A Roundtable Press Book. 1991. [https://books.google.co.uk/books?id=JLKGAAAAIAAJ]
*Pictorial Encyclopedia of Modern Japan. Gakken. 1986. [https://books.google.co.uk/books?id=0FgKAQAAIAAJ]
*Boye Layfayette De Mente. Japan Encyclopedia. 1995. [https://books.google.co.uk/books?id=f9c7AAAAMAAJ]
**Boye De Mente. Everything Japanese. [The Authoritave Reference on Japan Today]. 1989. [https://books.google.co.uk/books?id=Duku89bARgoC]

Reference books
*Nihon No Sanko Tosho. Volume 1: 1965. Volume 2: 1972.
**Guide to Japanese Reference Books. American Library Association. Chicago. 1966: [https://books.google.co.uk/books?id=0rflAAAAMAAJ]. Supplement. 1979: [https://books.google.co.uk/books?id=j05_F9OHzkQC]. Commentary: Encyclopedia of Library and Information Science, vol 21, [https://books.google.co.uk/books?id=H1pNvzr_n98C&amp;pg=PA149#v=onepage&amp;q&amp;f=false p 149].

Media
*[https://www.bbc.com/news/world-asia-pacific-15217593 Japan media guide]. News. BBC. 20 March 2023.
*Masaaki Kasagi. Mass Media in Japan. (Orientation seminars on Japan, number 14). 1983. [https://books.google.co.uk/books?id=odkgAAAAIAAJ]
*Routledge Handbook of Japanese Media [https://books.google.co.uk/books?id=zilKDwAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]

Publishers
*[https://www.publishersweekly.com/pw/by-topic/international/international-book-news/article/99729-get-to-know-these-japanese-publishing-companies.html Get to Know These Japanese Publishing Companies]. Publishers Weekly. 20 February 2026.

Press and journalism
*[https://reutersinstitute.politics.ox.ac.uk/digital-news-report/2025/japan Japan]. Reuters Institute for the Study of Journalism. 17 June 2025.
*Marjane Aalam and Philippe Régnier. The Japanese Press and Information System. The Graduate Institute of International Studies. Geneva. [https://books.google.co.uk/books?id=RTcbAQAAIAAJ]
*The Japanese Press: Past and Present. Japan Newspaper Publishers' and Editors' Association. [https://books.google.co.uk/books?id=5tcQAAAAIAAJ 1949].
*Anthony Rausch. Japanese Journalism and the Japanese Newspaper: A Supplemental Reader. [https://books.google.co.uk/books?id=mZrToQEACAAJ]
*Frank L Martin. The Journalism of Japan. 1918. [https://books.google.com/books?id=ruYzAQAAMAAJ]
*William De Lange. A History of Japanese Journalism. Japan Library. 1998. [https://books.google.co.uk/books?id=Rd5tb0cuz8QC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Kanesada Hanazono. The Development of Japanese Journalism. Osaka. 1924. [https://books.google.co.uk/books?id=z99ZAAAAMAAJ]
*Kanesada Hanazono. Journalism in Japan and Its Early Pioneers. 1926. [https://books.google.co.uk/books?id=IGTFfLc4bq0C]
*César Castellvi. A Sociology of Journalism in Japan: The Last Empire of the Press. 2024. [https://books.google.co.uk/books?id=a2z8EAAAQBAJ&amp;pg=PR4#v=onepage&amp;q&amp;f=false]
*&quot;Japan&quot;. Christopher H Sterling (ed). Encyclopedia of Journalism. A Sage Reference Publication. 2009. ISBN 9780761929574. vol 3. pp [https://books.google.co.uk/books?id=ZQhDq8fPj2IC&amp;pg=PA809#v=onepage&amp;q&amp;f=false 809] to 815.

Press annuals
*The Japanese Press. (Nihon Shinbun Kyokai). [https://books.google.co.uk/books?id=AfvyAAAAMAAJ 1979] [https://books.google.co.uk/books?id=Au3yAAAAMAAJ 1998]

Summaries of the press
*Daily Summary of Japanese Press

Foreign correspondents
*Foreign Correspondents in Japan: Reporting a Half Century of Upheavals, from 1945 to the Present. Tuttle. 1998. [https://books.google.co.uk/books?id=YI3TAgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Periodicals
*G Raymond Nunn (comp). Japanese Periodicals and Newspapers in Western Languages: An International Union List. Mansell. 1979. [https://books.google.co.uk/books?id=jEROAQAAIAAJ]
*Japan Periodicals. Keizai Koho Center. 3rd Ed [https://books.google.co.uk/books?id=ATm0AAAAIAAJ]. Japan Periodicals, 1982. [https://books.google.co.uk/books?id=PkMyAAAAMAAJ]
*Japanese Periodicals Index
**Humanities and Social Sciences [https://books.google.co.uk/books?id=nXX_RpPGf3AC]
**Natural Sciences [https://books.google.co.uk/books?id=FCJIAAAAYAAJ]
*Current Japanese Periodicals [https://books.google.co.uk/books?id=FjO5AAAAIAAJ]
*Check-list of Japanese Periodicals Held in British University and Research Libraries. [https://books.google.co.uk/books?id=VZgsAAAAYAAJ]
*Union List of Current Japanese Periodicals in the East Asian Libraries of Columbia, Harvard, Princeton, and Yale Universities. [https://books.google.co.uk/books?id=yw7kAAAAMAAJ]
*List of Japanese Periodicals in the Library of the School of Oriental &amp; African Studies. [https://books.google.co.uk/books?id=RREjAQAAIAAJ]
*Gianni Simone. [https://www.japantimes.co.jp/community/2011/04/26/issues/english-mags-approach-milestone-crossroads/ English mags approach milestone, crossroads]. The Japan Times. 26 April 2011.
*Japan Report (1955 onwards) (Consulate General of Japan, Japan Information Center). Vol 39 published in 1993. [https://books.google.co.uk/books?id=MX4BN_frv4IC&amp;pg=PP7#v=onepage&amp;q&amp;f=false] editions:jYuMSMIQC-AC
**Japan Information
*Japan Now [https://books.google.co.uk/books?id=Nul7DRQaexMC&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Japan Quarterly. (Asahi Shimbun). 1954 to 2001. [https://books.google.co.uk/books?id=nZMMAQAAMAAJ] [https://books.google.co.uk/books?id=_RwVAAAAMAAJ] 189 issues.
*Japan Illustrated: The Japan Times Quarterly [Pictorial] Magazine (October 1963 to Summer 1977) 15 vols [https://books.google.co.uk/books?id=D7UThOmE8T4C]
*[[w:Japan Spotlight|Japan Spotlight]]. Economy, Culture &amp; History: Japan Spotlight: Bimonthly. [https://books.google.co.uk/books?id=i7C0AAAAIAAJ]
*Focus Japan. (Japan External Trade Organization, JETRO). [https://books.google.co.uk/books?id=2fG2hsEZpRkC]
*The Japan Journal [https://books.google.co.uk/books?id=2V3hAAAAMAAJ] [https://books.google.co.uk/books?id=CJwoAQAAMAAJ]
*Japan Magazine. Muromachi Publicity Corporation. (vols 1 to 5: 1957 to 1963). [https://books.google.co.uk/books?id=Swd18PnVeUgC]
*The Japan Magazine: A Representative Monthly of Things Japanese [https://books.google.co.uk/books?id=ubGKo-p6O_0C] [https://archive.org/details/jm-1914-v4.9-5.2/mode/1up]
*Transactions and Proceedings of the Japan Society, London [https://books.google.co.uk/books?id=B75nnph5qHgC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
**Bulletin. [Bulletin of the Japan Society, London.] [https://books.google.co.uk/books?id=Pd9KvyhnpjMC]
**The Japan Society of London Bulletin [https://books.google.co.uk/books?id=XxlxAAAAMAAJ]
*About Japan. Japan Society, New York. [https://books.google.co.uk/books?id=Nf5OAQAAIAAJ]
**News Bulletin [https://archive.org/details/bub_gb_QcA3AQAAIAAJ/page/n2/mode/1up]
*[[w:en:Metropolis (free magazine)|Metropolis]] (metropolisjapan.com)
*[[w:en:Tokyo Weekender|Tokyo Weekender]] (トーキョー・ウィークエンダー) [https://www.tokyoweekender.com/japan-life/news-and-opinion/nhk-world-features-the-tokyo-weekender-magazine/]
*The Japan Gazette [https://books.google.co.uk/books?id=WSopAAAAYAAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*The Tokio Times [https://books.google.co.uk/books?id=UDfiFBu0vB4C&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*[[w:en:Look Japan|Look Japan]]. (Look Japan Ltd). [https://books.google.co.uk/books?id=QnO6AAAAIAAJ]. Commentary: Gale Directory of Publications and Broadcast Media [https://books.google.co.uk/books?id=ve4dAQAAMAAJ]
*[[w:en:Japan Echo|Japan Echo]]. 1974 to 2010. [https://books.google.co.uk/books?id=Cmq6AAAAIAAJ] [https://books.google.co.uk/books?id=fpmEPpl-85UC]
*PHP Intersect. (Where Japan Meets Asia and the World). PHP Institute. [https://books.google.co.uk/books?id=i74TAQAAMAAJ]
**Intersect Japan [https://books.google.co.uk/books?id=sL8TAQAAMAAJ]
*Speaking of Japan [https://books.google.co.uk/books?id=U7S0AAAAIAAJ]. [Speeches.]
*The Hansei Zasshi: A Monthly Magazine [https://books.google.co.uk/books?id=6qBhfHZo7Q0C&amp;pg=PP5#v=onepage&amp;q&amp;f=false][https://books.google.co.uk/books?id=dyIsvnYjpwEC&amp;pg=PP6#v=onepage&amp;q&amp;f=false]
**The Orient. 1899 onwards [https://books.google.co.uk/books?id=nS1omYYnnd4C&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
*Today's Japan. Orient/West Incorporated. [https://books.google.co.uk/books?id=g2ASAAAAMAAJ]
*Japan Review: Bulletin of the International Research Center for Japanese Studies. [https://books.google.co.uk/books?id=GggOAQAAMAAJ]
*[https://www.bloomberg.com/account/newsletters/next-japan Next Japan]. Bloomberg.

Newspapers

See also [[w:List of newspapers in Japan]]
*Haruhara Akihiko, &quot;English-language newspapers in Japan&quot; (1994) 41 Japan Quarterly [https://www.proquest.com/openview/8e2b760f2a2fa37ba164ea675c095353/1 474] (Issue 4: October 1994)
*James Charles Tanner. English Language Newspapers in Bakumatsu Japan. 1977. [https://books.google.co.uk/books?id=Bn2zgzZy_3oC]
*[https://www.japantimes.co.jp/news/2009/03/03/reference/newspapers-here-soldiering-on/ Newspapers here soldiering on]. The Japan Times. 3 March 2009.

*[[w:The Japan Times|The Japan Times]]
**The Japan Times: Weekly Edition [https://books.google.co.uk/books?id=KoQ-AQAAMAAJ] [https://books.google.co.uk/books?id=yYQ-AQAAMAAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*Japan Daily Mail
*Japan Weekly Mail
*The Japan Chronicle
**Weekly Edition [https://books.google.co.uk/books?id=vXdRAQAAIAAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*The Japan News. (The Japan News by The Yomiuri Shimbun)
**Yomiuri Japan News (from 1955)
**The Yomiuri (from 1958)
**The Daily Yomiuri (from 1970)
*The Asahi Shimbun: Asia &amp; Japan Watch. [https://www.asahi.com/sp/ajw/]
**Asahi Evening News (from 1954)
***Tokyo Evening News (1952 to 1954) [https://ndlsearch.ndl.go.jp/books/R100000002-I000000145073]
*The Mainichi. [https://mainichi.jp/english/]
**Mainichi Daily News (1922 to 2001) [https://www.nytimes.com/2001/02/27/business/worldbusiness/IHT-tech-briefstop-the-presses.html] [https://ndlsearch.ndl.go.jp/books/R100000002-I000000144910]

Sports newspapers; sports dailies
*Louise do Rosario, &quot;News-stand stars&quot; in &quot;Japan&quot; (1992) [https://books.google.co.uk/books?id=T_GzAAAAIAAJ 155] [[w:en:Far Eastern Economic Review|Far Eastern Economic Review]], 24 to 31 December 1992, p 21
*[[w:ja:岡崎満義|Mitsuyoshi Okazaki]], &quot;Unsportsmanlike Journalism: Japan's sports dailies may be popular, but are they sporting?&quot; in &quot;Sport&quot;, [[w:en:Look Japan|Look Japan]], [https://books.google.co.uk/books?id=lD3tAAAAMAAJ January 1995], p 39

News
*[[w:en:Japan Today|Japan Today]] (ジャパントゥデイ). GPlusMedia. Gakken Holdings.

Annuals and year books 
*This is Japan. Asahi Shimbun. 1954 to 1971. [https://books.google.co.uk/books?id=2X9DAQAAIAAJ]. Commentary: A Victorian Sailor's Grave in the Seto Inland Sea, p 244 [https://books.google.co.uk/books?id=OegkAgAAQBAJ&amp;pg=PA244#v=onepage&amp;q&amp;f=false]
*The Japan Year Book. The Japan Year Book Office. 1905 onwards. [https://archive.org/details/bub_gb_arFPAAAAMAAJ/page/n10/mode/1up 1906]. [https://archive.org/details/in.ernet.dli.2015.553496/page/n27/mode/1up 1915].
*The &quot;Japan Gazette&quot; Japan Year Book. The Japan Gazette. [https://archive.org/details/japan-year-book-1913-1914/page/n15/mode/1up 1913-14]
*The Japan Times Year Book

Almanacs
*Asahi Shimbun Japan Almanac. [https://books.google.co.uk/books?id=SEEEAQAAIAAJ 1995].
*Japan Almanac. (The Mainichi Newspapers). [https://books.google.co.uk/books?id=ufAIAQAAIAAJ 1972]. [https://books.google.co.uk/books?id=X4eXWRkbtFsC 1973]. [https://books.google.co.uk/books?id=7rMrAAAAIAAJ] [https://books.google.co.uk/books?id=krMrAAAAIAAJ]
*[[w:Boyé Lafayette De Mente|Boye De Mente]]. Passport's Japan Almanac. [https://books.google.co.uk/books?id=741wAAAAMAAJ]

General
*Japan: A Country Study. (Area Handbook series). 4th Ed: 1983: [https://books.google.co.uk/books?id=HkM5N3JNc5IC]. 5th Ed: 1992: [https://books.google.co.uk/books?id=ze-wupXxpvEC]
*Area Handbook for Japan. 2nd Ed: 1964: [https://books.google.co.uk/books?id=WucdAAAAMAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]. 3rd Ed: 1974: [https://books.google.co.uk/books?id=LG2aoq1U_eoC&amp;pg=PR1#v=onepage&amp;q&amp;f=false] (DA Pam 550-30).
*Colin Simpson. Picture of Japan.
**Japan: An Intimate View. A S Barnes. [https://books.google.co.uk/books?id=3hkeAAAAMAAJ]
**This is Japan. Angus &amp; Robertson. [https://books.google.co.uk/books?id=HJEJAQAAIAAJ]
*Japan. (The World and Its Peoples). Greystone Press, New York. 1964. Volume 1: [https://books.google.co.uk/books?id=yysUAQAAMAAJ]. Volume 2 &quot;Japan Korea&quot;, including Korea: [https://books.google.co.uk/books?id=uQAUAQAAMAAJ]. See pp 1 to 375 for Japan, and pp 376 to 379 for Ryukyu and Bonin Islands.
*Japan. (World and its Peoples: Eastern and Southern Asia, volume 8). Marshall Cavendish. 2008. ISBN 9780761476412.
*Edward Seidensticker. This Country, Japan. Kodansha International. 1979. ISBN 9780870112294. [https://books.google.co.uk/books?id=88wwAQAAIAAJ]
*Hall and Beardsley. Twelve Doors to Japan. McGraw-Hill. New York. 1965. [https://books.google.co.uk/books?id=0KpxAAAAMAAJ]
*&quot;Japan&quot;. Louis Barron (ed). &quot;Asia &amp; Australasia&quot;. Moshe Y Sachs (ed and pub). Worldmark Encyclopedia of the Nations. Worldmark Press, Inc. Harper &amp; Row New York. 1963. pp 145 to 160. [https://books.google.co.uk/books?id=I0oYAQAAMAAJ]
**&quot;Japan&quot;. Asia &amp; Oceania. 7th Ed: 1988. ISBN 0-471 62406-3. vol 4. pp 153 to 168.
**&quot;Japan&quot;. Asia &amp; Oceania. 8th Ed: 1995. Gale Research Inc. ISBN 0-8103-9882-6. vol 4. pp 203 to 220.

Handbooks
*Patrick Heenan (ed). The Japan Handbook. (Regional Handbooks of Economic Development). 1998. [https://books.google.co.uk/books?id=IMG2AgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Introduction
*Introducing Japan Through Books: A Selected Bibliography. Public Information Bureau, Ministry of Foreign Affairs, Japan. 1968. [https://books.google.co.uk/books?id=FvsyAQAAIAAJ]. 2nd Ed: 1973: [https://books.google.co.uk/books?id=Vj0XAQAAMAAJ].
*Donald Ritchie. Introducing Japan. 1st Ed: 1978. Revised Ed: 1986. 6th printing: 1989: [https://books.google.co.uk/books?id=FE-nxxoKayQC]. 2nd Revised Ed: 1990. 2nd printing: 1991: [https://books.google.co.uk/books?id=hz4UAQAAIAAJ]. 1994: [https://books.google.co.uk/books?id=FMvT6m4SgIQC&amp;pg=PP1#v=onepage&amp;q&amp;f=false].
*Herschel Webb. An Introduction to Japan. Columbia University Press. 2nd Ed: 1957: [https://books.google.co.uk/books?id=YQ8MAQAAIAAJ].
*Introducing Modern Japan. A publication of the Japan Information and Culture Center, Embassy of Japan.

Today and yesterday
*Ray Downs. Japan Yesterday and Today. Praeger Publishers. 1970. [https://books.google.co.uk/books?id=PwKxAAAAIAAJ]

Today
*Roger Buckley. Japan Today. Cambridge University Press. 3rd Ed [https://books.google.co.uk/books?id=thyqBtJp2DcC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Contemporary
*Routledge Handbook of Contemporary Japan. 2021. [https://books.google.co.uk/books?id=yfH3DwAAQBAJ&amp;pg=PA2011#v=onepage&amp;q&amp;f=false]
*Duncan McCargo. Contemporary Japan. 3rd Ed: 2012. [https://books.google.co.uk/books?id=8I5KEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Jeff Kingston. Contemporary Japan: History, Politics, and Social Change since the 1980s. 2011. [https://books.google.co.uk/books?id=enJQZA3R4FMC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

[Series]
*Routledge Contemporary Japan Series

Modern
*Hugh Cortazzi. Modern Japan: A Concise Survey. Palgrave Macmillan. 1993. [https://books.google.co.uk/books?id=Cf--DAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

The Japanese
*Peter Tasker. The Japanese: Portrait of a Nation. 1989 [https://books.google.com/books?id=Q1N8ld78wwQC]
**The Japanese: A Major Exploration of Modern Japan. [https://books.google.co.uk/books?id=CW-6AAAAIAAJ]
**Inside Japan: Wealth, Work and Power in the New Japanese Empire. 1987. [https://books.google.co.uk/books?id=2OJuAAAAMAAJ]
*Edwin O Reischauer. The Japanese. The Belknap Press of Harvard University Press. [https://books.google.co.uk/books?id=zrEqAAAAYAAJ]
*Edwin O Reischauer and Marius B Jansen. The Japanese Today: Change and Continuity. 1995. [https://books.google.co.uk/books?id=BTPNlLIy2soC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Japaneseness
*Ray T. Donahue (ed). Exploring Japaneseness: On Japanese Enactments of Culture and Consciousness. Ablex Publishing. 2002. [https://books.google.co.uk/books?id=V_NwAAAAMAAJ]
*Yoji Yamakuse. Japaneseness: A Guide to Values and Virtues. 2016. [https://books.google.co.uk/books?id=tB0iDAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Travel books
*DK Eyewitness Travel: Japan. Reprinted with revisions. 2015: [https://books.google.co.uk/books?id=g2NaBgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. 2017: [https://books.google.co.uk/books?id=vg15DQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false].
*Dodd and Richmond. The Rough Guide to Japan. 2nd Ed: 2001: [https://books.google.co.uk/books?id=pRGq95ytWZoC&amp;pg=PP1#v=onepage&amp;q&amp;f=false].
*Frommer's Japan. 5th Ed: 2000: [https://books.google.co.uk/books?id=-QC8mVyvPa8C].
*Fodor's Japan YYYY. 1984. [https://books.google.co.uk/books?id=aH2Ow27HUQ0C 1986]. [https://books.google.co.uk/books?id=3gTTf6nbv20C 1987]. 1988.
**Fodor's YY Japan. [https://books.google.co.uk/books?id=9QMHllzldlYC 91]. 92. 93.
**Fodor's Japan. 13th Ed: 1996: [https://books.google.co.uk/books?id=cZxZAAAAYAAJ]
*The New Official Guide: Japan. Japan Travel Bureau. 1966. [https://books.google.co.uk/books?id=HoxxAAAAMAAJ]
*Here is Japan. Asahi Broadcasting Corporation. [https://books.google.co.uk/books?id=8QXRCTMNG7MC]
*Japan. (Nagel Travel Guide Series, vol 32). 1964. [https://books.google.co.uk/books?id=QsbXAAAAMAAJ]
*Clark. All the Best in Japan: with Manila, Hong Kong, and Macao. (&quot;All the Best&quot; series). 1959. Reprinted 1964. [https://books.google.co.uk/books?id=yUq4YaaryrwC]. Reviews: [https://archive.dartmouthalumnimagazine.com/article/1958/6/1/all-the-best-in-japan] (1958) 110 Travel 51 [https://books.google.co.uk/books?id=UVwXAQAAMAAJ] 3 Bulletin of the Japan Society, London, No 11: June 1960, p 25 [https://books.google.co.uk/books?id=2oy74hRRXk4C]
**All the Best in Japan and the Orient. 1967.

Languages

See [[Universal Bibliography/Languages/Japanese|Japanese]]

Literature

See [[Universal Bibliography/Literature#Japanese|Japanese literature]]

Music

See [[Universal Bibliography/Music#Japanese and Japan|Music of Japan]]

Cinema

See [[Universal Bibliography/Cinema#Japanese|Cinema of Japan]]

Television

See [[Universal Bibliography/Television#Japanese|Japanese television]]

Culture

See [[Universal Bibliography/Culture#Japanese|Culture of Japan]]

==Korea==
*Korea Journal [https://books.google.co.uk/books?id=O6XfBexsp6gC]

Bibliography and literature
*Thomas H Kang. &quot;Korean Literature and Bibliography&quot;. Kent, Lancour and Daily (eds). Encyclopedia of Library and Information Science. Marcel Dekker. 1977. vol 21. pp [https://books.google.co.uk/books?id=H1pNvzr_n98C&amp;pg=PA176#v=onepage&amp;q&amp;f=false 176] to 240.

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      <text bytes="40061" sha1="k74a3eug7ryyne9onmc444rw6z5ff6x" xml:space="preserve">{{Bibliography}}

See also [[Universal Bibliography/Geography|Geography]].

See [[w:Category:Bibliographies of countries or regions]] and [[w:Category:Works about countries]].

This part of the [[Universal Bibliography]] is a bibliography of countries (including former countries).

==Countries==
*Bateman and Egan (eds). The Encyclopedia of World Geography: A Country by Country Guide. 1993. Revised 1997.
*Peter Stalker. Handbook of the World. 2000. A Guide to Countries of the World. (Oxford Guide to Countries of the World. 2nd Ed: 2004, 2nd Revised Ed: 2007 [https://books.google.co.uk/books?id=GtztAAAAMAAJ], 3rd Ed: 2010 [https://books.google.co.uk/books?id=gvKvfxkbZ1AC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Countries of the World and Their Leaders Yearbook. Gale. [https://books.google.co.uk/books?id=5etKAAAAYAAJ] [https://books.google.co.uk/books?id=p41OAAAAIAAJ]
*Hutchinson Guide to Countries of the World [https://books.google.co.uk/books?id=GgpjUe4kN_IC]
*The World Guide: Global Reference, Country by Country. 11th Ed: 2007 [https://books.google.co.uk/books?id=EoWoLgAACAAJ]
*Spence. The World Today: A Nation-by-Nation Guide. Cassell. 1994. 1999. [https://books.google.com/books?id=Ub8qOQAACAAJ]
*Worldmark Encyclopedia of the Nations [https://books.google.co.uk/books?id=I0oYAQAAMAAJ]
*Kurian. Encyclopedia of the World's Nations. Facts on File. Reviews: [https://books.google.co.uk/books?id=Y1EnAQAAIAAJ] [https://books.google.co.uk/books?id=lz0RAQAAMAAJ]
*Michael O'Mara. Facts about the World's Nations. 1999. [https://books.google.co.uk/books?id=mygYAAAAIAAJ]
*Status of the World's Nations. 1965 [https://books.google.co.uk/books?id=sftEyRbAXMUC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. 1973 [https://books.google.co.uk/books?id=kw2U_Cg2gKYC&amp;pg=PP3#v=onepage&amp;q&amp;f=false].
*[[s:Author:John Alexander Hammerton|Hammerton, John Alexander]] (ed). Countries of the World. Published at the Fleetway House. 6 vols. [https://books.google.co.uk/books?id=e6IaAQAAMAAJ] [https://books.google.co.uk/books?id=K5oaAQAAMAAJ]
*[[s:Author:Robert Brown (1842-1895)|Brown, Robert]]. The Countries of the World. [https://books.google.co.uk/books?id=nO0DAAAAQAAJ&amp;pg=PP13#v=onepage&amp;q&amp;f=false]
*A Morely Dell. The Countries of the World. (Harrap's New Geographical Series). 1932. (School certificate). Reviews: [https://books.google.co.uk/books?id=oSS9PB_Jf7AC] [https://books.google.co.uk/books?id=BicVAAAAIAAJ] [https://books.google.co.uk/books?id=5qBOAAAAIAAJ] [https://books.google.co.uk/books?id=YbwcAQAAIAAJ] [https://books.google.co.uk/books?id=sc1AAAAAIAAJ]

General series:
*National Geographic Countries of the World [https://books.google.co.uk/books?id=IT2wfzVIPykC]
*Countries of the World. Evans Brothers. (GCSE) [https://books.google.co.uk/books?id=a3sZvWc7E1EC&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*One Europe. Longman. [https://search.worldcat.org/en/title/west-germany-adapted-by-lj-russon-from-the-original-german-by-sylvia-lof-ingrid-mallberg-dietrich-rosenthal/oclc/561591761]
*Collier's Nations of the World. The Nations of the World: An Historical Series. [https://books.google.co.uk/books?id=VJY-AAAAYAAJ&amp;pg=PP8#v=onepage&amp;q&amp;f=false]
*Collier's History of Nations. The History of Nations. [https://books.google.co.uk/books?id=fmSUfTY5E80C]
*The Story of the Nations. T Fisher Unwin.
*The World and Its Peoples. (The Illustrated Library of the World and Its Peoples). Greystone Press, New York.
*World and Its Peoples. Marshall Cavendish. [https://books.google.co.uk/books?id=oms5xjI7ba0C&amp;pg=PA141#v=onepage&amp;q&amp;f=false]

==England==
===Counties===
See [[s:Portal:Counties]]

* Harrison, &quot;County Bibliography&quot; (1886) 3 Library Chronicle [https://books.google.co.uk/books?id=Wz9FAAAAYAAJ&amp;pg=PA49#v=onepage&amp;q&amp;f=false 49]

General series
*Victoria County History
*Oxford County Histories
*Pinnock's County Histories
*Shire County Guides. Shire Publications.
*Cambridge County Geographies
*Pike's New Century Series
*[[s:Page:County Churches of Cornwall.djvu/6|County Churches]]. G Allen.

Avon
*Moore. Avon Local History Handbook. Phillimore. 1979. [https://books.google.co.uk/books?id=h0kjAAAAMAAJ] Bibliography, p 102

Bedfordshire
*Conisbee, Lewis Ralph. A Bedfordshire Bibliography. Bedfordshire Historical Record Society. Bedford. 1962. Supplements 1967, 1971, 1978. Third supplement by Threadgill. Review: 6 Archives 52 [https://books.google.co.uk/books?id=oOMZAAAAYAAJ]. See also [https://books.google.co.uk/books?id=MjspAAAAYAAJ] [https://books.google.co.uk/books?id=PejgAAAAMAAJ]
*Godber. History of Bedfordshire. 1969. 1984. [https://books.google.co.uk/books?id=jdvwPQAACAAJ]
*Pinnock. The History and Topography of Bedfordshire [https://books.google.co.uk/books?id=9bJYAAAAcAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*Parry. Select Illustrations, Historical and Topographical, of Bedfordshire [https://books.google.co.uk/books?id=UTUJAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Blyth. The History of Bedford and Visitor's Guide. 1873 [https://books.google.co.uk/books?id=IuIGAAAAQAAJ&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
*Cambridge County Geographies [https://books.google.co.uk/books?id=kTc8AAAAIAAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Buckinghamshire
*Reed. A History of Buckinghamshire. 1993 [https://books.google.co.uk/books?id=BtkWAQAAIAAJ]

Cambridgeshire
*Carter. History of the County of Cambridge [https://books.google.co.uk/books?id=jXpbAAAAQAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*Babington. Ancient Cambridgeshire [https://books.google.co.uk/books?id=DPrCAwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Devon
*Ravenhill and Rowe. Devon Maps and Map-makers [https://books.google.co.uk/books?id=tjf2yAEACAAJ]
*Wright. A Plea for a Devonshire Bibliography. 1885 [https://books.google.co.uk/books?id=8ZUDAAAAQAAJ]

Derbyshire
*Woore. A Catalogue of Local Maps of Derbyshire, C.1528-1800. 2012. [https://books.google.co.uk/books?id=oWmCMwEACAAJ]
*O'Neal. A Bibliography of Derbyshire Lead Mining. 1961

Essex
*Cunnington. Catalogue of Books, Maps and Manuscripts, relating to or connected with the County of Essex. 1902 [https://books.google.co.uk/books?id=oIcqpibGE4MC]
*&quot;The Bibliography of Essex&quot; (1882) 1 Antiquarian Magazine &amp; Bibliographer [https://books.google.co.uk/books?id=dEkEAAAAQAAJ&amp;pg=PA72#v=onepage&amp;q&amp;f=false 72]. See also [https://books.google.co.uk/books?id=dEkEAAAAQAAJ&amp;pg=PA283#v=onepage&amp;q&amp;f=false p 283].
*&quot;The Bibliography of Essex&quot; (1891) 5 The Essex Naturalist 30 [https://books.google.co.uk/books?id=iIo1AQAAMAAJ]
*Moon. Essex Literature. 1900. Review: 61 Literary World 438 [https://books.google.co.uk/books?id=2T0ZAAAAYAAJ] See also [https://books.google.co.uk/books?id=1Y4UAQAAIAAJ] [https://books.google.co.uk/books?id=C_pEAAAAMAAJ]
*Fenn and Lowery, &quot;An Essex Bibliography&quot;, Journal of the South West Essex Technical College, vols 2 &amp; 3
*Victoria County History bibliography. 1959 [https://books.google.co.uk/books?id=F2EJAQAAIAAJ]
*O'Leary, John Gerard. A Supplement to the Essex Bibliography. Dagenham. 1962.
*A Bibliography of Essex Archaeology &amp; History
*Essex and Dagenham: A Catalogue of Books, Pamphlets and Maps. Dagenham. 1961
*Essex Archaeology and History: The Transactions of the Essex Society for Archaeological and History [https://books.google.co.uk/books?id=CtFAAAAAYAAJ]
*Essex Naturalist: Being the Journal of the Essex Field Club
*Wright. The History and Topography of the County of Essex [https://books.google.co.uk/books?id=SgQVAAAAQAAJ&amp;pg=PP9#v=onepage&amp;q&amp;f=false]
*Ogborne, The History of Essex [https://books.google.co.uk/books?id=IeVSAAAAcAAJ&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
*Suckling. Memorials of the Antiquities and Architecture, Family History and Heraldry of the County of Essex [https://books.google.co.uk/books?id=bcw_AAAAcAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Hunter, The Essex Landscape: A Study of Its Form and History [https://books.google.co.uk/books?id=w9kWAQAAIAAJ]
*Cambridge County Geography [https://books.google.co.uk/books?id=GPHa_X_0qo0C&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*Sokoll. Essex  Pauper Letters, 1731-1837 [https://books.google.co.uk/books?id=rCLia7XlqtMC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Morant. The History and Antiquities of Colchester in the County of Essex [https://books.google.co.uk/books?id=DDgtAAAAYAAJ&amp;pg=PP9#v=onepage&amp;q&amp;f=false]
*Wallen. The History and Antiquities of the Round Church at Little Maplestead, Essex [https://books.google.co.uk/books?id=FPYVAAAAYAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]

Kent
*Smith. Bibliotheca Cantiana. 1837. [https://books.google.co.uk/books?id=1dJDAAAAYAAJ&amp;pg=PP11#v=onepage&amp;q&amp;f=false]

Leicestershire
*Kirkby, C V (compiler). Catalogue of the books, pamphlets, &amp;c., relating to Leicestershire in the Central Reference Library. Leicester Free Public Libraries. 1893. Reviews: [https://books.google.co.uk/books?id=3boqAQAAIAAJ&amp;pg=PA84#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=UcHnAAAAMAAJ&amp;pg=PA728#v=onepage&amp;q&amp;f=false]
*Leicestershire and Rutland Bibliography, 1963-65 (1966) [https://books.google.co.uk/books?id=-OhVAAAAYAAJ 40] Leicestershire Archaeological and Historical Society: Transactions (1964/5) 92. Available as pdf from University of Leicester.
*Leicestershire and Rutland Bibliography, 1961-63. Available as pdf from University of Leicester.
*Leicestershire and Rutland Bibliography, 1960-61. Available as pdf from University of Leicester.
*A Bibliography of the Small Towns in Leicestershire and Rutland, 1600–1850. (Dissertation). [https://repository.lboro.ac.uk/articles/educational_resource/A_bibliography_of_the_small_towns_in_Leicestershire_and_Rutland_1600_1850/9414200]
*Loughborough's Heritage: A Bibliography of the Holdings of Leicestershire Libraries and Information Service and Record Office. [https://books.google.co.uk/books?id=Bwx2zgEACAAJ]
*Keith Ambrose and Frank Williams, &quot;Bibliography of the Geology of Leicestershire and Rutland: Part 2: 1971-2003&quot; (2004) [https://books.google.co.uk/books?id=U-tQAQAAIAAJ 16] The Mercian Geologist 5. Available as pdf from East Midlands Geological Society.
*Parsons and Brandwood. A Bibliography of Leicestershire Churches. 1978.
*Education in Leicestershire: A Bibliography. [https://books.google.co.uk/books?id=X6EfzQEACAAJ]

Sussex
*Brent, Fletcher and McCann. Sussex in the 16th and 17th Centuries: A Bibliography. 2nd Ed [https://books.google.co.uk/books?id=I7UtAAAAYAAJ]
*Farrant. Sussex in the 18th and 19th Centuries: A Bibliography. 1st Ed: 1973, 2nd Ed: 1977 [https://books.google.co.uk/books?id=MLUtAAAAYAAJ], 3rd Ed: 1979

==France==
Bibliography:
*Bibliographie de la France. Commentary: Encyclopedia of Library and Information Science, vol 37, supplement 2, [https://books.google.co.uk/books?id=10rgjNvOV8oC&amp;pg=PA145#v=onepage&amp;q&amp;f=false p 145]; The Bookseller, 6 January 1881, [https://books.google.co.uk/books?id=4dsiAQAAMAAJ&amp;pg=PA10#v=onepage&amp;q&amp;f=false p 10]; Stein, Manuel de bibliographie générale, [https://books.google.co.uk/books?id=lJYPyKjV1qYC&amp;pg=PA23#v=onepage&amp;q&amp;f=false p 23]. 
*Girault de Saint-Fargeau. Bibliographie historique et topographique de la France. 1845 [https://books.google.co.uk/books?id=kClB9CQNZoMC&amp;pg=PP9#v=onepage&amp;q&amp;f=false]
*Catalogue d'une collection d'ouvrages sur l'histoire des provinces de la France. 1842 [https://books.google.co.uk/books?id=qQBX5WZouzAC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Landscape:
*Beaujeu-Garnier. France. (The World's Landscapes). 1975. [https://books.google.com/books?id=nwxDAQAAIAAJ]

Agenais:
*Andrieu. Bibliographie générale de l’Agenais et des parties du Condomois et du Bazadais. 1886 to 1891. Reprinted 1969.

Alsace:
*Ristelhuber. Bibliographie alsacienne. 1869 to 1873 [https://books.google.co.uk/books?id=0mhLAQAAMAAJ&amp;pg=PP13#v=onepage&amp;q&amp;f=false]
*Bibliographie alsacienne: Revue critique des publications concernant l'Alsace. 1918 to 1936
*Ritter. Répertoire bibliographique des livres imprimés en Alsace aux XVe et XVIe siècles [https://books.google.co.uk/books?id=DewaAQAAMAAJ]

Angoumois:
*Castaigne. Essai d'une bibliothèque historique de l'Angoumois, ou Catalogue raisonné des principaux ouvrages qui traitent des différentes branches de l'histoire de cette province. 1847 [https://books.google.co.uk/books?id=R-UanmmlvAEC&amp;pg=PP7#v=onepage&amp;q&amp;f=false]

Anjou:
*Braguier and Braguier. Archéologie en Anjou: bibliographie. 1984 [https://books.google.co.uk/books?id=LvsmAQAAIAAJ]

Auvergne:
*Gonot. Catalogue des ouvrages imprimés et manuscrits concernant l'Auvergne, extrait du catalogue général de la Bibliotlèque de Clermont-Fd (Puy-de-Dome). 1849. [https://books.google.co.uk/books?id=yCFtbObRCbUC&amp;pg=PP13#v=onepage&amp;q&amp;f=false]
*Catalogue des livres et estampes concernant l'ancienne Province d'Auvergne (Puy-de-Dôme, Cantal, Haute-Loire) réunis par feu M. G. Desbouis. 1865. [https://books.google.co.uk/books?id=Ui4S8_D0N74C&amp;pg=PP7#v=onepage&amp;q&amp;f=false]

Béarn
*&quot;Bibliographie Béarnaise&quot;, Revue de Pau et du Béarn [https://books.google.co.uk/books?id=FuZnAAAAMAAJ] Commentary: [https://books.google.co.uk/books?id=FQYqvPo9D9IC&amp;pg=PA158#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=RL9VAAAAYAAJ]

Brittany
*Sacher. Bibliographie de la Bretagne, ou Catalogue général des ouvrages historiques, littéraires et scientifiques parus sur la Bretagne, avec la liste des revues publiées en cette province, les prix approximatifs des volumes rares, etc. 1881 [https://archive.org/details/bibliographiede00sach]

Burgundy:
*Milsand. Bibliographie bourguignonne; ou, Catalogue méthodique d'ouvrages relatifs à la Bourgogne: Sciences - Arts - Histoire. 1885 [https://archive.org/details/bibliographiebo00milsgoog] [https://archive.org/details/bibliographiebo00sciegoog] [https://books.google.co.uk/books?id=CxIIAAAAQAAJ]
*Catalogue des manuscrits de la Bibliothèque royale des ducs de Bourgogne. 1842 [https://books.google.co.uk/books?id=FX5MAAAAcAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*The Companion Guide to Burgundy [https://books.google.co.uk/books?id=NraRP0AkDT0C&amp;pg=PP3#v=onepage&amp;q&amp;f=false]
*Lecat. The Golden Book of Burgundy. (The Golden Book) [https://books.google.co.uk/books?id=FyzR9qU1Zl4C&amp;lpg=PP1&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Gwynn. Burgundy: With Chapters on the Jura and Savoy. (Kitbag Travel Books). 1935 [https://books.google.co.uk/books?id=ny1LAAAAMAAJ]
*Bazin. Wonderful Burgundy. 1988. 1997 [https://books.google.co.uk/books?id=Yt1CRdICWCUC]
*Bailey. Burgundy. (Insight Guides). 1993 [https://books.google.co.uk/books?id=Q69a1dMW2NQC]
*Dunlop. Burgundy. Hamilton.1990 [https://books.google.co.uk/books?id=S_1OAAAAMAAJ]

Champagne:
*Lhermitte. Ouvrages sur la Champagne: contribution à la bibliographie champenoise. 1992. [https://books.google.co.uk/books?id=jbPfAAAAMAAJ]

Dauphiné:
*Mélanges biographiques et bibliographiques relatifs à l'histoire littéraire du Dauphiné par Colomb de Batines et Ollivier Jules. 1837 [https://books.google.co.uk/books?id=2F5MAAAAcAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

Lorraine:
*Bibliographie lorraine. Académie nationale de Metz [https://books.google.co.uk/books?id=n-DfAAAAMAAJ]

Maine:
*Desportes. Bibliographie du Maine, précédée de la description topographique et hydrographique du diocése du Mans, Sarthe et Mayenne. 1844. [https://books.google.co.uk/books?id=hSk-AAAAYAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

Normandy:
*Frère. Manuel du bibliographe Normand ou dictionnaire bibliographique et historique. 1858 to 1860. [https://books.google.co.uk/books?id=dp6geJClg1YC&amp;pg=PP13#v=onepage&amp;q&amp;f=false vol 1]

==Japan==
Bibliography and literature
*Hideo Kaneko. &quot;Japanese Literature and Bibliography&quot;. Kent, Lancour and Daily (eds). Encyclopedia of Library and Information Science. Marcel Dekker. 1977. vol 21. pp [https://books.google.co.uk/books?id=H1pNvzr_n98C&amp;pg=PA131#v=onepage&amp;q&amp;f=false 131] to 176.

Bibliography
*Jozef Rogala. A Collector's Guide to Books on Japan in English: An Annotated List of Over 2500 Titles with Subject Index. 2001. [https://books.google.co.uk/books?id=7KI9ao-w2FEC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Ria Koopmans-de Bruijn. Area Bibliography of Japan. (Scarecrow Area Bibliographies). Scarecrow Press. 1998. [https://books.google.co.uk/books?id=Hlx2OMjgUi0C&amp;pg=PR1#v=onepage&amp;q&amp;f=false]
*Frank Joseph Shulman. Japan. (World Bibliographical Series, vol 103). Clio Press. 1989. [https://books.google.co.uk/books?id=LsoUAQAAIAAJ]
*Eibun Nihon Kankei Tosho Mokuroku, 1945-1981. (Japanese: 英文日本関係図書目録, 1945-1981). (English: Catalogue of Books in English on Japan, 1945-1981). Japan Foundation. Tokyo. 1986.
*Japan: analytical bibliography: with supplementary research aids: and selected data on Okinawa . . . Department of the Army. Washington. 1972. [https://books.google.co.uk/books?id=h4d4nYxrxtMC&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Books on Japan in Western Languages. The International Christian University Library. 1971. [https://books.google.co.uk/books?id=F2bQAAAAMAAJ]
*Books on Japan: A List of Acquisitions, 1955-1970. International House of Japan Library. 1971. [https://books.google.co.uk/books?id=F8sWAQAAIAAJ]
*Fukuda. Union Catalog of Books on Japan in Western Languages. 1968. [https://books.google.co.uk/books?id=HKYyAQAAIAAJ]
*A Classified List of Books in Western Languages Relating to Japan. University of Tokyo Press. 1965. [https://books.google.co.uk/books?id=U8MUAQAAIAAJ]
*Katsuji Yabuki (ed). Japan Bibliographic Annual. Published by the Hokuseido Press for the Japan Writers Society. 1956 and 1957.
**Japan Bibliographic Annual 1956. [https://books.google.co.uk/books?id=9XLQAAAAMAAJ]
**Japan Bibliographic Annual 1957. [https://books.google.co.uk/books?id=vesSAAAAIAAJ]. Reviews: (1957) 13 Monumenta Nipponica 166 (April-July) [https://books.google.co.uk/books?id=8S1yb-iwrOwC] (1957) 25 The Oriental Economist 212 (April) [https://books.google.co.uk/books?id=QELoAAAAMAAJ]
*Haring. Books on Japan: A Reference List. 1955. [https://books.google.co.uk/books?id=RbDoAAAAMAAJ]
*Borton. A Selected List of Books and Articles on Japan in English, French, and German. 1940: [https://books.google.co.uk/books?id=YYIsAAAAYAAJ]. Revised and enlarged. Harvard University Press. 1954: [https://books.google.co.uk/books?id=F8O2VwJUPUkC].
**A Selected List of Books on Japan in Western Languages (1945-1960). (Studies on Asia Abroad, vol 1). The Information Centre of Asian Studies, The Toyo Bunko. 1964. [https://books.google.co.uk/books?id=i1_QAAAAMAAJ]
*Oskar Nachod. Bibliography of the Japanese Empire 1906-1926. 1928. [https://archive.org/details/bibliographyofja0001oska/page/n8/mode/1up vol 1]. [https://archive.org/details/bibliographyofja0002oska/page/n6/mode/1up vol 2].
*Fr. von Wenckstern. A Bibliography of the Japanese Empire: being a Classified List of All Books, Essays and Maps in European Languages relating to Dai Nihon (Great Japan) published in Europe, America and in the East from 1859-93 . . . 1895. vol 1. [https://books.google.co.uk/books?id=dcVAAAAAYAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=v7lO4ddqDywC&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
**Volume 2, from 1894 to the middle of 1906. 1907. [https://archive.org/details/bibliographyofja0002frvo/page/n6/mode/1up]
*Hyman Kublin. What Shall I Read on Japan? An Introductory Guide. Japan Society, New York. 1971. [https://books.google.co.uk/books?id=yRRUAAAAYAAJ]

Japanese studies
*An Introductory Bibliography for Japanese Studies. The Japan Foundation. [https://books.google.co.uk/books?id=53O6AAAAIAAJ]
*Richard Perren. Japanese Studies from Pre-History to 1990: A Bibliographical Guide. 1992. [https://books.google.co.uk/books?id=CN9RAQAAIAAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. &quot;Bibliographies&quot; at pp 1 to 3.
*K.B.S. Bibliography of Standard Reference Books for Japanese Studies, with Descriptive Notes. University of Tokyo Press. [https://books.google.co.uk/books?id=95wbAAAAMAAJ]
*[[w:en:Monumenta Nipponica|Monumenta Nipponica]]
*[[w:en:Japan Forum|Japan Forum]]. British Association for Japanese Studies. [https://www.tandfonline.com/journals/rjfo20]
*Japanese Studies. Japanese Studies Association of Australia. ISSN 1037-1397. [https://www.tandfonline.com/journals/cjst20]
*[[w:en:The Journal of Japanese Studies|The Journal of Japanese Studies]]. University of California Press.
*Nichibunken Newsletter. [[w:en:International Research Center for Japanese Studies|International Research Center for Japanese Studies]]. [https://books.google.co.uk/books?id=5TnjAAAAMAAJ] [https://www.nichibun.ac.jp/en/publications/data/news/] [https://newsletter.nichibun.ac.jp/en/]

History and culture
*John W Dower. Japanese History &amp; Culture from Ancient to Modern Times: Seven Basic Bibliographies. 1986. [https://books.google.co.uk/books?id=NX67AAAAIAAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. &quot;Bibliographies &amp; Research Guides&quot; at chapter 6.

Research guides
*Mindy L Kotler. Information Gathering on Japan: A Primer. Search Associates. 1988. ISBN 9780962546006. Catalogue: [https://search.worldcat.org/zh-cn/title/Information-gathering-on-Japan-Joho-:-a-primer/oclc/20530148]. Review: (1989) [https://books.google.co.uk/books?id=NZLiAAAAMAAJ 27] Choice 82

Encyclopedias

See also [[w:ja:Japanese encyclopedias]]
*Louis-Frédéric. Japan Encyclopedia. 2002. [https://books.google.co.uk/books?id=p2QnPijAEmEC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Japan: An Illustrated Encyclopedia. Kodansha. 1993.
**Japan: Profile of a Nation. Kodansha. 1995. Revised Edition. 1999.
*[[w:Kodansha Encyclopedia of Japan|Kodansha Encyclopedia of Japan]]. 1983. Supplement. 1986. [https://books.google.co.uk/books?id=WvApAQAAMAAJ]
*Dorothy Perkins. Encyclopedia of Japan: Japanese History and Culture, from Abacus to Zori. Facts on File. A Roundtable Press Book. 1991. [https://books.google.co.uk/books?id=JLKGAAAAIAAJ]
*Pictorial Encyclopedia of Modern Japan. Gakken. 1986. [https://books.google.co.uk/books?id=0FgKAQAAIAAJ]
*Boye Layfayette De Mente. Japan Encyclopedia. 1995. [https://books.google.co.uk/books?id=f9c7AAAAMAAJ]
**Boye De Mente. Everything Japanese. [The Authoritave Reference on Japan Today]. 1989. [https://books.google.co.uk/books?id=Duku89bARgoC]

Reference books
*Nihon No Sanko Tosho. Volume 1: 1965. Volume 2: 1972.
**Guide to Japanese Reference Books. American Library Association. Chicago. 1966: [https://books.google.co.uk/books?id=0rflAAAAMAAJ]. Supplement. 1979: [https://books.google.co.uk/books?id=j05_F9OHzkQC]. Commentary: Encyclopedia of Library and Information Science, vol 21, [https://books.google.co.uk/books?id=H1pNvzr_n98C&amp;pg=PA149#v=onepage&amp;q&amp;f=false p 149].

Media
*[https://www.bbc.com/news/world-asia-pacific-15217593 Japan media guide]. News. BBC. 20 March 2023.
*Masaaki Kasagi. Mass Media in Japan. (Orientation seminars on Japan, number 14). 1983. [https://books.google.co.uk/books?id=odkgAAAAIAAJ]
*Routledge Handbook of Japanese Media [https://books.google.co.uk/books?id=zilKDwAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]

Publishers
*[https://www.publishersweekly.com/pw/by-topic/international/international-book-news/article/99729-get-to-know-these-japanese-publishing-companies.html Get to Know These Japanese Publishing Companies]. Publishers Weekly. 20 February 2026.

Press and journalism
*[https://reutersinstitute.politics.ox.ac.uk/digital-news-report/2025/japan Japan]. Reuters Institute for the Study of Journalism. 17 June 2025.
*Marjane Aalam and Philippe Régnier. The Japanese Press and Information System. The Graduate Institute of International Studies. Geneva. [https://books.google.co.uk/books?id=RTcbAQAAIAAJ]
*The Japanese Press: Past and Present. Japan Newspaper Publishers' and Editors' Association. [https://books.google.co.uk/books?id=5tcQAAAAIAAJ 1949].
*Anthony Rausch. Japanese Journalism and the Japanese Newspaper: A Supplemental Reader. [https://books.google.co.uk/books?id=mZrToQEACAAJ]
*Frank L Martin. The Journalism of Japan. 1918. [https://books.google.com/books?id=ruYzAQAAMAAJ]
*William De Lange. A History of Japanese Journalism. Japan Library. 1998. [https://books.google.co.uk/books?id=Rd5tb0cuz8QC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Kanesada Hanazono. The Development of Japanese Journalism. Osaka. 1924. [https://books.google.co.uk/books?id=z99ZAAAAMAAJ]
*Kanesada Hanazono. Journalism in Japan and Its Early Pioneers. 1926. [https://books.google.co.uk/books?id=IGTFfLc4bq0C]
*César Castellvi. A Sociology of Journalism in Japan: The Last Empire of the Press. 2024. [https://books.google.co.uk/books?id=a2z8EAAAQBAJ&amp;pg=PR4#v=onepage&amp;q&amp;f=false]
*&quot;Japan&quot;. Christopher H Sterling (ed). Encyclopedia of Journalism. A Sage Reference Publication. 2009. ISBN 9780761929574. vol 3. pp [https://books.google.co.uk/books?id=ZQhDq8fPj2IC&amp;pg=PA809#v=onepage&amp;q&amp;f=false 809] to 815.

Press annuals
*The Japanese Press. (Nihon Shinbun Kyokai). [https://books.google.co.uk/books?id=AfvyAAAAMAAJ 1979] [https://books.google.co.uk/books?id=Au3yAAAAMAAJ 1998]

Summaries of the press
*Daily Summary of Japanese Press

Foreign correspondents
*Foreign Correspondents in Japan: Reporting a Half Century of Upheavals, from 1945 to the Present. Tuttle. 1998. [https://books.google.co.uk/books?id=YI3TAgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Periodicals
*G Raymond Nunn (comp). Japanese Periodicals and Newspapers in Western Languages: An International Union List. Mansell. 1979. [https://books.google.co.uk/books?id=jEROAQAAIAAJ]
*Japan Periodicals. Keizai Koho Center. 3rd Ed [https://books.google.co.uk/books?id=ATm0AAAAIAAJ]. Japan Periodicals, 1982. [https://books.google.co.uk/books?id=PkMyAAAAMAAJ]
*Japanese Periodicals Index
**Humanities and Social Sciences [https://books.google.co.uk/books?id=nXX_RpPGf3AC]
**Natural Sciences [https://books.google.co.uk/books?id=FCJIAAAAYAAJ]
*Current Japanese Periodicals [https://books.google.co.uk/books?id=FjO5AAAAIAAJ]
*Check-list of Japanese Periodicals Held in British University and Research Libraries. [https://books.google.co.uk/books?id=VZgsAAAAYAAJ]
*Union List of Current Japanese Periodicals in the East Asian Libraries of Columbia, Harvard, Princeton, and Yale Universities. [https://books.google.co.uk/books?id=yw7kAAAAMAAJ]
*List of Japanese Periodicals in the Library of the School of Oriental &amp; African Studies. [https://books.google.co.uk/books?id=RREjAQAAIAAJ]
*Gianni Simone. [https://www.japantimes.co.jp/community/2011/04/26/issues/english-mags-approach-milestone-crossroads/ English mags approach milestone, crossroads]. The Japan Times. 26 April 2011.
*Japan Report (1955 onwards) (Consulate General of Japan, Japan Information Center). Vol 39 published in 1993. [https://books.google.co.uk/books?id=MX4BN_frv4IC&amp;pg=PP7#v=onepage&amp;q&amp;f=false] editions:jYuMSMIQC-AC
**Japan Information
*Japan Now [https://books.google.co.uk/books?id=Nul7DRQaexMC&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Japan Quarterly. (Asahi Shimbun). 1954 to 2001. [https://books.google.co.uk/books?id=nZMMAQAAMAAJ] [https://books.google.co.uk/books?id=_RwVAAAAMAAJ] 189 issues.
*Japan Illustrated: The Japan Times Quarterly [Pictorial] Magazine (October 1963 to Summer 1977) 15 vols [https://books.google.co.uk/books?id=D7UThOmE8T4C]
*[[w:Japan Spotlight|Japan Spotlight]]. Economy, Culture &amp; History: Japan Spotlight: Bimonthly. [https://books.google.co.uk/books?id=i7C0AAAAIAAJ]
*Focus Japan. (Japan External Trade Organization, JETRO). [https://books.google.co.uk/books?id=2fG2hsEZpRkC]
*The Japan Journal [https://books.google.co.uk/books?id=2V3hAAAAMAAJ] [https://books.google.co.uk/books?id=CJwoAQAAMAAJ]
*Japan Magazine. Muromachi Publicity Corporation. (vols 1 to 5: 1957 to 1963). [https://books.google.co.uk/books?id=Swd18PnVeUgC]
*The Japan Magazine: A Representative Monthly of Things Japanese [https://books.google.co.uk/books?id=ubGKo-p6O_0C] [https://archive.org/details/jm-1914-v4.9-5.2/mode/1up]
*Transactions and Proceedings of the Japan Society, London [https://books.google.co.uk/books?id=B75nnph5qHgC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
**Bulletin. [Bulletin of the Japan Society, London.] [https://books.google.co.uk/books?id=Pd9KvyhnpjMC]
**The Japan Society of London Bulletin [https://books.google.co.uk/books?id=XxlxAAAAMAAJ]
*About Japan. Japan Society, New York. [https://books.google.co.uk/books?id=Nf5OAQAAIAAJ]
**News Bulletin [https://archive.org/details/bub_gb_QcA3AQAAIAAJ/page/n2/mode/1up]
*[[w:en:Metropolis (free magazine)|Metropolis]] (metropolisjapan.com)
*[[w:en:Tokyo Weekender|Tokyo Weekender]] (トーキョー・ウィークエンダー) [https://www.tokyoweekender.com/japan-life/news-and-opinion/nhk-world-features-the-tokyo-weekender-magazine/]
*The Japan Gazette [https://books.google.co.uk/books?id=WSopAAAAYAAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*The Tokio Times [https://books.google.co.uk/books?id=UDfiFBu0vB4C&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*[[w:en:Look Japan|Look Japan]]. (Look Japan Ltd). [https://books.google.co.uk/books?id=QnO6AAAAIAAJ]. Commentary: Gale Directory of Publications and Broadcast Media [https://books.google.co.uk/books?id=ve4dAQAAMAAJ]
*[[w:en:Japan Echo|Japan Echo]]. 1974 to 2010. [https://books.google.co.uk/books?id=Cmq6AAAAIAAJ] [https://books.google.co.uk/books?id=fpmEPpl-85UC]
*PHP Intersect. (Where Japan Meets Asia and the World). PHP Institute. [https://books.google.co.uk/books?id=i74TAQAAMAAJ]
**Intersect Japan [https://books.google.co.uk/books?id=sL8TAQAAMAAJ]
*Speaking of Japan [https://books.google.co.uk/books?id=U7S0AAAAIAAJ]. [Speeches.]
*The Hansei Zasshi: A Monthly Magazine [https://books.google.co.uk/books?id=6qBhfHZo7Q0C&amp;pg=PP5#v=onepage&amp;q&amp;f=false][https://books.google.co.uk/books?id=dyIsvnYjpwEC&amp;pg=PP6#v=onepage&amp;q&amp;f=false]
**The Orient. 1899 onwards [https://books.google.co.uk/books?id=nS1omYYnnd4C&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
*Today's Japan. Orient/West Incorporated. [https://books.google.co.uk/books?id=g2ASAAAAMAAJ]
*Japan Review: Bulletin of the International Research Center for Japanese Studies. [https://books.google.co.uk/books?id=GggOAQAAMAAJ]
*[https://www.bloomberg.com/account/newsletters/next-japan Next Japan]. Bloomberg.

Newspapers

See also [[w:List of newspapers in Japan]]
*Haruhara Akihiko, &quot;English-language newspapers in Japan&quot; (1994) 41 Japan Quarterly [https://www.proquest.com/openview/8e2b760f2a2fa37ba164ea675c095353/1 474] (Issue 4: October 1994)
*James Charles Tanner. English Language Newspapers in Bakumatsu Japan. 1977. [https://books.google.co.uk/books?id=Bn2zgzZy_3oC]
*[https://www.japantimes.co.jp/news/2009/03/03/reference/newspapers-here-soldiering-on/ Newspapers here soldiering on]. The Japan Times. 3 March 2009.

*[[w:The Japan Times|The Japan Times]]
**The Japan Times: Weekly Edition [https://books.google.co.uk/books?id=KoQ-AQAAMAAJ] [https://books.google.co.uk/books?id=yYQ-AQAAMAAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*Japan Daily Mail
*Japan Weekly Mail
*The Japan Chronicle
**Weekly Edition [https://books.google.co.uk/books?id=vXdRAQAAIAAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*The Japan News. (The Japan News by The Yomiuri Shimbun)
**Yomiuri Japan News (from 1955)
**The Yomiuri (from 1958)
**The Daily Yomiuri (from 1970)
*The Asahi Shimbun: Asia &amp; Japan Watch. [https://www.asahi.com/sp/ajw/]
**Asahi Evening News (from 1954)
***Tokyo Evening News (1952 to 1954) [https://ndlsearch.ndl.go.jp/books/R100000002-I000000145073]
*The Mainichi. [https://mainichi.jp/english/]
**Mainichi Daily News (1922 to 2001) [https://www.nytimes.com/2001/02/27/business/worldbusiness/IHT-tech-briefstop-the-presses.html] [https://ndlsearch.ndl.go.jp/books/R100000002-I000000144910]

Sports newspapers; sports dailies
*Louise do Rosario, &quot;News-stand stars&quot; in &quot;Japan&quot; (1992) [https://books.google.co.uk/books?id=T_GzAAAAIAAJ 155] [[w:en:Far Eastern Economic Review|Far Eastern Economic Review]], 24 to 31 December 1992, p 21
*[[w:ja:岡崎満義|Mitsuyoshi Okazaki]], &quot;Unsportsmanlike Journalism: Japan's sports dailies may be popular, but are they sporting?&quot; in &quot;Sport&quot;, [[w:en:Look Japan|Look Japan]], [https://books.google.co.uk/books?id=lD3tAAAAMAAJ January 1995], p 39

News
*[[w:en:Japan Today|Japan Today]] (ジャパントゥデイ). GPlusMedia. Gakken Holdings.

Annuals and year books 
*This is Japan. Asahi Shimbun. 1954 to 1971. [https://books.google.co.uk/books?id=2X9DAQAAIAAJ]. Commentary: A Victorian Sailor's Grave in the Seto Inland Sea, p 244 [https://books.google.co.uk/books?id=OegkAgAAQBAJ&amp;pg=PA244#v=onepage&amp;q&amp;f=false]
*The Japan Year Book. The Japan Year Book Office. 1905 onwards. [https://archive.org/details/bub_gb_arFPAAAAMAAJ/page/n10/mode/1up 1906]. [https://archive.org/details/in.ernet.dli.2015.553496/page/n27/mode/1up 1915].
*The &quot;Japan Gazette&quot; Japan Year Book. The Japan Gazette. [https://archive.org/details/japan-year-book-1913-1914/page/n15/mode/1up 1913-14]
*The Japan Times Year Book
*New Japan. Mainichi Newspapers. [https://books.google.co.uk/books?id=gRFCAQAAIAAJ]

Almanacs
*Asahi Shimbun Japan Almanac. [https://books.google.co.uk/books?id=SEEEAQAAIAAJ 1995].
*Japan Almanac. (The Mainichi Newspapers). [https://books.google.co.uk/books?id=ufAIAQAAIAAJ 1972]. [https://books.google.co.uk/books?id=X4eXWRkbtFsC 1973]. [https://books.google.co.uk/books?id=7rMrAAAAIAAJ] [https://books.google.co.uk/books?id=krMrAAAAIAAJ]
*[[w:Boyé Lafayette De Mente|Boye De Mente]]. Passport's Japan Almanac. [https://books.google.co.uk/books?id=741wAAAAMAAJ]

General
*Japan: A Country Study. (Area Handbook series). 4th Ed: 1983: [https://books.google.co.uk/books?id=HkM5N3JNc5IC]. 5th Ed: 1992: [https://books.google.co.uk/books?id=ze-wupXxpvEC]
*Area Handbook for Japan. 2nd Ed: 1964: [https://books.google.co.uk/books?id=WucdAAAAMAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]. 3rd Ed: 1974: [https://books.google.co.uk/books?id=LG2aoq1U_eoC&amp;pg=PR1#v=onepage&amp;q&amp;f=false] (DA Pam 550-30).
*Colin Simpson. Picture of Japan.
**Japan: An Intimate View. A S Barnes. [https://books.google.co.uk/books?id=3hkeAAAAMAAJ]
**This is Japan. Angus &amp; Robertson. [https://books.google.co.uk/books?id=HJEJAQAAIAAJ]
*Japan. (The World and Its Peoples). Greystone Press, New York. 1964. Volume 1: [https://books.google.co.uk/books?id=yysUAQAAMAAJ]. Volume 2 &quot;Japan Korea&quot;, including Korea: [https://books.google.co.uk/books?id=uQAUAQAAMAAJ]. See pp 1 to 375 for Japan, and pp 376 to 379 for Ryukyu and Bonin Islands.
*Japan. (World and its Peoples: Eastern and Southern Asia, volume 8). Marshall Cavendish. 2008. ISBN 9780761476412.
*Edward Seidensticker. This Country, Japan. Kodansha International. 1979. ISBN 9780870112294. [https://books.google.co.uk/books?id=88wwAQAAIAAJ]
*Hall and Beardsley. Twelve Doors to Japan. McGraw-Hill. New York. 1965. [https://books.google.co.uk/books?id=0KpxAAAAMAAJ]
*&quot;Japan&quot;. Louis Barron (ed). &quot;Asia &amp; Australasia&quot;. Moshe Y Sachs (ed and pub). Worldmark Encyclopedia of the Nations. Worldmark Press, Inc. Harper &amp; Row New York. 1963. pp 145 to 160. [https://books.google.co.uk/books?id=I0oYAQAAMAAJ]
**&quot;Japan&quot;. Asia &amp; Oceania. 7th Ed: 1988. ISBN 0-471 62406-3. vol 4. pp 153 to 168.
**&quot;Japan&quot;. Asia &amp; Oceania. 8th Ed: 1995. Gale Research Inc. ISBN 0-8103-9882-6. vol 4. pp 203 to 220.

Handbooks
*Patrick Heenan (ed). The Japan Handbook. (Regional Handbooks of Economic Development). 1998. [https://books.google.co.uk/books?id=IMG2AgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Introduction
*Introducing Japan Through Books: A Selected Bibliography. Public Information Bureau, Ministry of Foreign Affairs, Japan. 1968. [https://books.google.co.uk/books?id=FvsyAQAAIAAJ]. 2nd Ed: 1973: [https://books.google.co.uk/books?id=Vj0XAQAAMAAJ].
*Donald Ritchie. Introducing Japan. 1st Ed: 1978. Revised Ed: 1986. 6th printing: 1989: [https://books.google.co.uk/books?id=FE-nxxoKayQC]. 2nd Revised Ed: 1990. 2nd printing: 1991: [https://books.google.co.uk/books?id=hz4UAQAAIAAJ]. 1994: [https://books.google.co.uk/books?id=FMvT6m4SgIQC&amp;pg=PP1#v=onepage&amp;q&amp;f=false].
*Herschel Webb. An Introduction to Japan. Columbia University Press. 2nd Ed: 1957: [https://books.google.co.uk/books?id=YQ8MAQAAIAAJ].
*Introducing Modern Japan. A publication of the Japan Information and Culture Center, Embassy of Japan.

Today and yesterday
*Ray Downs. Japan Yesterday and Today. Praeger Publishers. 1970. [https://books.google.co.uk/books?id=PwKxAAAAIAAJ]

Today
*Roger Buckley. Japan Today. Cambridge University Press. 3rd Ed [https://books.google.co.uk/books?id=thyqBtJp2DcC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Contemporary
*Routledge Handbook of Contemporary Japan. 2021. [https://books.google.co.uk/books?id=yfH3DwAAQBAJ&amp;pg=PA2011#v=onepage&amp;q&amp;f=false]
*Duncan McCargo. Contemporary Japan. 3rd Ed: 2012. [https://books.google.co.uk/books?id=8I5KEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Jeff Kingston. Contemporary Japan: History, Politics, and Social Change since the 1980s. 2011. [https://books.google.co.uk/books?id=enJQZA3R4FMC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

[Series]
*Routledge Contemporary Japan Series

Modern
*Hugh Cortazzi. Modern Japan: A Concise Survey. Palgrave Macmillan. 1993. [https://books.google.co.uk/books?id=Cf--DAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

The Japanese
*Peter Tasker. The Japanese: Portrait of a Nation. 1989 [https://books.google.com/books?id=Q1N8ld78wwQC]
**The Japanese: A Major Exploration of Modern Japan. [https://books.google.co.uk/books?id=CW-6AAAAIAAJ]
**Inside Japan: Wealth, Work and Power in the New Japanese Empire. 1987. [https://books.google.co.uk/books?id=2OJuAAAAMAAJ]
*Edwin O Reischauer. The Japanese. The Belknap Press of Harvard University Press. [https://books.google.co.uk/books?id=zrEqAAAAYAAJ]
*Edwin O Reischauer and Marius B Jansen. The Japanese Today: Change and Continuity. 1995. [https://books.google.co.uk/books?id=BTPNlLIy2soC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Japaneseness
*Ray T. Donahue (ed). Exploring Japaneseness: On Japanese Enactments of Culture and Consciousness. Ablex Publishing. 2002. [https://books.google.co.uk/books?id=V_NwAAAAMAAJ]
*Yoji Yamakuse. Japaneseness: A Guide to Values and Virtues. 2016. [https://books.google.co.uk/books?id=tB0iDAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Travel books
*DK Eyewitness Travel: Japan. Reprinted with revisions. 2015: [https://books.google.co.uk/books?id=g2NaBgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. 2017: [https://books.google.co.uk/books?id=vg15DQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false].
*Dodd and Richmond. The Rough Guide to Japan. 2nd Ed: 2001: [https://books.google.co.uk/books?id=pRGq95ytWZoC&amp;pg=PP1#v=onepage&amp;q&amp;f=false].
*Frommer's Japan. 5th Ed: 2000: [https://books.google.co.uk/books?id=-QC8mVyvPa8C].
*Fodor's Japan YYYY. 1984. [https://books.google.co.uk/books?id=aH2Ow27HUQ0C 1986]. [https://books.google.co.uk/books?id=3gTTf6nbv20C 1987]. 1988.
**Fodor's YY Japan. [https://books.google.co.uk/books?id=9QMHllzldlYC 91]. 92. 93.
**Fodor's Japan. 13th Ed: 1996: [https://books.google.co.uk/books?id=cZxZAAAAYAAJ]
*The New Official Guide: Japan. Japan Travel Bureau. 1966. [https://books.google.co.uk/books?id=HoxxAAAAMAAJ]
*Here is Japan. Asahi Broadcasting Corporation. [https://books.google.co.uk/books?id=8QXRCTMNG7MC]
*Japan. (Nagel Travel Guide Series, vol 32). 1964. [https://books.google.co.uk/books?id=QsbXAAAAMAAJ]
*Clark. All the Best in Japan: with Manila, Hong Kong, and Macao. (&quot;All the Best&quot; series). 1959. Reprinted 1964. [https://books.google.co.uk/books?id=yUq4YaaryrwC]. Reviews: [https://archive.dartmouthalumnimagazine.com/article/1958/6/1/all-the-best-in-japan] (1958) 110 Travel 51 [https://books.google.co.uk/books?id=UVwXAQAAMAAJ] 3 Bulletin of the Japan Society, London, No 11: June 1960, p 25 [https://books.google.co.uk/books?id=2oy74hRRXk4C]
**All the Best in Japan and the Orient. 1967.

Languages

See [[Universal Bibliography/Languages/Japanese|Japanese]]

Literature

See [[Universal Bibliography/Literature#Japanese|Japanese literature]]

Music

See [[Universal Bibliography/Music#Japanese and Japan|Music of Japan]]

Cinema

See [[Universal Bibliography/Cinema#Japanese|Cinema of Japan]]

Television

See [[Universal Bibliography/Television#Japanese|Japanese television]]

Culture

See [[Universal Bibliography/Culture#Japanese|Culture of Japan]]

==Korea==
*Korea Journal [https://books.google.co.uk/books?id=O6XfBexsp6gC]

Bibliography and literature
*Thomas H Kang. &quot;Korean Literature and Bibliography&quot;. Kent, Lancour and Daily (eds). Encyclopedia of Library and Information Science. Marcel Dekker. 1977. vol 21. pp [https://books.google.co.uk/books?id=H1pNvzr_n98C&amp;pg=PA176#v=onepage&amp;q&amp;f=false 176] to 240.

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See also [[Universal Bibliography/Geography|Geography]].

See [[w:Category:Bibliographies of countries or regions]] and [[w:Category:Works about countries]].

This part of the [[Universal Bibliography]] is a bibliography of countries (including former countries).

==Countries==
*Bateman and Egan (eds). The Encyclopedia of World Geography: A Country by Country Guide. 1993. Revised 1997.
*Peter Stalker. Handbook of the World. 2000. A Guide to Countries of the World. (Oxford Guide to Countries of the World. 2nd Ed: 2004, 2nd Revised Ed: 2007 [https://books.google.co.uk/books?id=GtztAAAAMAAJ], 3rd Ed: 2010 [https://books.google.co.uk/books?id=gvKvfxkbZ1AC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Countries of the World and Their Leaders Yearbook. Gale. [https://books.google.co.uk/books?id=5etKAAAAYAAJ] [https://books.google.co.uk/books?id=p41OAAAAIAAJ]
*Hutchinson Guide to Countries of the World [https://books.google.co.uk/books?id=GgpjUe4kN_IC]
*The World Guide: Global Reference, Country by Country. 11th Ed: 2007 [https://books.google.co.uk/books?id=EoWoLgAACAAJ]
*Spence. The World Today: A Nation-by-Nation Guide. Cassell. 1994. 1999. [https://books.google.com/books?id=Ub8qOQAACAAJ]
*Worldmark Encyclopedia of the Nations [https://books.google.co.uk/books?id=I0oYAQAAMAAJ]
*Kurian. Encyclopedia of the World's Nations. Facts on File. Reviews: [https://books.google.co.uk/books?id=Y1EnAQAAIAAJ] [https://books.google.co.uk/books?id=lz0RAQAAMAAJ]
*Michael O'Mara. Facts about the World's Nations. 1999. [https://books.google.co.uk/books?id=mygYAAAAIAAJ]
*Status of the World's Nations. 1965 [https://books.google.co.uk/books?id=sftEyRbAXMUC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. 1973 [https://books.google.co.uk/books?id=kw2U_Cg2gKYC&amp;pg=PP3#v=onepage&amp;q&amp;f=false].
*[[s:Author:John Alexander Hammerton|Hammerton, John Alexander]] (ed). Countries of the World. Published at the Fleetway House. 6 vols. [https://books.google.co.uk/books?id=e6IaAQAAMAAJ] [https://books.google.co.uk/books?id=K5oaAQAAMAAJ]
*[[s:Author:Robert Brown (1842-1895)|Brown, Robert]]. The Countries of the World. [https://books.google.co.uk/books?id=nO0DAAAAQAAJ&amp;pg=PP13#v=onepage&amp;q&amp;f=false]
*A Morely Dell. The Countries of the World. (Harrap's New Geographical Series). 1932. (School certificate). Reviews: [https://books.google.co.uk/books?id=oSS9PB_Jf7AC] [https://books.google.co.uk/books?id=BicVAAAAIAAJ] [https://books.google.co.uk/books?id=5qBOAAAAIAAJ] [https://books.google.co.uk/books?id=YbwcAQAAIAAJ] [https://books.google.co.uk/books?id=sc1AAAAAIAAJ]

General series:
*National Geographic Countries of the World [https://books.google.co.uk/books?id=IT2wfzVIPykC]
*Countries of the World. Evans Brothers. (GCSE) [https://books.google.co.uk/books?id=a3sZvWc7E1EC&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*One Europe. Longman. [https://search.worldcat.org/en/title/west-germany-adapted-by-lj-russon-from-the-original-german-by-sylvia-lof-ingrid-mallberg-dietrich-rosenthal/oclc/561591761]
*Collier's Nations of the World. The Nations of the World: An Historical Series. [https://books.google.co.uk/books?id=VJY-AAAAYAAJ&amp;pg=PP8#v=onepage&amp;q&amp;f=false]
*Collier's History of Nations. The History of Nations. [https://books.google.co.uk/books?id=fmSUfTY5E80C]
*The Story of the Nations. T Fisher Unwin.
*The World and Its Peoples. (The Illustrated Library of the World and Its Peoples). Greystone Press, New York.
*World and Its Peoples. Marshall Cavendish. [https://books.google.co.uk/books?id=oms5xjI7ba0C&amp;pg=PA141#v=onepage&amp;q&amp;f=false]

==England==
===Counties===
See [[s:Portal:Counties]]

* Harrison, &quot;County Bibliography&quot; (1886) 3 Library Chronicle [https://books.google.co.uk/books?id=Wz9FAAAAYAAJ&amp;pg=PA49#v=onepage&amp;q&amp;f=false 49]

General series
*Victoria County History
*Oxford County Histories
*Pinnock's County Histories
*Shire County Guides. Shire Publications.
*Cambridge County Geographies
*Pike's New Century Series
*[[s:Page:County Churches of Cornwall.djvu/6|County Churches]]. G Allen.

Avon
*Moore. Avon Local History Handbook. Phillimore. 1979. [https://books.google.co.uk/books?id=h0kjAAAAMAAJ] Bibliography, p 102

Bedfordshire
*Conisbee, Lewis Ralph. A Bedfordshire Bibliography. Bedfordshire Historical Record Society. Bedford. 1962. Supplements 1967, 1971, 1978. Third supplement by Threadgill. Review: 6 Archives 52 [https://books.google.co.uk/books?id=oOMZAAAAYAAJ]. See also [https://books.google.co.uk/books?id=MjspAAAAYAAJ] [https://books.google.co.uk/books?id=PejgAAAAMAAJ]
*Godber. History of Bedfordshire. 1969. 1984. [https://books.google.co.uk/books?id=jdvwPQAACAAJ]
*Pinnock. The History and Topography of Bedfordshire [https://books.google.co.uk/books?id=9bJYAAAAcAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*Parry. Select Illustrations, Historical and Topographical, of Bedfordshire [https://books.google.co.uk/books?id=UTUJAAAAQAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Blyth. The History of Bedford and Visitor's Guide. 1873 [https://books.google.co.uk/books?id=IuIGAAAAQAAJ&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
*Cambridge County Geographies [https://books.google.co.uk/books?id=kTc8AAAAIAAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Buckinghamshire
*Reed. A History of Buckinghamshire. 1993 [https://books.google.co.uk/books?id=BtkWAQAAIAAJ]

Cambridgeshire
*Carter. History of the County of Cambridge [https://books.google.co.uk/books?id=jXpbAAAAQAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*Babington. Ancient Cambridgeshire [https://books.google.co.uk/books?id=DPrCAwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Devon
*Ravenhill and Rowe. Devon Maps and Map-makers [https://books.google.co.uk/books?id=tjf2yAEACAAJ]
*Wright. A Plea for a Devonshire Bibliography. 1885 [https://books.google.co.uk/books?id=8ZUDAAAAQAAJ]

Derbyshire
*Woore. A Catalogue of Local Maps of Derbyshire, C.1528-1800. 2012. [https://books.google.co.uk/books?id=oWmCMwEACAAJ]
*O'Neal. A Bibliography of Derbyshire Lead Mining. 1961

Essex
*Cunnington. Catalogue of Books, Maps and Manuscripts, relating to or connected with the County of Essex. 1902 [https://books.google.co.uk/books?id=oIcqpibGE4MC]
*&quot;The Bibliography of Essex&quot; (1882) 1 Antiquarian Magazine &amp; Bibliographer [https://books.google.co.uk/books?id=dEkEAAAAQAAJ&amp;pg=PA72#v=onepage&amp;q&amp;f=false 72]. See also [https://books.google.co.uk/books?id=dEkEAAAAQAAJ&amp;pg=PA283#v=onepage&amp;q&amp;f=false p 283].
*&quot;The Bibliography of Essex&quot; (1891) 5 The Essex Naturalist 30 [https://books.google.co.uk/books?id=iIo1AQAAMAAJ]
*Moon. Essex Literature. 1900. Review: 61 Literary World 438 [https://books.google.co.uk/books?id=2T0ZAAAAYAAJ] See also [https://books.google.co.uk/books?id=1Y4UAQAAIAAJ] [https://books.google.co.uk/books?id=C_pEAAAAMAAJ]
*Fenn and Lowery, &quot;An Essex Bibliography&quot;, Journal of the South West Essex Technical College, vols 2 &amp; 3
*Victoria County History bibliography. 1959 [https://books.google.co.uk/books?id=F2EJAQAAIAAJ]
*O'Leary, John Gerard. A Supplement to the Essex Bibliography. Dagenham. 1962.
*A Bibliography of Essex Archaeology &amp; History
*Essex and Dagenham: A Catalogue of Books, Pamphlets and Maps. Dagenham. 1961
*Essex Archaeology and History: The Transactions of the Essex Society for Archaeological and History [https://books.google.co.uk/books?id=CtFAAAAAYAAJ]
*Essex Naturalist: Being the Journal of the Essex Field Club
*Wright. The History and Topography of the County of Essex [https://books.google.co.uk/books?id=SgQVAAAAQAAJ&amp;pg=PP9#v=onepage&amp;q&amp;f=false]
*Ogborne, The History of Essex [https://books.google.co.uk/books?id=IeVSAAAAcAAJ&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
*Suckling. Memorials of the Antiquities and Architecture, Family History and Heraldry of the County of Essex [https://books.google.co.uk/books?id=bcw_AAAAcAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Hunter, The Essex Landscape: A Study of Its Form and History [https://books.google.co.uk/books?id=w9kWAQAAIAAJ]
*Cambridge County Geography [https://books.google.co.uk/books?id=GPHa_X_0qo0C&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*Sokoll. Essex  Pauper Letters, 1731-1837 [https://books.google.co.uk/books?id=rCLia7XlqtMC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Morant. The History and Antiquities of Colchester in the County of Essex [https://books.google.co.uk/books?id=DDgtAAAAYAAJ&amp;pg=PP9#v=onepage&amp;q&amp;f=false]
*Wallen. The History and Antiquities of the Round Church at Little Maplestead, Essex [https://books.google.co.uk/books?id=FPYVAAAAYAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]

Kent
*Smith. Bibliotheca Cantiana. 1837. [https://books.google.co.uk/books?id=1dJDAAAAYAAJ&amp;pg=PP11#v=onepage&amp;q&amp;f=false]

Leicestershire
*Kirkby, C V (compiler). Catalogue of the books, pamphlets, &amp;c., relating to Leicestershire in the Central Reference Library. Leicester Free Public Libraries. 1893. Reviews: [https://books.google.co.uk/books?id=3boqAQAAIAAJ&amp;pg=PA84#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=UcHnAAAAMAAJ&amp;pg=PA728#v=onepage&amp;q&amp;f=false]
*Leicestershire and Rutland Bibliography, 1963-65 (1966) [https://books.google.co.uk/books?id=-OhVAAAAYAAJ 40] Leicestershire Archaeological and Historical Society: Transactions (1964/5) 92. Available as pdf from University of Leicester.
*Leicestershire and Rutland Bibliography, 1961-63. Available as pdf from University of Leicester.
*Leicestershire and Rutland Bibliography, 1960-61. Available as pdf from University of Leicester.
*A Bibliography of the Small Towns in Leicestershire and Rutland, 1600–1850. (Dissertation). [https://repository.lboro.ac.uk/articles/educational_resource/A_bibliography_of_the_small_towns_in_Leicestershire_and_Rutland_1600_1850/9414200]
*Loughborough's Heritage: A Bibliography of the Holdings of Leicestershire Libraries and Information Service and Record Office. [https://books.google.co.uk/books?id=Bwx2zgEACAAJ]
*Keith Ambrose and Frank Williams, &quot;Bibliography of the Geology of Leicestershire and Rutland: Part 2: 1971-2003&quot; (2004) [https://books.google.co.uk/books?id=U-tQAQAAIAAJ 16] The Mercian Geologist 5. Available as pdf from East Midlands Geological Society.
*Parsons and Brandwood. A Bibliography of Leicestershire Churches. 1978.
*Education in Leicestershire: A Bibliography. [https://books.google.co.uk/books?id=X6EfzQEACAAJ]

Sussex
*Brent, Fletcher and McCann. Sussex in the 16th and 17th Centuries: A Bibliography. 2nd Ed [https://books.google.co.uk/books?id=I7UtAAAAYAAJ]
*Farrant. Sussex in the 18th and 19th Centuries: A Bibliography. 1st Ed: 1973, 2nd Ed: 1977 [https://books.google.co.uk/books?id=MLUtAAAAYAAJ], 3rd Ed: 1979

==France==
Bibliography:
*Bibliographie de la France. Commentary: Encyclopedia of Library and Information Science, vol 37, supplement 2, [https://books.google.co.uk/books?id=10rgjNvOV8oC&amp;pg=PA145#v=onepage&amp;q&amp;f=false p 145]; The Bookseller, 6 January 1881, [https://books.google.co.uk/books?id=4dsiAQAAMAAJ&amp;pg=PA10#v=onepage&amp;q&amp;f=false p 10]; Stein, Manuel de bibliographie générale, [https://books.google.co.uk/books?id=lJYPyKjV1qYC&amp;pg=PA23#v=onepage&amp;q&amp;f=false p 23]. 
*Girault de Saint-Fargeau. Bibliographie historique et topographique de la France. 1845 [https://books.google.co.uk/books?id=kClB9CQNZoMC&amp;pg=PP9#v=onepage&amp;q&amp;f=false]
*Catalogue d'une collection d'ouvrages sur l'histoire des provinces de la France. 1842 [https://books.google.co.uk/books?id=qQBX5WZouzAC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Landscape:
*Beaujeu-Garnier. France. (The World's Landscapes). 1975. [https://books.google.com/books?id=nwxDAQAAIAAJ]

Agenais:
*Andrieu. Bibliographie générale de l’Agenais et des parties du Condomois et du Bazadais. 1886 to 1891. Reprinted 1969.

Alsace:
*Ristelhuber. Bibliographie alsacienne. 1869 to 1873 [https://books.google.co.uk/books?id=0mhLAQAAMAAJ&amp;pg=PP13#v=onepage&amp;q&amp;f=false]
*Bibliographie alsacienne: Revue critique des publications concernant l'Alsace. 1918 to 1936
*Ritter. Répertoire bibliographique des livres imprimés en Alsace aux XVe et XVIe siècles [https://books.google.co.uk/books?id=DewaAQAAMAAJ]

Angoumois:
*Castaigne. Essai d'une bibliothèque historique de l'Angoumois, ou Catalogue raisonné des principaux ouvrages qui traitent des différentes branches de l'histoire de cette province. 1847 [https://books.google.co.uk/books?id=R-UanmmlvAEC&amp;pg=PP7#v=onepage&amp;q&amp;f=false]

Anjou:
*Braguier and Braguier. Archéologie en Anjou: bibliographie. 1984 [https://books.google.co.uk/books?id=LvsmAQAAIAAJ]

Auvergne:
*Gonot. Catalogue des ouvrages imprimés et manuscrits concernant l'Auvergne, extrait du catalogue général de la Bibliotlèque de Clermont-Fd (Puy-de-Dome). 1849. [https://books.google.co.uk/books?id=yCFtbObRCbUC&amp;pg=PP13#v=onepage&amp;q&amp;f=false]
*Catalogue des livres et estampes concernant l'ancienne Province d'Auvergne (Puy-de-Dôme, Cantal, Haute-Loire) réunis par feu M. G. Desbouis. 1865. [https://books.google.co.uk/books?id=Ui4S8_D0N74C&amp;pg=PP7#v=onepage&amp;q&amp;f=false]

Béarn
*&quot;Bibliographie Béarnaise&quot;, Revue de Pau et du Béarn [https://books.google.co.uk/books?id=FuZnAAAAMAAJ] Commentary: [https://books.google.co.uk/books?id=FQYqvPo9D9IC&amp;pg=PA158#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=RL9VAAAAYAAJ]

Brittany
*Sacher. Bibliographie de la Bretagne, ou Catalogue général des ouvrages historiques, littéraires et scientifiques parus sur la Bretagne, avec la liste des revues publiées en cette province, les prix approximatifs des volumes rares, etc. 1881 [https://archive.org/details/bibliographiede00sach]

Burgundy:
*Milsand. Bibliographie bourguignonne; ou, Catalogue méthodique d'ouvrages relatifs à la Bourgogne: Sciences - Arts - Histoire. 1885 [https://archive.org/details/bibliographiebo00milsgoog] [https://archive.org/details/bibliographiebo00sciegoog] [https://books.google.co.uk/books?id=CxIIAAAAQAAJ]
*Catalogue des manuscrits de la Bibliothèque royale des ducs de Bourgogne. 1842 [https://books.google.co.uk/books?id=FX5MAAAAcAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*The Companion Guide to Burgundy [https://books.google.co.uk/books?id=NraRP0AkDT0C&amp;pg=PP3#v=onepage&amp;q&amp;f=false]
*Lecat. The Golden Book of Burgundy. (The Golden Book) [https://books.google.co.uk/books?id=FyzR9qU1Zl4C&amp;lpg=PP1&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Gwynn. Burgundy: With Chapters on the Jura and Savoy. (Kitbag Travel Books). 1935 [https://books.google.co.uk/books?id=ny1LAAAAMAAJ]
*Bazin. Wonderful Burgundy. 1988. 1997 [https://books.google.co.uk/books?id=Yt1CRdICWCUC]
*Bailey. Burgundy. (Insight Guides). 1993 [https://books.google.co.uk/books?id=Q69a1dMW2NQC]
*Dunlop. Burgundy. Hamilton.1990 [https://books.google.co.uk/books?id=S_1OAAAAMAAJ]

Champagne:
*Lhermitte. Ouvrages sur la Champagne: contribution à la bibliographie champenoise. 1992. [https://books.google.co.uk/books?id=jbPfAAAAMAAJ]

Dauphiné:
*Mélanges biographiques et bibliographiques relatifs à l'histoire littéraire du Dauphiné par Colomb de Batines et Ollivier Jules. 1837 [https://books.google.co.uk/books?id=2F5MAAAAcAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

Lorraine:
*Bibliographie lorraine. Académie nationale de Metz [https://books.google.co.uk/books?id=n-DfAAAAMAAJ]

Maine:
*Desportes. Bibliographie du Maine, précédée de la description topographique et hydrographique du diocése du Mans, Sarthe et Mayenne. 1844. [https://books.google.co.uk/books?id=hSk-AAAAYAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]

Normandy:
*Frère. Manuel du bibliographe Normand ou dictionnaire bibliographique et historique. 1858 to 1860. [https://books.google.co.uk/books?id=dp6geJClg1YC&amp;pg=PP13#v=onepage&amp;q&amp;f=false vol 1]

==Japan==
Bibliography and literature
*Hideo Kaneko. &quot;Japanese Literature and Bibliography&quot;. Kent, Lancour and Daily (eds). Encyclopedia of Library and Information Science. Marcel Dekker. 1977. vol 21. pp [https://books.google.co.uk/books?id=H1pNvzr_n98C&amp;pg=PA131#v=onepage&amp;q&amp;f=false 131] to 176.

Bibliography
*Jozef Rogala. A Collector's Guide to Books on Japan in English: An Annotated List of Over 2500 Titles with Subject Index. 2001. [https://books.google.co.uk/books?id=7KI9ao-w2FEC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Ria Koopmans-de Bruijn. Area Bibliography of Japan. (Scarecrow Area Bibliographies). Scarecrow Press. 1998. [https://books.google.co.uk/books?id=Hlx2OMjgUi0C&amp;pg=PR1#v=onepage&amp;q&amp;f=false]
*Frank Joseph Shulman. Japan. (World Bibliographical Series, vol 103). Clio Press. 1989. [https://books.google.co.uk/books?id=LsoUAQAAIAAJ]
*Eibun Nihon Kankei Tosho Mokuroku, 1945-1981. (Japanese: 英文日本関係図書目録, 1945-1981). (English: Catalogue of Books in English on Japan, 1945-1981). Japan Foundation. Tokyo. 1986.
*Japan: analytical bibliography: with supplementary research aids: and selected data on Okinawa . . . Department of the Army. Washington. 1972. [https://books.google.co.uk/books?id=h4d4nYxrxtMC&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Books on Japan in Western Languages. The International Christian University Library. 1971. [https://books.google.co.uk/books?id=F2bQAAAAMAAJ]
*Books on Japan: A List of Acquisitions, 1955-1970. International House of Japan Library. 1971. [https://books.google.co.uk/books?id=F8sWAQAAIAAJ]
*Fukuda. Union Catalog of Books on Japan in Western Languages. 1968. [https://books.google.co.uk/books?id=HKYyAQAAIAAJ]
*A Classified List of Books in Western Languages Relating to Japan. University of Tokyo Press. 1965. [https://books.google.co.uk/books?id=U8MUAQAAIAAJ]
*Katsuji Yabuki (ed). Japan Bibliographic Annual. Published by the Hokuseido Press for the Japan Writers Society. 1956 and 1957.
**Japan Bibliographic Annual 1956. [https://books.google.co.uk/books?id=9XLQAAAAMAAJ]
**Japan Bibliographic Annual 1957. [https://books.google.co.uk/books?id=vesSAAAAIAAJ]. Reviews: (1957) 13 Monumenta Nipponica 166 (April-July) [https://books.google.co.uk/books?id=8S1yb-iwrOwC] (1957) 25 The Oriental Economist 212 (April) [https://books.google.co.uk/books?id=QELoAAAAMAAJ]
*Haring. Books on Japan: A Reference List. 1955. [https://books.google.co.uk/books?id=RbDoAAAAMAAJ]
*Borton. A Selected List of Books and Articles on Japan in English, French, and German. 1940: [https://books.google.co.uk/books?id=YYIsAAAAYAAJ]. Revised and enlarged. Harvard University Press. 1954: [https://books.google.co.uk/books?id=F8O2VwJUPUkC].
**A Selected List of Books on Japan in Western Languages (1945-1960). (Studies on Asia Abroad, vol 1). The Information Centre of Asian Studies, The Toyo Bunko. 1964. [https://books.google.co.uk/books?id=i1_QAAAAMAAJ]
*Oskar Nachod. Bibliography of the Japanese Empire 1906-1926. 1928. [https://archive.org/details/bibliographyofja0001oska/page/n8/mode/1up vol 1]. [https://archive.org/details/bibliographyofja0002oska/page/n6/mode/1up vol 2].
*Fr. von Wenckstern. A Bibliography of the Japanese Empire: being a Classified List of All Books, Essays and Maps in European Languages relating to Dai Nihon (Great Japan) published in Europe, America and in the East from 1859-93 . . . 1895. vol 1. [https://books.google.co.uk/books?id=dcVAAAAAYAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=v7lO4ddqDywC&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
**Volume 2, from 1894 to the middle of 1906. 1907. [https://archive.org/details/bibliographyofja0002frvo/page/n6/mode/1up]
*Hyman Kublin. What Shall I Read on Japan? An Introductory Guide. Japan Society, New York. 1971. [https://books.google.co.uk/books?id=yRRUAAAAYAAJ]

Japanese studies
*An Introductory Bibliography for Japanese Studies. The Japan Foundation. [https://books.google.co.uk/books?id=53O6AAAAIAAJ]
*Richard Perren. Japanese Studies from Pre-History to 1990: A Bibliographical Guide. 1992. [https://books.google.co.uk/books?id=CN9RAQAAIAAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. &quot;Bibliographies&quot; at pp 1 to 3.
*K.B.S. Bibliography of Standard Reference Books for Japanese Studies, with Descriptive Notes. University of Tokyo Press. [https://books.google.co.uk/books?id=95wbAAAAMAAJ]
*[[w:en:Monumenta Nipponica|Monumenta Nipponica]]
*[[w:en:Japan Forum|Japan Forum]]. British Association for Japanese Studies. [https://www.tandfonline.com/journals/rjfo20]
*Japanese Studies. Japanese Studies Association of Australia. ISSN 1037-1397. [https://www.tandfonline.com/journals/cjst20]
*[[w:en:The Journal of Japanese Studies|The Journal of Japanese Studies]]. University of California Press.
*Nichibunken Newsletter. [[w:en:International Research Center for Japanese Studies|International Research Center for Japanese Studies]]. [https://books.google.co.uk/books?id=5TnjAAAAMAAJ] [https://www.nichibun.ac.jp/en/publications/data/news/] [https://newsletter.nichibun.ac.jp/en/]

History and culture
*John W Dower. Japanese History &amp; Culture from Ancient to Modern Times: Seven Basic Bibliographies. 1986. [https://books.google.co.uk/books?id=NX67AAAAIAAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. &quot;Bibliographies &amp; Research Guides&quot; at chapter 6.

Research guides
*Mindy L Kotler. Information Gathering on Japan: A Primer. Search Associates. 1988. ISBN 9780962546006. Catalogue: [https://search.worldcat.org/zh-cn/title/Information-gathering-on-Japan-Joho-:-a-primer/oclc/20530148]. Review: (1989) [https://books.google.co.uk/books?id=NZLiAAAAMAAJ 27] Choice 82

Encyclopedias

See also [[w:ja:Japanese encyclopedias]]
*Louis-Frédéric. Japan Encyclopedia. 2002. [https://books.google.co.uk/books?id=p2QnPijAEmEC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Japan: An Illustrated Encyclopedia. Kodansha. 1993.
**Japan: Profile of a Nation. Kodansha. 1995. Revised Edition. 1999.
*[[w:Kodansha Encyclopedia of Japan|Kodansha Encyclopedia of Japan]]. 1983. Supplement. 1986. [https://books.google.co.uk/books?id=WvApAQAAMAAJ]
*Dorothy Perkins. Encyclopedia of Japan: Japanese History and Culture, from Abacus to Zori. Facts on File. A Roundtable Press Book. 1991. [https://books.google.co.uk/books?id=JLKGAAAAIAAJ]
*Pictorial Encyclopedia of Modern Japan. Gakken. 1986. [https://books.google.co.uk/books?id=0FgKAQAAIAAJ]
*Boye Layfayette De Mente. Japan Encyclopedia. 1995. [https://books.google.co.uk/books?id=f9c7AAAAMAAJ]
**Boye De Mente. Everything Japanese. [The Authoritave Reference on Japan Today]. 1989. [https://books.google.co.uk/books?id=Duku89bARgoC]

Reference books
*Nihon No Sanko Tosho. Volume 1: 1965. Volume 2: 1972.
**Guide to Japanese Reference Books. American Library Association. Chicago. 1966: [https://books.google.co.uk/books?id=0rflAAAAMAAJ]. Supplement. 1979: [https://books.google.co.uk/books?id=j05_F9OHzkQC]. Commentary: Encyclopedia of Library and Information Science, vol 21, [https://books.google.co.uk/books?id=H1pNvzr_n98C&amp;pg=PA149#v=onepage&amp;q&amp;f=false p 149].

Media
*[https://www.bbc.com/news/world-asia-pacific-15217593 Japan media guide]. News. BBC. 20 March 2023.
*Masaaki Kasagi. Mass Media in Japan. (Orientation seminars on Japan, number 14). 1983. [https://books.google.co.uk/books?id=odkgAAAAIAAJ]
*Routledge Handbook of Japanese Media [https://books.google.co.uk/books?id=zilKDwAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]

Publishers
*[https://www.publishersweekly.com/pw/by-topic/international/international-book-news/article/99729-get-to-know-these-japanese-publishing-companies.html Get to Know These Japanese Publishing Companies]. Publishers Weekly. 20 February 2026.

Press and journalism
*[https://reutersinstitute.politics.ox.ac.uk/digital-news-report/2025/japan Japan]. Reuters Institute for the Study of Journalism. 17 June 2025.
*Marjane Aalam and Philippe Régnier. The Japanese Press and Information System. The Graduate Institute of International Studies. Geneva. [https://books.google.co.uk/books?id=RTcbAQAAIAAJ]
*The Japanese Press: Past and Present. Japan Newspaper Publishers' and Editors' Association. [https://books.google.co.uk/books?id=5tcQAAAAIAAJ 1949].
*Anthony Rausch. Japanese Journalism and the Japanese Newspaper: A Supplemental Reader. [https://books.google.co.uk/books?id=mZrToQEACAAJ]
*Frank L Martin. The Journalism of Japan. 1918. [https://books.google.com/books?id=ruYzAQAAMAAJ]
*William De Lange. A History of Japanese Journalism. Japan Library. 1998. [https://books.google.co.uk/books?id=Rd5tb0cuz8QC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Kanesada Hanazono. The Development of Japanese Journalism. Osaka. 1924. [https://books.google.co.uk/books?id=z99ZAAAAMAAJ]
*Kanesada Hanazono. Journalism in Japan and Its Early Pioneers. 1926. [https://books.google.co.uk/books?id=IGTFfLc4bq0C]
*César Castellvi. A Sociology of Journalism in Japan: The Last Empire of the Press. 2024. [https://books.google.co.uk/books?id=a2z8EAAAQBAJ&amp;pg=PR4#v=onepage&amp;q&amp;f=false]
*&quot;Japan&quot;. Christopher H Sterling (ed). Encyclopedia of Journalism. A Sage Reference Publication. 2009. ISBN 9780761929574. vol 3. pp [https://books.google.co.uk/books?id=ZQhDq8fPj2IC&amp;pg=PA809#v=onepage&amp;q&amp;f=false 809] to 815.

Press annuals
*The Japanese Press. (Nihon Shinbun Kyokai). [https://books.google.co.uk/books?id=AfvyAAAAMAAJ 1979] [https://books.google.co.uk/books?id=Au3yAAAAMAAJ 1998]

Summaries of the press
*Daily Summary of Japanese Press

Foreign correspondents
*Foreign Correspondents in Japan: Reporting a Half Century of Upheavals, from 1945 to the Present. Tuttle. 1998. [https://books.google.co.uk/books?id=YI3TAgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Periodicals
*G Raymond Nunn (comp). Japanese Periodicals and Newspapers in Western Languages: An International Union List. Mansell. 1979. [https://books.google.co.uk/books?id=jEROAQAAIAAJ]
*Japan Periodicals. Keizai Koho Center. 3rd Ed [https://books.google.co.uk/books?id=ATm0AAAAIAAJ]. Japan Periodicals, 1982. [https://books.google.co.uk/books?id=PkMyAAAAMAAJ]
*Japanese Periodicals Index
**Humanities and Social Sciences [https://books.google.co.uk/books?id=nXX_RpPGf3AC]
**Natural Sciences [https://books.google.co.uk/books?id=FCJIAAAAYAAJ]
*Current Japanese Periodicals [https://books.google.co.uk/books?id=FjO5AAAAIAAJ]
*Check-list of Japanese Periodicals Held in British University and Research Libraries. [https://books.google.co.uk/books?id=VZgsAAAAYAAJ]
*Union List of Current Japanese Periodicals in the East Asian Libraries of Columbia, Harvard, Princeton, and Yale Universities. [https://books.google.co.uk/books?id=yw7kAAAAMAAJ]
*List of Japanese Periodicals in the Library of the School of Oriental &amp; African Studies. [https://books.google.co.uk/books?id=RREjAQAAIAAJ]
*Gianni Simone. [https://www.japantimes.co.jp/community/2011/04/26/issues/english-mags-approach-milestone-crossroads/ English mags approach milestone, crossroads]. The Japan Times. 26 April 2011.
*Japan Report (1955 onwards) (Consulate General of Japan, Japan Information Center). Vol 39 published in 1993. [https://books.google.co.uk/books?id=MX4BN_frv4IC&amp;pg=PP7#v=onepage&amp;q&amp;f=false] editions:jYuMSMIQC-AC
**Japan Information
*Japan Now [https://books.google.co.uk/books?id=Nul7DRQaexMC&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Japan Quarterly. (Asahi Shimbun). 1954 to 2001. [https://books.google.co.uk/books?id=nZMMAQAAMAAJ] [https://books.google.co.uk/books?id=_RwVAAAAMAAJ] 189 issues.
*Japan Illustrated: The Japan Times Quarterly [Pictorial] Magazine (October 1963 to Summer 1977) 15 vols [https://books.google.co.uk/books?id=D7UThOmE8T4C]
*[[w:Japan Spotlight|Japan Spotlight]]. Economy, Culture &amp; History: Japan Spotlight: Bimonthly. [https://books.google.co.uk/books?id=i7C0AAAAIAAJ]
*Focus Japan. (Japan External Trade Organization, JETRO). [https://books.google.co.uk/books?id=2fG2hsEZpRkC]
*The Japan Journal [https://books.google.co.uk/books?id=2V3hAAAAMAAJ] [https://books.google.co.uk/books?id=CJwoAQAAMAAJ]
*Japan Magazine. Muromachi Publicity Corporation. (vols 1 to 5: 1957 to 1963). [https://books.google.co.uk/books?id=Swd18PnVeUgC]
*The Japan Magazine: A Representative Monthly of Things Japanese [https://books.google.co.uk/books?id=ubGKo-p6O_0C] [https://archive.org/details/jm-1914-v4.9-5.2/mode/1up]
*Transactions and Proceedings of the Japan Society, London [https://books.google.co.uk/books?id=B75nnph5qHgC&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
**Bulletin. [Bulletin of the Japan Society, London.] [https://books.google.co.uk/books?id=Pd9KvyhnpjMC]
**The Japan Society of London Bulletin [https://books.google.co.uk/books?id=XxlxAAAAMAAJ]
*About Japan. Japan Society, New York. [https://books.google.co.uk/books?id=Nf5OAQAAIAAJ]
**News Bulletin [https://archive.org/details/bub_gb_QcA3AQAAIAAJ/page/n2/mode/1up]
*[[w:en:Metropolis (free magazine)|Metropolis]] (metropolisjapan.com)
*[[w:en:Tokyo Weekender|Tokyo Weekender]] (トーキョー・ウィークエンダー) [https://www.tokyoweekender.com/japan-life/news-and-opinion/nhk-world-features-the-tokyo-weekender-magazine/]
*The Japan Gazette [https://books.google.co.uk/books?id=WSopAAAAYAAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*The Tokio Times [https://books.google.co.uk/books?id=UDfiFBu0vB4C&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*[[w:en:Look Japan|Look Japan]]. (Look Japan Ltd). [https://books.google.co.uk/books?id=QnO6AAAAIAAJ]. Commentary: Gale Directory of Publications and Broadcast Media [https://books.google.co.uk/books?id=ve4dAQAAMAAJ]
*[[w:en:Japan Echo|Japan Echo]]. 1974 to 2010. [https://books.google.co.uk/books?id=Cmq6AAAAIAAJ] [https://books.google.co.uk/books?id=fpmEPpl-85UC]
*PHP Intersect. (Where Japan Meets Asia and the World). PHP Institute. [https://books.google.co.uk/books?id=i74TAQAAMAAJ]
**Intersect Japan [https://books.google.co.uk/books?id=sL8TAQAAMAAJ]
*Japan Digest [https://books.google.co.uk/books?id=8AcOAQAAMAAJ]
*Speaking of Japan [https://books.google.co.uk/books?id=U7S0AAAAIAAJ]. [Speeches.]
*The Hansei Zasshi: A Monthly Magazine [https://books.google.co.uk/books?id=6qBhfHZo7Q0C&amp;pg=PP5#v=onepage&amp;q&amp;f=false][https://books.google.co.uk/books?id=dyIsvnYjpwEC&amp;pg=PP6#v=onepage&amp;q&amp;f=false]
**The Orient. 1899 onwards [https://books.google.co.uk/books?id=nS1omYYnnd4C&amp;pg=PP5#v=onepage&amp;q&amp;f=false]
*Today's Japan. Orient/West Incorporated. [https://books.google.co.uk/books?id=g2ASAAAAMAAJ]
*Japan Review: Bulletin of the International Research Center for Japanese Studies. [https://books.google.co.uk/books?id=GggOAQAAMAAJ]
*[https://www.bloomberg.com/account/newsletters/next-japan Next Japan]. Bloomberg.

Newspapers

See also [[w:List of newspapers in Japan]]
*Haruhara Akihiko, &quot;English-language newspapers in Japan&quot; (1994) 41 Japan Quarterly [https://www.proquest.com/openview/8e2b760f2a2fa37ba164ea675c095353/1 474] (Issue 4: October 1994)
*James Charles Tanner. English Language Newspapers in Bakumatsu Japan. 1977. [https://books.google.co.uk/books?id=Bn2zgzZy_3oC]
*[https://www.japantimes.co.jp/news/2009/03/03/reference/newspapers-here-soldiering-on/ Newspapers here soldiering on]. The Japan Times. 3 March 2009.

*[[w:The Japan Times|The Japan Times]]
**The Japan Times: Weekly Edition [https://books.google.co.uk/books?id=KoQ-AQAAMAAJ] [https://books.google.co.uk/books?id=yYQ-AQAAMAAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*Japan Daily Mail
*Japan Weekly Mail
*The Japan Chronicle
**Weekly Edition [https://books.google.co.uk/books?id=vXdRAQAAIAAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*The Japan News. (The Japan News by The Yomiuri Shimbun)
**Yomiuri Japan News (from 1955)
**The Yomiuri (from 1958)
**The Daily Yomiuri (from 1970)
*The Asahi Shimbun: Asia &amp; Japan Watch. [https://www.asahi.com/sp/ajw/]
**Asahi Evening News (from 1954)
***Tokyo Evening News (1952 to 1954) [https://ndlsearch.ndl.go.jp/books/R100000002-I000000145073]
*The Mainichi. [https://mainichi.jp/english/]
**Mainichi Daily News (1922 to 2001) [https://www.nytimes.com/2001/02/27/business/worldbusiness/IHT-tech-briefstop-the-presses.html] [https://ndlsearch.ndl.go.jp/books/R100000002-I000000144910]

Sports newspapers; sports dailies
*Louise do Rosario, &quot;News-stand stars&quot; in &quot;Japan&quot; (1992) [https://books.google.co.uk/books?id=T_GzAAAAIAAJ 155] [[w:en:Far Eastern Economic Review|Far Eastern Economic Review]], 24 to 31 December 1992, p 21
*[[w:ja:岡崎満義|Mitsuyoshi Okazaki]], &quot;Unsportsmanlike Journalism: Japan's sports dailies may be popular, but are they sporting?&quot; in &quot;Sport&quot;, [[w:en:Look Japan|Look Japan]], [https://books.google.co.uk/books?id=lD3tAAAAMAAJ January 1995], p 39

News
*[[w:en:Japan Today|Japan Today]] (ジャパントゥデイ). GPlusMedia. Gakken Holdings.

Annuals and year books 
*This is Japan. Asahi Shimbun. 1954 to 1971. [https://books.google.co.uk/books?id=2X9DAQAAIAAJ]. Commentary: A Victorian Sailor's Grave in the Seto Inland Sea, p 244 [https://books.google.co.uk/books?id=OegkAgAAQBAJ&amp;pg=PA244#v=onepage&amp;q&amp;f=false]
*The Japan Year Book. The Japan Year Book Office. 1905 onwards. [https://archive.org/details/bub_gb_arFPAAAAMAAJ/page/n10/mode/1up 1906]. [https://archive.org/details/in.ernet.dli.2015.553496/page/n27/mode/1up 1915].
*The &quot;Japan Gazette&quot; Japan Year Book. The Japan Gazette. [https://archive.org/details/japan-year-book-1913-1914/page/n15/mode/1up 1913-14]
*The Japan Times Year Book
*New Japan. Mainichi Newspapers. [https://books.google.co.uk/books?id=gRFCAQAAIAAJ]

Almanacs
*Asahi Shimbun Japan Almanac. [https://books.google.co.uk/books?id=SEEEAQAAIAAJ 1995].
*Japan Almanac. (The Mainichi Newspapers). [https://books.google.co.uk/books?id=ufAIAQAAIAAJ 1972]. [https://books.google.co.uk/books?id=X4eXWRkbtFsC 1973]. [https://books.google.co.uk/books?id=7rMrAAAAIAAJ] [https://books.google.co.uk/books?id=krMrAAAAIAAJ]
*[[w:Boyé Lafayette De Mente|Boye De Mente]]. Passport's Japan Almanac. [https://books.google.co.uk/books?id=741wAAAAMAAJ]

General
*Japan: A Country Study. (Area Handbook series). 4th Ed: 1983: [https://books.google.co.uk/books?id=HkM5N3JNc5IC]. 5th Ed: 1992: [https://books.google.co.uk/books?id=ze-wupXxpvEC]
*Area Handbook for Japan. 2nd Ed: 1964: [https://books.google.co.uk/books?id=WucdAAAAMAAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]. 3rd Ed: 1974: [https://books.google.co.uk/books?id=LG2aoq1U_eoC&amp;pg=PR1#v=onepage&amp;q&amp;f=false] (DA Pam 550-30).
*Colin Simpson. Picture of Japan.
**Japan: An Intimate View. A S Barnes. [https://books.google.co.uk/books?id=3hkeAAAAMAAJ]
**This is Japan. Angus &amp; Robertson. [https://books.google.co.uk/books?id=HJEJAQAAIAAJ]
*Japan. (The World and Its Peoples). Greystone Press, New York. 1964. Volume 1: [https://books.google.co.uk/books?id=yysUAQAAMAAJ]. Volume 2 &quot;Japan Korea&quot;, including Korea: [https://books.google.co.uk/books?id=uQAUAQAAMAAJ]. See pp 1 to 375 for Japan, and pp 376 to 379 for Ryukyu and Bonin Islands.
*Japan. (World and its Peoples: Eastern and Southern Asia, volume 8). Marshall Cavendish. 2008. ISBN 9780761476412.
*Edward Seidensticker. This Country, Japan. Kodansha International. 1979. ISBN 9780870112294. [https://books.google.co.uk/books?id=88wwAQAAIAAJ]
*Hall and Beardsley. Twelve Doors to Japan. McGraw-Hill. New York. 1965. [https://books.google.co.uk/books?id=0KpxAAAAMAAJ]
*&quot;Japan&quot;. Louis Barron (ed). &quot;Asia &amp; Australasia&quot;. Moshe Y Sachs (ed and pub). Worldmark Encyclopedia of the Nations. Worldmark Press, Inc. Harper &amp; Row New York. 1963. pp 145 to 160. [https://books.google.co.uk/books?id=I0oYAQAAMAAJ]
**&quot;Japan&quot;. Asia &amp; Oceania. 7th Ed: 1988. ISBN 0-471 62406-3. vol 4. pp 153 to 168.
**&quot;Japan&quot;. Asia &amp; Oceania. 8th Ed: 1995. Gale Research Inc. ISBN 0-8103-9882-6. vol 4. pp 203 to 220.

Handbooks
*Patrick Heenan (ed). The Japan Handbook. (Regional Handbooks of Economic Development). 1998. [https://books.google.co.uk/books?id=IMG2AgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Introduction
*Introducing Japan Through Books: A Selected Bibliography. Public Information Bureau, Ministry of Foreign Affairs, Japan. 1968. [https://books.google.co.uk/books?id=FvsyAQAAIAAJ]. 2nd Ed: 1973: [https://books.google.co.uk/books?id=Vj0XAQAAMAAJ].
*Donald Ritchie. Introducing Japan. 1st Ed: 1978. Revised Ed: 1986. 6th printing: 1989: [https://books.google.co.uk/books?id=FE-nxxoKayQC]. 2nd Revised Ed: 1990. 2nd printing: 1991: [https://books.google.co.uk/books?id=hz4UAQAAIAAJ]. 1994: [https://books.google.co.uk/books?id=FMvT6m4SgIQC&amp;pg=PP1#v=onepage&amp;q&amp;f=false].
*Herschel Webb. An Introduction to Japan. Columbia University Press. 2nd Ed: 1957: [https://books.google.co.uk/books?id=YQ8MAQAAIAAJ].
*Introducing Modern Japan. A publication of the Japan Information and Culture Center, Embassy of Japan.

Today and yesterday
*Ray Downs. Japan Yesterday and Today. Praeger Publishers. 1970. [https://books.google.co.uk/books?id=PwKxAAAAIAAJ]

Today
*Roger Buckley. Japan Today. Cambridge University Press. 3rd Ed [https://books.google.co.uk/books?id=thyqBtJp2DcC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Contemporary
*Routledge Handbook of Contemporary Japan. 2021. [https://books.google.co.uk/books?id=yfH3DwAAQBAJ&amp;pg=PA2011#v=onepage&amp;q&amp;f=false]
*Duncan McCargo. Contemporary Japan. 3rd Ed: 2012. [https://books.google.co.uk/books?id=8I5KEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Jeff Kingston. Contemporary Japan: History, Politics, and Social Change since the 1980s. 2011. [https://books.google.co.uk/books?id=enJQZA3R4FMC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

[Series]
*Routledge Contemporary Japan Series

Modern
*Hugh Cortazzi. Modern Japan: A Concise Survey. Palgrave Macmillan. 1993. [https://books.google.co.uk/books?id=Cf--DAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

The Japanese
*Peter Tasker. The Japanese: Portrait of a Nation. 1989 [https://books.google.com/books?id=Q1N8ld78wwQC]
**The Japanese: A Major Exploration of Modern Japan. [https://books.google.co.uk/books?id=CW-6AAAAIAAJ]
**Inside Japan: Wealth, Work and Power in the New Japanese Empire. 1987. [https://books.google.co.uk/books?id=2OJuAAAAMAAJ]
*Edwin O Reischauer. The Japanese. The Belknap Press of Harvard University Press. [https://books.google.co.uk/books?id=zrEqAAAAYAAJ]
*Edwin O Reischauer and Marius B Jansen. The Japanese Today: Change and Continuity. 1995. [https://books.google.co.uk/books?id=BTPNlLIy2soC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Japaneseness
*Ray T. Donahue (ed). Exploring Japaneseness: On Japanese Enactments of Culture and Consciousness. Ablex Publishing. 2002. [https://books.google.co.uk/books?id=V_NwAAAAMAAJ]
*Yoji Yamakuse. Japaneseness: A Guide to Values and Virtues. 2016. [https://books.google.co.uk/books?id=tB0iDAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Travel books
*DK Eyewitness Travel: Japan. Reprinted with revisions. 2015: [https://books.google.co.uk/books?id=g2NaBgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. 2017: [https://books.google.co.uk/books?id=vg15DQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false].
*Dodd and Richmond. The Rough Guide to Japan. 2nd Ed: 2001: [https://books.google.co.uk/books?id=pRGq95ytWZoC&amp;pg=PP1#v=onepage&amp;q&amp;f=false].
*Frommer's Japan. 5th Ed: 2000: [https://books.google.co.uk/books?id=-QC8mVyvPa8C].
*Fodor's Japan YYYY. 1984. [https://books.google.co.uk/books?id=aH2Ow27HUQ0C 1986]. [https://books.google.co.uk/books?id=3gTTf6nbv20C 1987]. 1988.
**Fodor's YY Japan. [https://books.google.co.uk/books?id=9QMHllzldlYC 91]. 92. 93.
**Fodor's Japan. 13th Ed: 1996: [https://books.google.co.uk/books?id=cZxZAAAAYAAJ]
*The New Official Guide: Japan. Japan Travel Bureau. 1966. [https://books.google.co.uk/books?id=HoxxAAAAMAAJ]
*Here is Japan. Asahi Broadcasting Corporation. [https://books.google.co.uk/books?id=8QXRCTMNG7MC]
*Japan. (Nagel Travel Guide Series, vol 32). 1964. [https://books.google.co.uk/books?id=QsbXAAAAMAAJ]
*Clark. All the Best in Japan: with Manila, Hong Kong, and Macao. (&quot;All the Best&quot; series). 1959. Reprinted 1964. [https://books.google.co.uk/books?id=yUq4YaaryrwC]. Reviews: [https://archive.dartmouthalumnimagazine.com/article/1958/6/1/all-the-best-in-japan] (1958) 110 Travel 51 [https://books.google.co.uk/books?id=UVwXAQAAMAAJ] 3 Bulletin of the Japan Society, London, No 11: June 1960, p 25 [https://books.google.co.uk/books?id=2oy74hRRXk4C]
**All the Best in Japan and the Orient. 1967.

Languages

See [[Universal Bibliography/Languages/Japanese|Japanese]]

Literature

See [[Universal Bibliography/Literature#Japanese|Japanese literature]]

Music

See [[Universal Bibliography/Music#Japanese and Japan|Music of Japan]]

Cinema

See [[Universal Bibliography/Cinema#Japanese|Cinema of Japan]]

Television

See [[Universal Bibliography/Television#Japanese|Japanese television]]

Culture

See [[Universal Bibliography/Culture#Japanese|Culture of Japan]]

==Korea==
*Korea Journal [https://books.google.co.uk/books?id=O6XfBexsp6gC]

Bibliography and literature
*Thomas H Kang. &quot;Korean Literature and Bibliography&quot;. Kent, Lancour and Daily (eds). Encyclopedia of Library and Information Science. Marcel Dekker. 1977. vol 21. pp [https://books.google.co.uk/books?id=H1pNvzr_n98C&amp;pg=PA176#v=onepage&amp;q&amp;f=false 176] to 240.

[[Category:Countries]]</text>
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    <title>User:Dc.samizdat/Real Euclidean four-dimensional space</title>
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      <text bytes="100221" sha1="6v9raulmqzxxgcvxi1j659y2h7bz48q" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - September 2026}}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

== Symmetries ==

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

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

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

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

== Special relativity describes Euclidean 4-space ==

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

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

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

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

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper spacetime coordinate systems.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}}

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions. In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. 

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity &lt;math&gt;c&lt;/math&gt; through space and proper time&lt;br&gt;
&lt;br&gt;
...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity&lt;br&gt;
&lt;br&gt;
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

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

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

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections.

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

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

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

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.{{Efn|
...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is &quot;just math&quot;, not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the &quot;math&quot; here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here...}}

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

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

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

== Distribution of stars in our galaxy ==

The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by their Hubble redshifts, and by assuming that they are distributed in three dimensions of space, astronomers have plotted their locations in 3-space. If we abandon the last of these three assumptions, we can reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. 

To map the galaxy's stars in 4-coordinate space we would have to supply the missing fourth coordinate for each star, which corresponds to its angle above or below our 3-space hyperplane in our fourth dimension, the direction of our motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. If we assume that our galaxy and all its stars originated in the same big-bang, and that they still lie near the surface of its expanding 3-sphere (a domain which may or may not be our entire visible universe), we can interpret the redshift-determined distances of the galaxy's stars as chordal distances from us on the surface of that universal 3-sphere, and consequently as angles below our hyperplane of ordinary 3-space. Because our galaxy is only a very small patch on the universal 3-sphere, those angles will be small, but not zero. They appear to be zero to us in our 3-dimensional visual perspective from earth, because the 4-ball of space around us projects into a 3-ball of space in our hyperplane, where we lose the separation between stars in our fourth dimension. Near each point in the sky where we observe multiple objects at various distances from us, apparently directly behind each other, those objects are actually separated by an angular distance in our fourth dimension corresponding to their redshift chordal distance. 

That small separation might not make much difference in our view of the night sky, but their actual separation in the fourth dimension may be much greater, large enough to significantly transform our map of the heavens. That is because it is unlikely that the stars in the galaxy all lie exactly on the surface of the expanding universal 3-sphere, after millions of years of expansion.{{Efn|

When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits? That would be an expected consequence of the special rotational symmetry group of 4-space &lt;math&gt;SO(4)&lt;/math&gt;, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. Also of interest would be whether the central region of the galaxy is a 4-ball or a 4-ellipsoid.}}

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

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

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

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

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

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

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

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

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

== Polycentric spherical relativity ==

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

This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

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

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. 

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

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

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

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

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

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

== Origins of the theory ==

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

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

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

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

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

== Boundaries ==

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{Efn|name=radially equilateral}}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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      <text bytes="100365" sha1="8crzodq51hzf3inmifqogdrosvtzaz8" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - September 2026}}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

== Symmetries ==

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

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

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

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

== Special relativity describes Euclidean 4-space ==

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

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

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

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

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper spacetime coordinate systems.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}}

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions. In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. 

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, yet. A good example ....{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity &lt;math&gt;c&lt;/math&gt; through space and proper time&lt;br&gt;
&lt;br&gt;
...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity&lt;br&gt;
&lt;br&gt;
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

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

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

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections.

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

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

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

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.{{Efn|
...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is &quot;just math&quot;, not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the &quot;math&quot; here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here...}}

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

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

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

== Distribution of stars in our galaxy ==

The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by their Hubble redshifts, and by assuming that they are distributed in three dimensions of space, astronomers have plotted their locations in 3-space. If we abandon the last of these three assumptions, we can reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. 

To map the galaxy's stars in 4-coordinate space we would have to supply the missing fourth coordinate for each star, which corresponds to its angle above or below our 3-space hyperplane in our fourth dimension, the direction of our motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. If we assume that our galaxy and all its stars originated in the same big-bang, and that they still lie near the surface of its expanding 3-sphere (a domain which may or may not be our entire visible universe), we can interpret the redshift-determined distances of the galaxy's stars as chordal distances from us on the surface of that universal 3-sphere, and consequently as angles below our hyperplane of ordinary 3-space. Because our galaxy is only a very small patch on the universal 3-sphere, those angles will be small, but not zero. They appear to be zero to us in our 3-dimensional visual perspective from earth, because the 4-ball of space around us projects into a 3-ball of space in our hyperplane, where we lose the separation between stars in our fourth dimension. Near each point in the sky where we observe multiple objects at various distances from us, apparently directly behind each other, those objects are actually separated by an angular distance in our fourth dimension corresponding to their redshift chordal distance. 

That small separation might not make much difference in our view of the night sky, but their actual separation in the fourth dimension may be much greater, large enough to significantly transform our map of the heavens. That is because it is unlikely that the stars in the galaxy all lie exactly on the surface of the expanding universal 3-sphere, after millions of years of expansion.{{Efn|

When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits? That would be an expected consequence of the special rotational symmetry group of 4-space &lt;math&gt;SO(4)&lt;/math&gt;, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. Also of interest would be whether the central region of the galaxy is a 4-ball or a 4-ellipsoid.}}

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

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

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

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

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

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

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

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

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

== Polycentric spherical relativity ==

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

This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

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

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. 

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

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

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

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

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

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

== Origins of the theory ==

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

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

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

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

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

== Boundaries ==

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{Efn|name=radially equilateral}}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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      <id>2831890</id>
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      <text bytes="100560" sha1="2vb0yuuz1tcktsr0z4xz1dpnoiqbj5i" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - September 2026}}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

== Symmetries ==

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

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

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

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

== Special relativity describes Euclidean 4-space ==

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

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

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

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

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper spacetime coordinate systems.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}}

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions. In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. 

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is their differing explanations for the gravitational coherence of galaxies: their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, versus their possession of experimentally undetected dark matter.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity &lt;math&gt;c&lt;/math&gt; through space and proper time&lt;br&gt;
&lt;br&gt;
...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity&lt;br&gt;
&lt;br&gt;
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

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

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

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections.

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

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

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

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.{{Efn|
...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is &quot;just math&quot;, not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the &quot;math&quot; here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here...}}

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

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

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

== Distribution of stars in our galaxy ==

The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by their Hubble redshifts, and by assuming that they are distributed in three dimensions of space, astronomers have plotted their locations in 3-space. If we abandon the last of these three assumptions, we can reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. 

To map the galaxy's stars in 4-coordinate space we would have to supply the missing fourth coordinate for each star, which corresponds to its angle above or below our 3-space hyperplane in our fourth dimension, the direction of our motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. If we assume that our galaxy and all its stars originated in the same big-bang, and that they still lie near the surface of its expanding 3-sphere (a domain which may or may not be our entire visible universe), we can interpret the redshift-determined distances of the galaxy's stars as chordal distances from us on the surface of that universal 3-sphere, and consequently as angles below our hyperplane of ordinary 3-space. Because our galaxy is only a very small patch on the universal 3-sphere, those angles will be small, but not zero. They appear to be zero to us in our 3-dimensional visual perspective from earth, because the 4-ball of space around us projects into a 3-ball of space in our hyperplane, where we lose the separation between stars in our fourth dimension. Near each point in the sky where we observe multiple objects at various distances from us, apparently directly behind each other, those objects are actually separated by an angular distance in our fourth dimension corresponding to their redshift chordal distance. 

That small separation might not make much difference in our view of the night sky, but their actual separation in the fourth dimension may be much greater, large enough to significantly transform our map of the heavens. That is because it is unlikely that the stars in the galaxy all lie exactly on the surface of the expanding universal 3-sphere, after millions of years of expansion.{{Efn|

When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits? That would be an expected consequence of the special rotational symmetry group of 4-space &lt;math&gt;SO(4)&lt;/math&gt;, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. Also of interest would be whether the central region of the galaxy is a 4-ball or a 4-ellipsoid.}}

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

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

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

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

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

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

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

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

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

== Polycentric spherical relativity ==

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

This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

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

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. 

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

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

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

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

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

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

== Origins of the theory ==

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

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

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

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

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

== Boundaries ==

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{Efn|name=radially equilateral}}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - September 2026}}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

== Symmetries ==

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

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

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

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

== Special relativity describes Euclidean 4-space ==

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

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

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

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

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper spacetime coordinate systems.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}}

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions. In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. 

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is their differing explanations for the gravitational coherence of galaxies: their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, versus their possession of experimentally undetected dark matter.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity &lt;math&gt;c&lt;/math&gt; through space and proper time&lt;br&gt;
&lt;br&gt;
...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity&lt;br&gt;
&lt;br&gt;
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

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

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

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections.

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

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

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

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.{{Efn|
...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is &quot;just math&quot;, not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the &quot;math&quot; here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here...}}

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

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

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

== Distribution of stars in our galaxy ==

The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by their Hubble redshifts, and by assuming that they are distributed in three dimensions of space, astronomers have plotted their locations in 3-space. If we abandon the last of these three assumptions, we can reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. 

To map the galaxy's stars in 4-coordinate space we would have to supply the missing fourth coordinate for each star, which corresponds to its angle above or below our 3-space hyperplane in our fourth dimension, the direction of our motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. If we assume that our galaxy and all its stars originated in the same big-bang, and that they still lie near the surface of its expanding 3-sphere (a domain which may or may not be our entire visible universe), we can interpret the redshift-determined distances of the galaxy's stars as chordal distances from us on the surface of that universal 3-sphere, and consequently as angles below our hyperplane of ordinary 3-space. Because our galaxy is only a very small patch on the universal 3-sphere, those angles will be small, but not zero. They appear to be zero to us in our 3-dimensional visual perspective from earth, because the 4-ball of space around us projects into a 3-ball of space in our hyperplane, where we lose the separation between stars in our fourth dimension. Near each point in the sky where we observe multiple objects at various distances from us, apparently directly behind each other, those objects are actually separated by an angular distance in our fourth dimension corresponding to their redshift chordal distance. 

That small separation might not make much difference in our view of the night sky, but their actual separation in the fourth dimension may be much greater, large enough to significantly transform our map of the heavens. That is because it is unlikely that the stars in the galaxy all lie exactly on the surface of the expanding universal 3-sphere, after millions of years of expansion.{{Efn|

When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits? That would be an expected consequence of the special rotational symmetry group of 4-space &lt;math&gt;SO(4)&lt;/math&gt;, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. Also of interest would be whether the central region of the galaxy is a 4-ball or a 4-ellipsoid.}}

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

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

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

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

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

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

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

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

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

== Polycentric spherical relativity ==

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

This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

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

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. 

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

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

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

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

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

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

== Origins of the theory ==

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

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

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

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

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

== Boundaries ==

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{Efn|name=radially equilateral}}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
      <sha1>1f5y5r7ime4vzpch6ubo6w3wzrhln3e</sha1>
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      <id>2831896</id>
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      <timestamp>2026-09-06T22:34:27Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <comment>/* Special relativity describes Euclidean 4-space */</comment>
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      <text bytes="100573" sha1="oc6xcna8my14ff4rta4y12ipz99mxra" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - September 2026}}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

== Symmetries ==

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

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

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

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

== Special relativity describes Euclidean 4-space ==

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

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

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

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

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper spacetime coordinate systems.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}}

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions. In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. 

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity &lt;math&gt;c&lt;/math&gt; through space and proper time&lt;br&gt;
&lt;br&gt;
...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity&lt;br&gt;
&lt;br&gt;
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

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

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

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections.

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

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

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

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.{{Efn|
...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is &quot;just math&quot;, not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the &quot;math&quot; here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here...}}

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

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

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

== Distribution of stars in our galaxy ==

The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by their Hubble redshifts, and by assuming that they are distributed in three dimensions of space, astronomers have plotted their locations in 3-space. If we abandon the last of these three assumptions, we can reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. 

To map the galaxy's stars in 4-coordinate space we would have to supply the missing fourth coordinate for each star, which corresponds to its angle above or below our 3-space hyperplane in our fourth dimension, the direction of our motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. If we assume that our galaxy and all its stars originated in the same big-bang, and that they still lie near the surface of its expanding 3-sphere (a domain which may or may not be our entire visible universe), we can interpret the redshift-determined distances of the galaxy's stars as chordal distances from us on the surface of that universal 3-sphere, and consequently as angles below our hyperplane of ordinary 3-space. Because our galaxy is only a very small patch on the universal 3-sphere, those angles will be small, but not zero. They appear to be zero to us in our 3-dimensional visual perspective from earth, because the 4-ball of space around us projects into a 3-ball of space in our hyperplane, where we lose the separation between stars in our fourth dimension. Near each point in the sky where we observe multiple objects at various distances from us, apparently directly behind each other, those objects are actually separated by an angular distance in our fourth dimension corresponding to their redshift chordal distance. 

That small separation might not make much difference in our view of the night sky, but their actual separation in the fourth dimension may be much greater, large enough to significantly transform our map of the heavens. That is because it is unlikely that the stars in the galaxy all lie exactly on the surface of the expanding universal 3-sphere, after millions of years of expansion.{{Efn|

When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits? That would be an expected consequence of the special rotational symmetry group of 4-space &lt;math&gt;SO(4)&lt;/math&gt;, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. Also of interest would be whether the central region of the galaxy is a 4-ball or a 4-ellipsoid.}}

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

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

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

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

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

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

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

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

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

== Polycentric spherical relativity ==

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

This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

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

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. 

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

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

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

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

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

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

== Origins of the theory ==

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

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

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

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

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

== Boundaries ==

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{Efn|name=radially equilateral}}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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  <page>
    <title>Bully Metric Timestamps</title>
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        <username>~2026-48171-60</username>
        <id>3110678</id>
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      <comment>/* The Heliosphere */</comment>
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      <text bytes="56605" sha1="gt70ytvz8yz3jen7wlym9dgd64qhcla" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;


=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]


[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.


=== Earth's sidereal orbit ===
[[File:Astronomical_unit_svg.svg|thumb|right|400px|'''TBD:''' The grey line indicates the Earth–Sun distance, which on average is about 1&amp;nbsp;astronomical unit.]]

&amp;hairsp;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
&amp;hairsp;

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Bully timestamp is a divisor of Earth's sidereal year.
  | The Sun orbits approximately one solar radius per Bully timestamp.
  }}
}}

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>gt70ytvz8yz3jen7wlym9dgd64qhcla</sha1>
    </revision>
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      <id>2831863</id>
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      <text bytes="56989" sha1="rbpzsdpojyetvvv1eep5449swbu4ruc" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;


=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]


[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.


=== Earth's sidereal orbit ===
[[File:Astronomical_unit_svg.svg|thumb|right|400px|'''TBD:''' The grey line indicates the Earth–Sun distance, which on average is about 1&amp;nbsp;astronomical unit.]]

&amp;hairsp;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
&amp;hairsp;

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Bully timestamp is a divisor of Earth's sidereal year.
  | The Sun orbits approximately one solar radius per Bully timestamp.
  }}
}}

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
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      <text bytes="56988" sha1="0ovy4jydvx77r6b378tirumw3el4cyx" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;


=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.


=== Earth's sidereal orbit ===
[[File:Astronomical_unit_svg.svg|thumb|right|400px|'''TBD:''' The grey line indicates the Earth–Sun distance, which on average is about 1&amp;nbsp;astronomical unit.]]

&amp;hairsp;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
&amp;hairsp;

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Bully timestamp is a divisor of Earth's sidereal year.
  | The Sun orbits approximately one solar radius per Bully timestamp.
  }}
}}

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>0ovy4jydvx77r6b378tirumw3el4cyx</sha1>
    </revision>
    <revision>
      <id>2831865</id>
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      <timestamp>2026-09-06T21:01:59Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
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      <comment>/* Naked-Eye Stars */</comment>
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      <text bytes="56906" sha1="29lzot173skmcy321jdvp5kasiq2z3m" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;


=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.


=== Earth's sidereal orbit ===
[[File:Astronomical_unit_svg.svg|thumb|right|400px|'''TBD:''' The grey line indicates the Earth–Sun distance, which on average is about 1&amp;nbsp;astronomical unit.]]

&amp;hairsp;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
&amp;hairsp;

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Bully timestamp is a divisor of Earth's sidereal year.
  | The Sun orbits approximately one solar radius per Bully timestamp.
  }}
}}

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>29lzot173skmcy321jdvp5kasiq2z3m</sha1>
    </revision>
    <revision>
      <id>2831866</id>
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      <comment>/* Naked-Eye Stars */</comment>
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      <text bytes="56988" sha1="bng6y0q08x9szckzvyzjwpl278r1tvm" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;


=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.


=== Earth's sidereal orbit ===
[[File:Astronomical_unit_svg.svg|thumb|right|400px|'''TBD:''' The grey line indicates the Earth–Sun distance, which on average is about 1&amp;nbsp;astronomical unit.]]

&amp;hairsp;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
&amp;hairsp;

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Bully timestamp is a divisor of Earth's sidereal year.
  | The Sun orbits approximately one solar radius per Bully timestamp.
  }}
}}

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
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      <text bytes="56694" sha1="6h4tuv0wj74o994p5qab4xz6omti874" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;


=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.


== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Bully timestamp is a divisor of Earth's sidereal year.
  | The Sun orbits approximately one solar radius per Bully timestamp.
  }}
}}

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>6h4tuv0wj74o994p5qab4xz6omti874</sha1>
    </revision>
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      <id>2831878</id>
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      <text bytes="60370" sha1="dgpipfhfpl0yms4x460xif4f194nwow" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;


=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Bully timestamp is a divisor of Earth's sidereal year.
  | The Sun orbits approximately one solar radius per Bully timestamp.
  }}
}}

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>dgpipfhfpl0yms4x460xif4f194nwow</sha1>
    </revision>
    <revision>
      <id>2831880</id>
      <parentid>2831878</parentid>
      <timestamp>2026-09-06T22:11:10Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Is the Bully system internally consistent? */</comment>
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      <text bytes="60364" sha1="cgh2h94qohc8ejibbl7z08mefjuybex" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;


=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year (2&lt;sup&gt;41&lt;/sup&gt; timestamps), introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Bully timestamp is a divisor of Earth's sidereal year.
  | The Sun orbits approximately one solar radius per Bully timestamp.
  }}
}}

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>cgh2h94qohc8ejibbl7z08mefjuybex</sha1>
    </revision>
    <revision>
      <id>2831882</id>
      <parentid>2831880</parentid>
      <timestamp>2026-09-06T22:11:54Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Is the Bully system internally consistent? */</comment>
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      <text bytes="60336" sha1="kjkk39d3en28f2o41mjzgn7hkfjj3id" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;


=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Bully timestamp is a divisor of Earth's sidereal year.
  | The Sun orbits approximately one solar radius per Bully timestamp.
  }}
}}

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>kjkk39d3en28f2o41mjzgn7hkfjj3id</sha1>
    </revision>
    <revision>
      <id>2831886</id>
      <parentid>2831882</parentid>
      <timestamp>2026-09-06T22:18:41Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Earth's sidereal year */</comment>
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      <text bytes="60088" sha1="9kop18qi5j02egebh0unb9j9o51sctt" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;


=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>9kop18qi5j02egebh0unb9j9o51sctt</sha1>
    </revision>
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      <id>2831888</id>
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        <username>Unitfreak</username>
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      <comment>/* Earth's Great Year */</comment>
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      <text bytes="60393" sha1="mejvznfhyhjlwwse7pe6kzinljgm0n5" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;


=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>mejvznfhyhjlwwse7pe6kzinljgm0n5</sha1>
    </revision>
    <revision>
      <id>2831891</id>
      <parentid>2831888</parentid>
      <timestamp>2026-09-06T22:28:39Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
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      <origin>2831891</origin>
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      <text bytes="60393" sha1="bz8gxosmbx5r1ufy7vg52462ftmnl2p" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;


=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>bz8gxosmbx5r1ufy7vg52462ftmnl2p</sha1>
    </revision>
    <revision>
      <id>2831893</id>
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        <username>Unitfreak</username>
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      <comment>/* One Solar Radius */</comment>
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      <text bytes="60392" sha1="2vdvdd2sr92fq59cxxyz0489haigj4k" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
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      <text bytes="60392" sha1="5bjdgs4hoag1kvyxnma8gz51bho8b21" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|430px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>5bjdgs4hoag1kvyxnma8gz51bho8b21</sha1>
    </revision>
    <revision>
      <id>2831897</id>
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      <text bytes="60392" sha1="b8sgtghjn8d5z7xruqzopo11erzgocq" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|430px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|430px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
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      <text bytes="60392" sha1="q9jbse2ckj9p22o7lvqz2o42oqu5uo7" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|430px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|430px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|430px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>q9jbse2ckj9p22o7lvqz2o42oqu5uo7</sha1>
    </revision>
    <revision>
      <id>2831900</id>
      <parentid>2831898</parentid>
      <timestamp>2026-09-06T22:35:59Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The Bully Milky Way */</comment>
      <origin>2831900</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="60392" sha1="kl1flnyzh2vvww097ehz6qlwafugw06" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|430px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|430px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|430px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|430px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|600px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
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    </revision>
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      <text bytes="60392" sha1="dykudlt8d4h7egnm6sguww9g6xcwu7k" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|430px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|430px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|430px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|430px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|430px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>dykudlt8d4h7egnm6sguww9g6xcwu7k</sha1>
    </revision>
    <revision>
      <id>2831903</id>
      <parentid>2831901</parentid>
      <timestamp>2026-09-06T22:37:28Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
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      <text bytes="60392" sha1="t5km6vgjo01d666f8lpaies5gyk968a" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|430px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|430px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|430px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|430px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|430px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|430px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|800px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>t5km6vgjo01d666f8lpaies5gyk968a</sha1>
    </revision>
    <revision>
      <id>2831904</id>
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        <username>Unitfreak</username>
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      <text bytes="60392" sha1="lnu62pr72ziugb3uno4wh406s2whq1v" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;


[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|430px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|430px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|430px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|430px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|430px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|430px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>lnu62pr72ziugb3uno4wh406s2whq1v</sha1>
    </revision>
    <revision>
      <id>2831907</id>
      <parentid>2831904</parentid>
      <timestamp>2026-09-06T22:41:09Z</timestamp>
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        <id>3110678</id>
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      <text bytes="60385" sha1="fl6lue9us18k4ulij8c2t8663t8p0zt" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|430px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|430px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|430px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|430px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|430px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
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      <text bytes="60397" sha1="mjfxas1z5g0ukpf4ojmdz7x440l0fzi" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=1.3|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|430px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|430px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|430px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|430px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|430px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
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      <id>2831909</id>
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      <text bytes="60397" sha1="7tkd5gbxtdoqjosaypmiyea3cfrkeib" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=3.5|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|430px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|430px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|430px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|430px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|430px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>7tkd5gbxtdoqjosaypmiyea3cfrkeib</sha1>
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      <text bytes="60397" sha1="0w9fcb6vjliwdilobbxv0s40g6eypg3" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.5|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|430px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|430px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|430px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|430px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|430px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
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      <text bytes="60397" sha1="lb0xtg7t8u4dlw9hvb9sv7oa8zh24zm" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|430px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|430px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|430px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|430px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|430px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>lb0xtg7t8u4dlw9hvb9sv7oa8zh24zm</sha1>
    </revision>
    <revision>
      <id>2831912</id>
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      <comment>/* The Heliosphere */</comment>
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      <text bytes="60403" sha1="5la7dg2gngkz9zge7eo72ekcqekyu15" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|upright=2.2|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|430px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|430px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|430px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|430px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
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      <text bytes="60409" sha1="353ceelth2zu1e6il70dypc81vt1v90" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|upright=2.2|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|upright=2.2|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|430px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|430px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|430px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>353ceelth2zu1e6il70dypc81vt1v90</sha1>
    </revision>
    <revision>
      <id>2831914</id>
      <parentid>2831913</parentid>
      <timestamp>2026-09-06T22:46:27Z</timestamp>
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        <username>~2026-48171-60</username>
        <id>3110678</id>
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      <comment>/* The Bully Milky Way */</comment>
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      <text bytes="60415" sha1="95i7i1678odef6gl8go14i890l5bsxx" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|upright=2.2|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|upright=2.2|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|upright=2.2|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|430px|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|430px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
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      <text bytes="60421" sha1="fx1e9iza5fl896v11q838omnlyv174h" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|upright=2.2|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|upright=2.2|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|upright=2.2|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|upright=2.2|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|430px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>fx1e9iza5fl896v11q838omnlyv174h</sha1>
    </revision>
    <revision>
      <id>2831916</id>
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      <comment>/* The Galactic Ecliptic Node near Sagittarius */</comment>
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      <text bytes="60427" sha1="g608f84k8wor3iufot4kk2tx73eix03" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|upright=2.2|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|upright=2.2|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|upright=2.2|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|upright=2.2|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|upright=2.2|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== Bullies in the Bully System ===
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>g608f84k8wor3iufot4kk2tx73eix03</sha1>
    </revision>
    <revision>
      <id>2831917</id>
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        <username>~2026-48171-60</username>
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      <comment>/* Bullies in the Bully System */</comment>
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      <text bytes="58474" sha1="0c8q95ck8rvb4gmavbek5acxkczltiq" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|upright=2.2|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|upright=2.2|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|upright=2.2|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|upright=2.2|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|upright=2.2|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

==== A surrogate for the Sun ====
The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>0c8q95ck8rvb4gmavbek5acxkczltiq</sha1>
    </revision>
    <revision>
      <id>2831918</id>
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      <comment>/* The Galactic Ecliptic Node near Sagittarius */</comment>
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      <text bytes="60429" sha1="9nqoenkxqutgdbg0x7us3t01g9cf0zo" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|upright=2.2|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|upright=2.2|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|upright=2.2|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|upright=2.2|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|upright=2.2|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

==== Bullies in the Bully System ====
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

==== A surrogate for the Sun ====
As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>9nqoenkxqutgdbg0x7us3t01g9cf0zo</sha1>
    </revision>
    <revision>
      <id>2831920</id>
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      <comment>/* A surrogate for the Sun */</comment>
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      <text bytes="60427" sha1="rg74axsu5jukwfguc3rpqmz9eouotja" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|upright=2.2|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|upright=2.2|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|upright=2.2|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|upright=2.2|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|upright=2.2|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

==== Bullies in the Bully System ====
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== A surrogate for the Sun ===
As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

The path of the Solar System's Galactic Ecliptic Node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
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      <text bytes="60389" sha1="anigd6wbzjzz81cf7fsv1mx8ts2k35y" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|upright=2.2|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|upright=2.2|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|upright=2.2|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|upright=2.2|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|upright=2.2|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

==== Bullies in the Bully System ====
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== A surrogate for the Sun ===
As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

The path of the Solar System's Galactic Ecliptic Node can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>anigd6wbzjzz81cf7fsv1mx8ts2k35y</sha1>
    </revision>
    <revision>
      <id>2831922</id>
      <parentid>2831921</parentid>
      <timestamp>2026-09-06T22:52:37Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
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      <comment>/* A surrogate for the Sun */</comment>
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      <text bytes="60356" sha1="1v5sbht8ra3b0lf6brqqvlqem150whq" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|upright=2.2|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|upright=2.2|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|upright=2.2|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|upright=2.2|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|upright=2.2|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

==== Bullies in the Bully System ====
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== A surrogate for the Sun ===
As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

The path of the node can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>1v5sbht8ra3b0lf6brqqvlqem150whq</sha1>
    </revision>
    <revision>
      <id>2831927</id>
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      <comment>/* The Bully Milky Way */</comment>
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      <text bytes="60432" sha1="m7093wm6hlum9si2sj7qhfkl71m4fku" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|upright=2.2|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|upright=2.2|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|upright=2.2|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively assuming a full orbital path around the Milky Way of roughly 50,000 parsecs.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|upright=2.2|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which is traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|upright=2.2|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

==== Bullies in the Bully System ====
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== A surrogate for the Sun ===
As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

The path of the node can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>m7093wm6hlum9si2sj7qhfkl71m4fku</sha1>
    </revision>
    <revision>
      <id>2831928</id>
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        <username>~2026-48171-60</username>
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      <comment>/* Idealized Galactic Weeks */</comment>
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      <text bytes="60459" sha1="e7l7o2qnjjv21rkm2goj0xugwc6oe4k" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|upright=2.2|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|upright=2.2|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|upright=2.2|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively assuming a full orbital path around the Milky Way of roughly 50,000 parsecs.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|upright=2.2|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which in this plot is assumed to be traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|upright=2.2|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

==== Bullies in the Bully System ====
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== A surrogate for the Sun ===
As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

The path of the node can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
      <sha1>e7l7o2qnjjv21rkm2goj0xugwc6oe4k</sha1>
    </revision>
    <revision>
      <id>2831929</id>
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        <username>~2026-48171-60</username>
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      <text bytes="60458" sha1="kaot52nwvtzagfnvms4ovsakgmtqxsc" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the Sun's orbit around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp occurs each time the Sun advances by roughly one solar radius along its path through the cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:
&amp;thinsp;
:&lt;math&gt;16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|upright=2.2|center|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

== One Solar Radius ==
The Sun hurtles around the Milky Way Galaxy at a blistering 0.076% of the speed of light ([https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]). Yet, even at this staggering pace, it takes about five-sixths of an hour for the Sun to traverse a distance equal to its own radius. This highlights the truly colossal size of our star, which boasts a radius of 2.3206 light-seconds (695,700 kilometers).

'''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''.

During each '''3,055-second''' period, the Sun orbits a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over '''2.33 light-seconds''', which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt; d_{\odot} \gtrapprox 2.33 \text{ ls} \gtrapprox R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== The Heliosphere ===
The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', it is a vast, oblong, bubble-like region that extends from the Sun into surrounding space. While somewhat analogous to Earth's atmosphere, the latter is a comparatively thin layer of gas held near the planetary surface, whereas the heliosphere is a plasma constantly blasted into space by the Sun's extreme heat and energy.

[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|upright=2.2|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

The heliosphere is so vast that if it were truly spherical, it would take the Sun roughly 6.344 years to orbit a distance equivalent to the heliosphere's diameter. The digit in the '''fifth position''' of a Bully timestamp represents this orbital distance.

Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. Timestamp 8209 ED00 0000 is defined to have occurred at exactly 12:00:00 TAI on June 21, 1998. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''.

Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space.

During each 6.344-year period, the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{4}\,d_{\odot} \gtrapprox 306 \text{ AU} \gtrapprox 16^{4}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

=== Naked-Eye Stars ===
'''Figure 3a''' illustrates the physical movement of the Sun (not to scale) across 16&lt;sup&gt;8&lt;/sup&gt; successive Bully timestamps. Timestamp '''8209 0000 0000''' corresponds to approximately 383,000 B.C., while timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., representing a total time lapse of '''416,000 years'''. 

The stacked histogram in Figure 3a has a cyan dashed line marking 100 parsecs. The Sun travels a little less than this distance during each 416,000-year interval, which is tracked by the digit in the '''ninth position''' of the Bully timestamp. Because a large percentage of naked-eye stars sit within this 100-parsec radius, the appearance of Earth's night sky changes completely over this timeframe.

[[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]]

[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|upright=2.2|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the Sun. A large percentage of these stars are closer to the Sun than 100 parsecs, which is the distance the Sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this 100-parsec travel distance of the Sun.]]

During each 415,792-year period, the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 97 parsecs, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;16^{8}\,d_{\odot} \gtrapprox 97 \text{ pc} \gtrapprox 16^{8}\,R_{\odot}
&lt;/math&gt;
&amp;hairsp;
[[Bully_Metric_Math_and_Mnemonics|See Full Calculations]]
&amp;hairsp;

==== The Bully Milky Way ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|upright=2.2|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

'''Figure 3e''' illustrates the division of the Milky Way into 32 equal polar sectors (yellow grid). Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000'''. These represent the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D., respectively assuming a full orbital path around the Milky Way of roughly 50,000 parsecs.

In the lower half of the image, cyan lines further divide a single yellow sector into 16 equal subsectors. The Sun is currently located directly below the Galactic Center in Figure 3e, corresponding to the 6 o'clock position, and orbits in a clockwise direction. A red grid line represents the polar angle of the Sun at Bully timestamp 820A 0000 0000, estimated to occur around 33,000 A.D. The nine cyan grid lines to the right of the red line mark the Sun's polar angle for Bully timestamps 8201 0000 0000 through 8209 0000 0000. Meanwhile, the five cyan grid lines to the left of the red line indicate the polar angle for timestamps 820B 0000 0000 through 820F 0000 0000.

== The Galactic Calendar ==
[[File:Galactic centre orbits.svg|thumb|300px|'''Figure 4a''':Inferred orbits of 6 stars around the supermassive black hole Sagittarius A* at the Milky Way's center&lt;ref name=&quot;Eisenhauer&quot;&gt;{{cite journal|last=Eisenhauer|first=F.|display-authors=et al. |title=SINFONI in the Galactic Center: Young Stars and Infrared Flares in the Central Light-Month|journal=The Astrophysical Journal|date=July 20, 2005|volume=628|issue=1|pages=246–259|doi=10.1086/430667|bibcode=2005ApJ...628..246E|arxiv=astro-ph/0502129|s2cid=122485461 }}&lt;/ref&gt;]]
[[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, labeled S2 in '''Figure 4a''', completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole.

By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance from the Sun to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π:
&amp;hairsp;
:&lt;math&gt;\begin{align}
{\text{Circumference}} &amp;= 2\pi \times 8,275{\text{ parsecs}} \\
&amp;\approx 51,993{\text{ parsecs}} \\
\end{align}&lt;/math&gt;
&amp;hairsp;
If we divide this '''roughly 52,000-parsec''' idealized orbit into &quot;Galactic Weeks&quot;, where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks.

==== Idealized Galactic Weeks ====
[[File:Milky_Way_map_by_Gaia_High_Density_Weeks_Grid.jpg|thumb|center|upright=2.2|'''Figure 3f''': Division of the Milky Way into 52 equal galactic weeks of solar travel (yellow grid).]]

'''Figure 3f''' illustrates the division of the Milky Way into 52 equal galactic weeks (yellow grid). Each week represents 1,000 parsecs of solar travel, which in this plot is assumed to be traversed by the Sun in roughly 4.09 million years. Three of the grid lines are labeled as Bully timestamps '''8200 0000 0000''', '''8280 0000 0000''', and '''8300 0000 0000''', respectively indicating the estimated polar angle of the Sun at approximately 4.1 million years B.C., 49 million years A.D., and 102 million years A.D.

The cyan lines in the lower half of the image further divide one sector into 10 equal subsectors of 100 parsecs each. The Sun is currently located directly below the Galactic Center, at the 6 o'clock position in Figure 3f, and orbits in a clockwise direction. A red grid line represents the polar angle the Sun had during Bully timestamp 8209 D89D 89D8 (approximately 31,000 B.C.), which is 1,000 parsecs of travel beyond the yellow line representing timestamp 8200 0000 0000. The nine cyan lines to the left of the red line represent the polar angles of the Sun after traveling 1,100 through 1,900 parsecs beyond timestamp 8200 0000 0000.

=== Idealized Galactic Years ===
Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4b''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;&quot;
|+ '''Figure 4b:''' The 66th Bully Galactic Calendar

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} &lt;br/&gt;'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8380 0000 0000}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} &lt;br/&gt; '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8389 D89D 89D8}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8393 B13B 13B1}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} &lt;br/&gt; '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} &lt;br/&gt; '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} &lt;br/&gt; '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} &lt;br/&gt; '''{{nowrap|839D 89D8 9D89}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83A7 6276 2762}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83B1 3B13 B13B}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} &lt;br/&gt; '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} &lt;br/&gt; '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83BB 13B1 3B13}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83C4 EC4E C4EC}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} &lt;br/&gt; '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} &lt;br/&gt; '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83CE C4EC 4EC4}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83D8 9D89 D89D}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83E2 7627 6276}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} &lt;br/&gt; '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} &lt;br/&gt; '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83EC 4EC4 EC4E}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} &lt;br/&gt; '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83F6 2762 7627}}'''
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | End of Quarter || {{color|blue|''13,000 parsecs''}} &lt;br/&gt; '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} &lt;br/&gt; '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} &lt;br/&gt; '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} &lt;br/&gt; '''{{nowrap|83FF FFFF FFFF}}'''
|}

Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''.

==== Is the Galactic Calendar Realistic? ====
[[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4c:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]]

The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4c). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4c''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits.

Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in Figure 4b states that the galactic week beginning on timestamp '''{{nowrap|8209 D89D 89D8}}''' corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate.

In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark.

==== Is the Bully system internally consistent? ====
In Figure 3a and Figure 3e, the Sun is shown to travel less than 50,000 parsecs per galactic year. However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per galactic year, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamp up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== Anchoring Bully Timestamps ==
To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored near the '''June solstice in 1998'''.

=== The Galactic Ecliptic Node near Sagittarius ===
'''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator.

[[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|upright=2.2|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]]

==== Bullies in the Bully System ====
A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending node of each giant planet's ecliptic where it intersects the Galactic Equator is shown in Figure 5a:

* '''Invariable Plane Node (+)''': Marked with a large plus sign.
* '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node.
* '''Uranus (⛢)''': Positioned to the right of Jupiter.
* '''Saturn (♄)''': Positioned on the inner left.
* '''Neptune (♆)''': Positioned on the far left.

As noted in the Merriam-Webster dictionary, the word &quot;bully&quot; had a positive connotation through much of history:
{{Blockquote|text=The earliest meaning of English bully was &quot;sweetheart&quot;. The word was probably borrowed from Dutch boel, &quot;lover&quot;. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker. “Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}}

Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of &quot;excellent&quot; or &quot;beautiful&quot; and in the modern meaning of being intimidating and threatening. 

{{Quote box| align  = center | width  = full | title  = The &quot;Bully&quot; Name | quote  = The specific &quot;bullies&quot; in the &quot;Bully&quot; timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}}

=== A surrogate for the Sun ===
As the Sun orbits the Galactic Center, the Galactic Ecliptic Node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving.

The path of the node can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°):

&lt;math&gt;
\begin{aligned}
d &amp;= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\
&amp;\approx 1,008.14 \text{ pc}
\end{aligned}
&lt;/math&gt;

Based on this calculation, the Galactic Ecliptic Node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4b''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year.

To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding to timestamp '''{{nowrap|8209 EF4D 094B}}'''. (Note: Figure 4a assumes an idealized travel distance of exactly 52,000 (2&lt;sup&gt;15.666224&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps, whereas Figure 5b uses the calculated distance of 51,993 (2&lt;sup&gt;15.666040&lt;/sup&gt;) parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps.)

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; text-align:center; max-width:300px;&quot;
|+ '''Figure 5b:''' Week one, 66th Galactic Year

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 3px; font-size: large;&quot; | Year 66 &lt;br /&gt; Galactic
|| {{nowrap|Bully timestamp}} || Solar Distance Traveled in parsecs
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B32}}''' || {{nowrap|{{color|blue|''1006.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87''}}}} 
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 094B}}''' || {{nowrap|{{color|blue|''1008.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5058}}''' || {{nowrap|{{color|blue|''1009.87''}}}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|1.100 Weeks}} ||'''{{nowrap|820A D4AD 4AD4}}''' || {{nowrap|{{color|blue|''1099.86''}}}}
|}

{{Quote box| align  = center| width  = full| title  = Bully Timestamp Anchor| quote  = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}}

=== The Earth and Moon ===
The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics.

{{Quote box| align  = center| width  = 100%| title  = Bully Timestamp Duration
| quote  = {{ordered list
  | The Sun orbits approximately one solar radius per Bully timestamp.
  | The Bully timestamp is a divisor of Earth's sidereal year.
| The Bully timestamp is a divisor of Earth's Great Year.
 }}
}}

==== Earth's sidereal year ====
The duration of Earth's sidereal year is '''31,558,149.76 seconds'''. While gravitational perturbations from neighboring planets cause this value to vary by 20 to 25 minutes annually, the averaged century-over-century lengthening is a mere 9.6 milliseconds. Given this relative stability, using a clean divisor of the sidereal year as the fundamental unit of the Bully timestamp system offers significant utility. Specifically, 3,055 seconds is an exact divisor of 31,558,150 seconds, meaning Earth's sidereal year—rounded to the nearest second—equals '''exactly 10,330 Bully timestamps'''.

==== Earth's tropical year ====
Earth's tropical year, which measures the complete cycle of seasons between successive vernal equinoxes, spans '''31,556,925.2 seconds'''. Due to axial precession, the tropical year is roughly 2/5 of a Bully timestamp shorter than the sidereal year.

==== Earth's Great Year ====
With Earth's sidereal year (&lt;math&gt;P&lt;/math&gt;) spanning 10,330 timestamps and the tropical year (&lt;math&gt;a_{t}&lt;/math&gt;) spanning 10,329.6 timestamps, a full precessional cycle requires a number of years, &lt;math&gt;N&lt;/math&gt;, where the cumulative annual difference equals exactly one year:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
N &amp;= \frac{1}{10,330 - 10,329.6} \\
&amp;= \frac{1}{0.4} \\
&amp;= \frac{5}{2}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Expressing this duration in terms of sidereal years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,329.6 \, P \\
&amp;= 25,824 \, P 
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

Alternatively, expressing the cycle in terms of tropical years yields:

&amp;hairsp;
&lt;math&gt; 
\begin{aligned}
1 \, \text{Great Year} &amp;= \frac{5}{2} \times  10,330 \, a_{t} \\
&amp;= 25,825 \, a_{t}
\end{aligned}
&lt;/math&gt;
&amp;hairsp;

The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]

==== Earth's Seasons and Milky Way Visibility ====
In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next 1,500 years until summer is a full 94 days long and winter is less than 89 days.

The Earth's orbital speed varies throughout the year, moving slowly during [[W:aphelion|aphelion]] and quickly during [[W:perihelion|perihelion]]. Consequently, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slowly and takes longer to get through that season.

As shown in Figure 5c, '''winter''' was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. It took approximately 5,250 years to cycle to '''spring''' being the longest season, and another 5,250 years to '''summer'''. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over '''21,000 years'''.

[[File:Earth_Seasons_and_Milky_Way_Visibility_Shifts_Over_Time.svg|thumb|center|430px|alt=Graph showing how the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.|'''Figure 5c''': The lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]]

Currently, the Milky Way is easy to view during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. 

The transition from '''spring to summer''' is correlated with a large '''green dot''' and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the Galactic Equator crossed the solstice points. A large '''red dot''' appears in 8329 CE to indicate the approximate crossing from '''summer to autumn''', and a large '''blue dot''', back in 4495 BCE, indicates the approximate crossing from '''winter to spring'''. The red and blue dots represent epochs when the coordinate latitude of the Sun, as viewed from Earth, is nearly zero in the ecliptic, celestial, and galactic coordinates at the same time. These large dots representing Galactic Equator crossings occur about once every 6,500 years. While it is beyond the range of the graph, it is clear that the Milky Way passes through all four seasons during a time period of roughly '''26,000 years''' (1 Great Year ≈ 25,824 sidereal years ≈ 25,825 tropical years).

{{Quote box | align = center | width = 100% | title = Bully Time Anchor | quote = The time anchor of the entire Bully system was selected to be '''12:00:00 TAI on June 21, 1998''', which is near the 1998 June solstice. This date was selected as the anchor because it occurred near the May 1998 CE date that Jean Meeus identified as a Galactic crossing. All of the Galactic crossings shown in Figure 5c, at 4495 BCE, 1998 CE, and 8329 CE, are roughly correlated with rounded Bully timestamps.
&lt;ol&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 E900 0000}}''' aligns with 4500 BCE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 ED00 0000}}''' aligns with 1998 CE.&lt;/li&gt;
  &lt;li&gt;Bully timestamp '''{{nowrap|8209 F100 0000}}''' aligns with 8494 CE.&lt;/li&gt;
&lt;/ol&gt;
}}

==== The Metonic cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp complete approximately three cycles per one Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moons
* July 23, 1998 — 8209 ED0'''0 038B'''
* July 23, 2017 — 8209 ED0'''3 0238'''
* July 23, 2036 — 8209 ED0'''6 00EA'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Bully Timestamp Realization ==
Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered &quot;realized&quot; when time is measured with an accuracy of 10&lt;sup&gt;-10&lt;/sup&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

== Bully Timestamp Estimation ==
[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 6a: History of the Universe with a few example Bully timestamps shown in red.]]
For the purpose of time estimation, the Bully system's time range is divided into three distinct sets:

==== First Set ====
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 6a'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

==== Second Set ====
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 6b'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 6b: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

==== Third Set ====
* ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|B000 0000 0000}}''
** [[w:Sun#Life_phases|Death of Sun (main-sequence)]]
&lt;/div&gt;

=== Time Estimation Using Cosmic Redshift ===
In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}.

If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars.

This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 6c contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6c: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Redshift z &lt;br /&gt; (z = ∞ to 2)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};”&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;;{{Text color default}};&quot; | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}}
|}

The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 6d (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years.

[[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 6d: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]]

Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 6d) measure &quot;lookback&quot; time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

The data illustrated in Figure 6e is the same as is shown in Figure 6d, but Figure 6e plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue.

[[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 6e: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]]

The table in Figure 6f is similar to the table in Figure 6c, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 6c was for large z values, Figure 6f shows small z values. Smaller z values correspond with the recent past. 

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates

|- style=&quot;background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Bully Timestamp &lt;br /&gt; (z = 1 to 0)
|| SHOES Team &lt;br /&gt; (12.7 Gyr) || Planck Collaboration &lt;br /&gt; (13.8 Gyr)
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093
|- style=&quot;font-size:small:small;background-color:#ffffff;{{Text color default}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{Text color default}};&quot; | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000
|}

===  Time Estimation Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 11: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]</text>
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AI-generated content is permitted where it follows good [[w:scholarly method|scholarly practice]]s, including:
* '''Edit summary''': The origin of contributed AI text is clearly indicated in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]] along with a publicly accessible link to the chatbot conversation (or a copy of the transcript) to maximise transparency.
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* '''Human revision''': AI text is revised and rewritten by the contributor (or originally human-written and improved using genAI)
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* '''Template''': Display the {{tl|AI-generated}} template at the top of pages, or below the description template for files, when the content contains substantial AI-generated material. 

Contributors wanting to use AI-generated content in ways not covered by this policy should seek community input by discussing at the [[Wikiversity:Colloquium|Colloquium]].

==See also==
;Meta
* [[meta:Artificial intelligence/Policies by project|Artificial intelligence/Policies by project]] (List)

;Wikimedia projects
* [[b:Wikibooks:Artificial intelligence|Wikibooks:Artificial intelligence]] (Policy)
* [[c:Commons:AI-generated media|Wikimedia Commons:AI-generated media]] (Policy)
* [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (Information page)
* [[w:Wikipedia:Writing articles with large language models|Writing articles with large language models]](Guideline)
* [[w:Wikipedia:Signs of AI writing|Wikipedia:Signs of AI writing]] (Detection)

;Wikiversity project guidelines
* [[Motivation and emotion/Assessment/Using generative AI|Using generative AI]] (Motivation and emotion)

==External links==
;Wiki Education Foundation
* [https://dashboard.wikiedu.org/training/students/generative-ai Using generative AI tools with Wikipedia] (Training module)

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AI-generated content is permitted where it follows good [[w:scholarly method|scholarly practice]]s, including:
* '''Edit summary''': The origin of contributed AI text is clearly indicated in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]] along with a publicly accessible link to the chatbot conversation (or a copy of the transcript) to maximise transparency.
* '''Verifiability''' / '''Citations''': AI text is [[Wikiversity:Verifiability|verified]] by the contributor. [[Wikiversity:Cite sources|Citations]] are [[w:Fact-checked|fact-checked]] for appropriateness and relevance by the contributor.
* '''Human revision''': AI text is revised and rewritten by the contributor (or originally human-written and improved using genAI)
* '''Copyright''': AI content must be compatible with Wikiversity's [[Wikiversity:Copyrights|licensing requirements]] (CC BY-SA).
* '''Template''': Display the {{tl|AI-generated}} template at the top of pages, or below the description template for files, when the content contains substantial AI-generated material. 

Contributors wanting to use AI-generated content in ways not covered by this policy should seek community input by discussing at the [[Wikiversity:Colloquium|Colloquium]].

==See also==
;Meta
* [[meta:Artificial intelligence/Policies by project|Artificial intelligence/Policies by project]] (List)

;Wikimedia projects
* [[b:Wikibooks:Artificial intelligence|Wikibooks:Artificial intelligence]] (Policy)
* [[c:Commons:AI-generated media|Wikimedia Commons:AI-generated media]] (Policy)
* [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (Information page)
* [[w:Wikipedia:Writing articles with large language models|Writing articles with large language models]](Guideline)
* [[w:Wikipedia:Signs of AI writing|Wikipedia:Signs of AI writing]] (Detection)

;Wikiversity project guidelines
* [[Motivation and emotion/Assessment/Using generative AI|Using generative AI]] (Motivation and emotion)

==External links==
;Wiki Education Foundation
* [https://dashboard.wikiedu.org/training/students/generative-ai Using generative AI tools with Wikipedia] (Training module)

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This policy specifies the requirements for contributing [[w:Generative artificial intelligence|AI-generated content]] (text and media) to [[Main page|Wikiversity]].

AI-generated content is permitted where it follows good [[w:scholarly method|scholarly practice]]s, including:
* '''Edit summary''': The origin of contributed AI text is clearly indicated in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]] along with a publicly accessible link to the chatbot conversation (or a copy of the transcript) to maximise transparency.
* '''Verifiability''' / '''Citations''': AI text is [[Wikiversity:Verifiability|verified]] by the contributor. [[Wikiversity:Cite sources|Citations]] are [[w:Fact-checked|fact-checked]] for appropriateness and relevance by the contributor.
* '''Human revision''': AI text is revised and rewritten by the contributor (or originally human-written and improved using genAI)
* '''Copyright''': AI content must be compatible with Wikiversity's [[Wikiversity:Copyrights|licensing requirements]] (CC BY-SA).
* '''Template''': Display the {{tl|AI-generated}} template at the top of pages, or below the description template for files, when the content contains substantial AI-generated material. 

Contributors wanting to use AI-generated content in ways not covered by this policy should seek community input by discussing at the [[Wikiversity:Colloquium|Colloquium]].

==See also==
;Meta
* [[meta:Artificial intelligence/Policies by project|Artificial intelligence/Policies by project]] (List)

;Wikimedia projects
* [[b:Wikibooks:Artificial intelligence|Wikibooks:Artificial intelligence]] (Policy)
* [[c:Commons:AI-generated media|Wikimedia Commons:AI-generated media]] (Policy)
* [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (Information page)
* [[w:Wikipedia:Writing articles with large language models|Writing articles with large language models]] (Guideline)
* [[w:Wikipedia:Signs of AI writing|Wikipedia:Signs of AI writing]] (Detection)

;Wikiversity project guidelines
* [[Motivation and emotion/Assessment/Using generative AI|Using generative AI]] (Motivation and emotion)

==External links==
;Wiki Education Foundation
* [https://dashboard.wikiedu.org/training/students/generative-ai Using generative AI tools with Wikipedia] (Training module)

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        <id>654933</id>
      </contributor>
      <origin>2831970</origin>
      <model>css</model>
      <format>text/css</format>
      <text bytes="2940" sha1="muq7r1pdn0ldk3ldvghuw2yhlg8bpwr" xml:space="preserve">/* Change font color to white 
body, #content, .mw-body-content {
    color: #00091A !important;
}*/

/* Change main text color to white 
body, #content, .mw-body-content {
    color: #00091A !important;
} */

/* Change link colors to ... was 4ebfbb .. and white before then 02ddc4 */
a:visited {
    color: #02ddc4 !important; 
}

/* Change link colors was 0289dd then 059dfc */
a {
    color: #057cfc !important;
}

/* Optional: Change hover color if desired */
a:hover {
    color: #86cafe !important; /* Light gray on hover, adjust as needed */
}

/* Reduce spacing between links in the sidebar */
#mw-panel .portal, #mw-panel .body, #mw-panel .vector-menu-content {
    margin: 0 !important; /* Remove outer margin if any */
    padding: 0 !important; /* Remove outer padding if any */
}

#mw-panel a, #mw-panel .vector-menu-content a {
    margin: 2px 0 !important; /* Adjust to control vertical space */
    padding: 2px 5px !important; /* Adjust padding */
    line-height: 1.2 !important; /* Adjust line height for tighter spacing */
}

/* trying Make the sidebar less wide 
.vector-column-start {
    width: 10em !important; 
}*/

.mw-enhanced-rc {
  font-size: 1.15em !important;
}

.mw-enhanced-rc-nested {
  font-size: 1.15em !important;
}
/* Uncreated page links (red links) */
a.new,
a.new:visited {
    color: #ff2222 !important;
}

/* Optional: distinct hover for uncreated links */
a.new:hover {
    color: #cc0000 !important;
}
/* Compact left sidebar */

/* @media screen and (min-width: 1000px) {
    .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
        column-gap: 1rem !important;
    }
} */

/* @media screen and (min-width: 1200px) {
    html.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
    }
} */

.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
    grid-template-columns: 10rem minmax(0, 1fr) !important;
}

html body .mw-parser-output a.external,
html body .mw-parser-output a.external:visited,
html body .mw-parser-output a.external *,
html body .mw-parser-output a.external:visited * {
    color: #02ddc4 !important;
    -webkit-text-fill-color: #02ddc4 !important;
    filter: none !important;
}

img[src=&quot;/static/images/mobile/copyright/wikiversity-wordmark-en.svg&quot;] {
    filter: invert(50%) !important;
}

.mw-logo-icon {
  filter: invert(70%) !important;
}

/* Invert colors for the MediaWiki/OOUI Toolbar */
.oo-ui-toolbar-bar,
.oo-ui-toolbar-tools,
.oo-ui-toolbar-popups,
.oo-ui-popupToolGroup-tools {
  filter: invert(100%) hue-rotate(180deg) !important;
  background-color: #ffffff !important; /* Ensures smooth background inversion */
}

/* Preserve media elements, images, or SVGs inside the toolbar if needed */
.oo-ui-toolbar-bar img,
.oo-ui-toolbar-bar video,
.oo-ui-toolbar-popups img {
  filter: invert(100%) hue-rotate(180deg) !important;
}</text>
      <sha1>muq7r1pdn0ldk3ldvghuw2yhlg8bpwr</sha1>
    </revision>
    <revision>
      <id>2831974</id>
      <parentid>2831970</parentid>
      <timestamp>2026-09-07T06:53:56Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
      </contributor>
      <origin>2831974</origin>
      <model>css</model>
      <format>text/css</format>
      <text bytes="2688" sha1="7okks82fm7f66gb6jaovroqbmatfho1" xml:space="preserve">/* Change font color to white 
body, #content, .mw-body-content {
    color: #00091A !important;
}*/

/* Change main text color to white 
body, #content, .mw-body-content {
    color: #00091A !important;
} */

/* Change link colors to ... was 4ebfbb .. and white before then 02ddc4 */
a:visited {
    color: #02ddc4 !important; 
}

/* Change link colors was 0289dd then 059dfc */
a {
    color: #057cfc !important;
}

/* Optional: Change hover color if desired */
a:hover {
    color: #86cafe !important; /* Light gray on hover, adjust as needed */
}

/* Reduce spacing between links in the sidebar */
#mw-panel .portal, #mw-panel .body, #mw-panel .vector-menu-content {
    margin: 0 !important; /* Remove outer margin if any */
    padding: 0 !important; /* Remove outer padding if any */
}

#mw-panel a, #mw-panel .vector-menu-content a {
    margin: 2px 0 !important; /* Adjust to control vertical space */
    padding: 2px 5px !important; /* Adjust padding */
    line-height: 1.2 !important; /* Adjust line height for tighter spacing */
}

/* trying Make the sidebar less wide 
.vector-column-start {
    width: 10em !important; 
}*/

.mw-enhanced-rc {
  font-size: 1.15em !important;
}

.mw-enhanced-rc-nested {
  font-size: 1.15em !important;
}
/* Uncreated page links (red links) */
a.new,
a.new:visited {
    color: #ff2222 !important;
}

/* Optional: distinct hover for uncreated links */
a.new:hover {
    color: #cc0000 !important;
}
/* Compact left sidebar */

/* @media screen and (min-width: 1000px) {
    .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
        column-gap: 1rem !important;
    }
} */

/* @media screen and (min-width: 1200px) {
    html.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
    }
} */

.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
    grid-template-columns: 10rem minmax(0, 1fr) !important;
}

html body .mw-parser-output a.external,
html body .mw-parser-output a.external:visited,
html body .mw-parser-output a.external *,
html body .mw-parser-output a.external:visited * {
    color: #02ddc4 !important;
    -webkit-text-fill-color: #02ddc4 !important;
    filter: none !important;
}

img[src=&quot;/static/images/mobile/copyright/wikiversity-wordmark-en.svg&quot;] {
    filter: invert(50%) !important;
}

.mw-logo-icon {
  filter: invert(70%) !important;
}

/* Target only the SVG icons/images within the OOUI toolbar */
.oo-ui-toolbar-bar .oo-ui-iconElement-icon,
.oo-ui-toolbar-popups .oo-ui-iconElement-icon,
.oo-ui-toolbar-bar img,
.oo-ui-toolbar-popups img {
  filter: invert(100%) !important;
}</text>
      <sha1>7okks82fm7f66gb6jaovroqbmatfho1</sha1>
    </revision>
    <revision>
      <id>2831976</id>
      <parentid>2831974</parentid>
      <timestamp>2026-09-07T06:56:32Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
      </contributor>
      <origin>2831976</origin>
      <model>css</model>
      <format>text/css</format>
      <text bytes="3002" sha1="as3qy7iy75gn65w65x9p8p8rc6swkms" xml:space="preserve">/* Change font color to white 
body, #content, .mw-body-content {
    color: #00091A !important;
}*/

/* Change main text color to white 
body, #content, .mw-body-content {
    color: #00091A !important;
} */

/* Change link colors to ... was 4ebfbb .. and white before then 02ddc4 */
a:visited {
    color: #02ddc4 !important; 
}

/* Change link colors was 0289dd then 059dfc */
a {
    color: #057cfc !important;
}

/* Optional: Change hover color if desired */
a:hover {
    color: #86cafe !important; /* Light gray on hover, adjust as needed */
}

/* Reduce spacing between links in the sidebar */
#mw-panel .portal, #mw-panel .body, #mw-panel .vector-menu-content {
    margin: 0 !important; /* Remove outer margin if any */
    padding: 0 !important; /* Remove outer padding if any */
}

#mw-panel a, #mw-panel .vector-menu-content a {
    margin: 2px 0 !important; /* Adjust to control vertical space */
    padding: 2px 5px !important; /* Adjust padding */
    line-height: 1.2 !important; /* Adjust line height for tighter spacing */
}

/* trying Make the sidebar less wide 
.vector-column-start {
    width: 10em !important; 
}*/

.mw-enhanced-rc {
  font-size: 1.15em !important;
}

.mw-enhanced-rc-nested {
  font-size: 1.15em !important;
}
/* Uncreated page links (red links) */
a.new,
a.new:visited {
    color: #ff2222 !important;
}

/* Optional: distinct hover for uncreated links */
a.new:hover {
    color: #cc0000 !important;
}
/* Compact left sidebar */

/* @media screen and (min-width: 1000px) {
    .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
        column-gap: 1rem !important;
    }
} */

/* @media screen and (min-width: 1200px) {
    html.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
    }
} */

.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
    grid-template-columns: 10rem minmax(0, 1fr) !important;
}

html body .mw-parser-output a.external,
html body .mw-parser-output a.external:visited,
html body .mw-parser-output a.external *,
html body .mw-parser-output a.external:visited * {
    color: #02ddc4 !important;
    -webkit-text-fill-color: #02ddc4 !important;
    filter: none !important;
}

img[src=&quot;/static/images/mobile/copyright/wikiversity-wordmark-en.svg&quot;] {
    filter: invert(50%) !important;
}

.mw-logo-icon {
  filter: invert(70%) !important;
}

/* Invert OOUI SVG icons and dropdown indicators for dark mode */
.oo-ui-iconElement-icon,
.oo-ui-indicatorElement-indicator {
  filter: invert(100%) !important;
}

/* Ensure the toolbar background remains transparent/dark */
.oo-ui-toolbar-bar,
.oo-ui-toolGroup-tools {
  background-color: transparent !important;
  border-color: #333333 !important;
}

/* Boost visibility for disabled toolbar buttons in dark themes */
.oo-ui-widget-disabled .oo-ui-iconElement-icon,
.oo-ui-widget-disabled .oo-ui-indicatorElement-indicator {
  opacity: 0.4 !important;
}</text>
      <sha1>as3qy7iy75gn65w65x9p8p8rc6swkms</sha1>
    </revision>
    <revision>
      <id>2831977</id>
      <parentid>2831976</parentid>
      <timestamp>2026-09-07T06:58:20Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
      </contributor>
      <origin>2831977</origin>
      <model>css</model>
      <format>text/css</format>
      <text bytes="2585" sha1="j4mwr1bhtek7eqm9uwljvcl09ynx93w" xml:space="preserve">/* Change font color to white 
body, #content, .mw-body-content {
    color: #00091A !important;
}*/

/* Change main text color to white 
body, #content, .mw-body-content {
    color: #00091A !important;
} */

/* Change link colors to ... was 4ebfbb .. and white before then 02ddc4 */
a:visited {
    color: #02ddc4 !important; 
}

/* Change link colors was 0289dd then 059dfc */
a {
    color: #057cfc !important;
}

/* Optional: Change hover color if desired */
a:hover {
    color: #86cafe !important; /* Light gray on hover, adjust as needed */
}

/* Reduce spacing between links in the sidebar */
#mw-panel .portal, #mw-panel .body, #mw-panel .vector-menu-content {
    margin: 0 !important; /* Remove outer margin if any */
    padding: 0 !important; /* Remove outer padding if any */
}

#mw-panel a, #mw-panel .vector-menu-content a {
    margin: 2px 0 !important; /* Adjust to control vertical space */
    padding: 2px 5px !important; /* Adjust padding */
    line-height: 1.2 !important; /* Adjust line height for tighter spacing */
}

/* trying Make the sidebar less wide 
.vector-column-start {
    width: 10em !important; 
}*/

.mw-enhanced-rc {
  font-size: 1.15em !important;
}

.mw-enhanced-rc-nested {
  font-size: 1.15em !important;
}
/* Uncreated page links (red links) */
a.new,
a.new:visited {
    color: #ff2222 !important;
}

/* Optional: distinct hover for uncreated links */
a.new:hover {
    color: #cc0000 !important;
}
/* Compact left sidebar */

/* @media screen and (min-width: 1000px) {
    .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
        column-gap: 1rem !important;
    }
} */

/* @media screen and (min-width: 1200px) {
    html.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
    }
} */

.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
    grid-template-columns: 10rem minmax(0, 1fr) !important;
}

html body .mw-parser-output a.external,
html body .mw-parser-output a.external:visited,
html body .mw-parser-output a.external *,
html body .mw-parser-output a.external:visited * {
    color: #02ddc4 !important;
    -webkit-text-fill-color: #02ddc4 !important;
    filter: none !important;
}

img[src=&quot;/static/images/mobile/copyright/wikiversity-wordmark-en.svg&quot;] {
    filter: invert(50%) !important;
}

.mw-logo-icon {
  filter: invert(70%) !important;
}

.oo-ui-toolbar-tools .oo-ui-iconElement-icon,
.oo-ui-toolbar-tools .oo-ui-indicatorElement-indicator {
  filter: invert(100%) !important;
}</text>
      <sha1>j4mwr1bhtek7eqm9uwljvcl09ynx93w</sha1>
    </revision>
    <revision>
      <id>2831978</id>
      <parentid>2831977</parentid>
      <timestamp>2026-09-07T06:59:47Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
      </contributor>
      <origin>2831978</origin>
      <model>css</model>
      <format>text/css</format>
      <text bytes="2724" sha1="lmeifqh4jhz71854790rjieshkohoap" xml:space="preserve">/* Change font color to white 
body, #content, .mw-body-content {
    color: #00091A !important;
}*/

/* Change main text color to white 
body, #content, .mw-body-content {
    color: #00091A !important;
} */

/* Change link colors to ... was 4ebfbb .. and white before then 02ddc4 */
a:visited {
    color: #02ddc4 !important; 
}

/* Change link colors was 0289dd then 059dfc */
a {
    color: #057cfc !important;
}

/* Optional: Change hover color if desired */
a:hover {
    color: #86cafe !important; /* Light gray on hover, adjust as needed */
}

/* Reduce spacing between links in the sidebar */
#mw-panel .portal, #mw-panel .body, #mw-panel .vector-menu-content {
    margin: 0 !important; /* Remove outer margin if any */
    padding: 0 !important; /* Remove outer padding if any */
}

#mw-panel a, #mw-panel .vector-menu-content a {
    margin: 2px 0 !important; /* Adjust to control vertical space */
    padding: 2px 5px !important; /* Adjust padding */
    line-height: 1.2 !important; /* Adjust line height for tighter spacing */
}

/* trying Make the sidebar less wide 
.vector-column-start {
    width: 10em !important; 
}*/

.mw-enhanced-rc {
  font-size: 1.15em !important;
}

.mw-enhanced-rc-nested {
  font-size: 1.15em !important;
}
/* Uncreated page links (red links) */
a.new,
a.new:visited {
    color: #ff2222 !important;
}

/* Optional: distinct hover for uncreated links */
a.new:hover {
    color: #cc0000 !important;
}
/* Compact left sidebar */

/* @media screen and (min-width: 1000px) {
    .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
        column-gap: 1rem !important;
    }
} */

/* @media screen and (min-width: 1200px) {
    html.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
    }
} */

.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
    grid-template-columns: 10rem minmax(0, 1fr) !important;
}

html body .mw-parser-output a.external,
html body .mw-parser-output a.external:visited,
html body .mw-parser-output a.external *,
html body .mw-parser-output a.external:visited * {
    color: #02ddc4 !important;
    -webkit-text-fill-color: #02ddc4 !important;
    filter: none !important;
}

img[src=&quot;/static/images/mobile/copyright/wikiversity-wordmark-en.svg&quot;] {
    filter: invert(50%) !important;
}

.mw-logo-icon {
  filter: invert(70%) !important;
}

/* Color OOUI toolbar icons green */
.oo-ui-toolbar-tools .oo-ui-iconElement-icon,
.oo-ui-toolbar-tools .oo-ui-indicatorElement-indicator {
  filter: none !important;
  background-color: #00ff66 !important; /* bright neon green, adjust hex to taste */
  opacity: 1 !important;
}</text>
      <sha1>lmeifqh4jhz71854790rjieshkohoap</sha1>
    </revision>
    <revision>
      <id>2831979</id>
      <parentid>2831978</parentid>
      <timestamp>2026-09-07T07:01:40Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
      </contributor>
      <origin>2831979</origin>
      <model>css</model>
      <format>text/css</format>
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body, #content, .mw-body-content {
    color: #00091A !important;
}*/

/* Change main text color to white 
body, #content, .mw-body-content {
    color: #00091A !important;
} */

/* Change link colors to ... was 4ebfbb .. and white before then 02ddc4 */
a:visited {
    color: #02ddc4 !important; 
}

/* Change link colors was 0289dd then 059dfc */
a {
    color: #057cfc !important;
}

/* Optional: Change hover color if desired */
a:hover {
    color: #86cafe !important; /* Light gray on hover, adjust as needed */
}

/* Reduce spacing between links in the sidebar */
#mw-panel .portal, #mw-panel .body, #mw-panel .vector-menu-content {
    margin: 0 !important; /* Remove outer margin if any */
    padding: 0 !important; /* Remove outer padding if any */
}

#mw-panel a, #mw-panel .vector-menu-content a {
    margin: 2px 0 !important; /* Adjust to control vertical space */
    padding: 2px 5px !important; /* Adjust padding */
    line-height: 1.2 !important; /* Adjust line height for tighter spacing */
}

/* trying Make the sidebar less wide 
.vector-column-start {
    width: 10em !important; 
}*/

.mw-enhanced-rc {
  font-size: 1.15em !important;
}

.mw-enhanced-rc-nested {
  font-size: 1.15em !important;
}
/* Uncreated page links (red links) */
a.new,
a.new:visited {
    color: #ff2222 !important;
}

/* Optional: distinct hover for uncreated links */
a.new:hover {
    color: #cc0000 !important;
}
/* Compact left sidebar */

/* @media screen and (min-width: 1000px) {
    .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
        column-gap: 1rem !important;
    }
} */

/* @media screen and (min-width: 1200px) {
    html.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
    }
} */

.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
    grid-template-columns: 10rem minmax(0, 1fr) !important;
}

html body .mw-parser-output a.external,
html body .mw-parser-output a.external:visited,
html body .mw-parser-output a.external *,
html body .mw-parser-output a.external:visited * {
    color: #02ddc4 !important;
    -webkit-text-fill-color: #02ddc4 !important;
    filter: none !important;
}

img[src=&quot;/static/images/mobile/copyright/wikiversity-wordmark-en.svg&quot;] {
    filter: invert(50%) !important;
}

.mw-logo-icon {
  filter: invert(70%) !important;
}

.oo-ui-toolbar-tools .oo-ui-iconElement-icon,
.oo-ui-toolbar-tools .oo-ui-indicatorElement-indicator {
  background-color: transparent !important;
  filter: brightness(0) saturate(100%) invert(80%) sepia(50%) saturate(2000%) hue-rotate(85deg) brightness(110%) !important;
}</text>
      <sha1>9s9n3bpqldmwp9qiq8ewp9ivu2ppqjl</sha1>
    </revision>
    <revision>
      <id>2831981</id>
      <parentid>2831979</parentid>
      <timestamp>2026-09-07T07:13:06Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
      </contributor>
      <origin>2831981</origin>
      <model>css</model>
      <format>text/css</format>
      <text bytes="3535" sha1="g7hnfa8wbjwpe5u3tqyuz060chusrn3" xml:space="preserve">/* Change font color to white 
body, #content, .mw-body-content {
    color: #00091A !important;
}*/

/* Change main text color to white 
body, #content, .mw-body-content {
    color: #00091A !important;
} */

/* Change link colors to ... was 4ebfbb .. and white before then 02ddc4 */
a:visited {
    color: #02ddc4 !important; 
}

/* Change link colors was 0289dd then 059dfc */
a {
    color: #057cfc !important;
}

/* Optional: Change hover color if desired */
a:hover {
    color: #86cafe !important; /* Light gray on hover, adjust as needed */
}

/* Reduce spacing between links in the sidebar */
#mw-panel .portal, #mw-panel .body, #mw-panel .vector-menu-content {
    margin: 0 !important; /* Remove outer margin if any */
    padding: 0 !important; /* Remove outer padding if any */
}

#mw-panel a, #mw-panel .vector-menu-content a {
    margin: 2px 0 !important; /* Adjust to control vertical space */
    padding: 2px 5px !important; /* Adjust padding */
    line-height: 1.2 !important; /* Adjust line height for tighter spacing */
}

/* trying Make the sidebar less wide 
.vector-column-start {
    width: 10em !important; 
}*/

.mw-enhanced-rc {
  font-size: 1.15em !important;
}

.mw-enhanced-rc-nested {
  font-size: 1.15em !important;
}
/* Uncreated page links (red links) */
a.new,
a.new:visited {
    color: #ff2222 !important;
}

/* Optional: distinct hover for uncreated links */
a.new:hover {
    color: #cc0000 !important;
}
/* Compact left sidebar */

/* @media screen and (min-width: 1000px) {
    .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
        column-gap: 1rem !important;
    }
} */

/* @media screen and (min-width: 1200px) {
    html.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
        grid-template-columns: 10rem minmax(0, 1fr) !important;
    }
} */

.vector-feature-main-menu-pinned-enabled .mw-page-container-inner {
    grid-template-columns: 10rem minmax(0, 1fr) !important;
}

html body .mw-parser-output a.external,
html body .mw-parser-output a.external:visited,
html body .mw-parser-output a.external *,
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    <title>Motivation and emotion/Book/2025/Cancer screening and emotion</title>
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      <text bytes="30684" sha1="3w2yt9n53at44oie7zu22qqqe7ewfsi" xml:space="preserve">{{title|Cancer screening and emotion:&lt;br&gt;How do emotions such as fear, anxiety, and relief influence cancer screening uptake?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=3}}
[[File:Diagram showing T stages of bowel cancer CRUK 276.svg|thumb|right|300px|Diagram of T-stages in bowel cancer]]

;Imagine ...

You are 23 years old and notice something unusual with your body. Weeks pass, but you ignore it. Many of your symptoms match those linked to [https://www.bowelcanceraustralia.org/bowel-cancer/early-onset/ Bowel Cancer] , but that seems impossible, right? You’re only 23. Fear and anxiety take over, and you delay seeing a doctor or undergoing a screening, convincing yourself that not knowing is safer than facing the possibility of bad news. By the time you seek help, your health has deteriorated rapidly. A screening confirms bowel cancer, but it’s already at stage four. The only treatment option left is [https://en.wikipedia.org/wiki/Palliative%20care palliative care].

Now, let’s rewind and change the scenario. You’re the same 23-year-old, noticing something is wrong. You still feel fear and anxiety but this time, those emotions push you to act. You want relief and don’t want to keep carrying the weight of uncertainty, so you seek answers to ease your mind. You see your doctor immediately, who recommends a cancer screening. The result is still bowel cancer, but it’s been caught early. Surgery successfully removes the tumor, and your survival chance is over 90%.

These two stories show how the same emotions fear and anxiety can either prevent action and lead to devastating outcomes or motivate action and lead to life-saving results.
{{RoundBoxBottom}}

Many people wonder, if early bowel cancer detection improves survival then why do so many people avoid screening? The truth is that cancer diagnosis isn’t just a medical decision as there are various emotions attached to it. Emotions such as fear, anxiety, embarrassment, and shame can delay individual's action to screen, while relief and reassurance drive others to screen. These emotions can make cancer screening feel overwhelming, even when it’s free or accessible. Understanding these challenges helps explain why bowel cancer screening participation rates remain lower than expected and shows both the barriers and opportunities for encouraging more people to take part in life-saving cancer screening (Ireland et al., 2022).

This chapter explores how emotions shape cancer screening. It begins by explaining what screening is and why early detection matters. It then examines barriers such as fear, anxiety, embarrassment, and stigma, alongside positive emotions like relief, hope, and empowerment. Public health campaigns are considered for their role in shaping behaviour. Finally, three psychological theories: the Health Belief Model, Protection Motivation Theory, and Theory of Planned Behaviour are applied to explain these emotional patterns and suggest strategies for improving participation.

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* How do fear and anxiety influence decisions about cancer screening uptake?
* What role does relief-seeking play in motivating individuals to undergo screening?
* In what ways can anxiety act as both a motivator and a barrier to screening participation?
* Why are some individuals more likely than others to seek medical answers promptly?
{{RoundBoxBottom}}

==What is cancer screening?==
'''Screening vs diagnosis'''

Cancer screening checks for disease in people without symptoms, aiming to detect cancer early when treatment is most effective (Better Health Channel). In Australia, national programs exist for breast, cervical, bowel, and lung cancer. Screening differs from diagnosis, as screening looks for possible disease while diagnosis confirms cancer through further investigation.

'''Importance of early detection'''

According to the Australian Government Department of Health (2025), cancer often develops slowly and may remain symptomless until later stages, when treatment is less effective. Early detection allows intervention before spread, improving outcomes. The AIHW (2022) reports that breast cancer mortality among women aged 50–74 dropped from 74 deaths per 100,000 in 1991 to 41 in 2020 since BreastScreen Australia began, highlighting the life-saving potential of screening. It is important to note however Australia only represents a small portion of the human population. 

'''Examples of screening programs'''

Australia offers national screening for breast, cervical, bowel, and lung cancer. Other high-income countries provide similar programs, with some differences. The UK screens for breast cancer every three years rather than two, while some US groups recommend starting at 40. Australia uses HPV testing for cervical screening, whereas many countries still use Pap smears. Bowel screening here is via mailed FIT kits, but in Germany and the US colonoscopy is common. Lung cancer screening is not routine in Australia, while the US and Canada recommend low-dose CT scans for high-risk groups. Germany and Austria also offer skin cancer screening (Ebell et al., 2018).

'''Survival rates'''

Early detection greatly improves survival across cancers. For lung cancer, five-year survival for stage 1 is ~64% (Cancer Treatment Centers of America, n.d.). For breast cancer, survival is close to 100% at stage 1 but only 32% at stage 4 (National Breast Cancer Foundation, n.d.). Cervical cancer survival is 91% when detected early versus 19% for distant stage (National Cancer Institute, n.d.). In bowel cancer, the AIHW (2025) reported 7,265 diagnoses and 1,793 deaths in Australians aged 50–74 during 2024, showing the impact of early detection.

[[File:Lead time bias.svg|Lead_time_bias]]

Figure 1. Comparison of cancer detected through screening versus symptoms, showing how earlier detection can increase perceived survival time. This earlier diagnosis may reduce anxiety and provide relief, but fear of the result can also deter some individuals from screening.

{| class=&quot;wikitable&quot;
|+ '''Table 1. Survival rates by cancer type and stage of detection'''
! Cancer type
! Early detection survival rate
! Late detection survival rate
|-
| Lung (Stage 1)
| 64%
| Much lower in later stages
|-
| Breast
| 100% (Stage 1)
| 32% (Stage 4)
|-
| Cervical
| 91% (early stage)
| 19% (distant stage)
|-
| Bowel (Australia, 2024)
| 7,265 diagnosed (50–74)
| 1,793 deaths (50–74)
|}

==Emotional barriers to screening==
If survival is so much higher with early detection{{f}}, what stops people from screening? Often, it comes down to emotion. Have you ever avoided something because you feared the result? “Ignorance is bliss” captures the mindset many adopt. Avoiding stressful situations can feel easier than confronting them.{{f}}

Despite the life-saving potential of screening, many avoid it due to emotional barriers. Fear, anxiety, embarrassment, and stigma can outweigh rational awareness of benefits. These barriers are shaped not only by individual psychology but also by broader cultural and social influences.{{f}}

'''Fear of diagnosis'''

Avoiding threats is human nature. Furedi (2007) argues a “culture of fear” encourages avoidance. In cancer screening, fear of bad news can create denial and delay. For many{{f}}, seeking help makes the issue feel more real, while ignorance feels safer.
The Health Belief Model (HBM) suggests fear heightens severity and susceptibility but can also raise barriers{{f}}. A relatable example is procrastinating on an assignment: the stress of confronting it outweighs the relief of finishing it. Similarly, fear of {{what}} results can outweigh benefits of early detection{{f}}.
Fear increases risk perception (“I could have cancer”) but often leads to avoidance (“I don’t want to know”). Many postpone mammograms despite knowing the risks, convincing themselves not knowing is preferable{{f}}.
According to the HBM, behaviour occurs when perceived benefits outweigh barriers (Conner &amp; Norman, 2015). In screening, fear raises awareness but also amplifies distress{{f}}. Thus, fear can motivate or paralyse, depending on threat perception and coping ability.

'''Anxiety about pain, discomfort, or embarrassment'''

Biardeau et al. (2017) found that 59.4% of patients reported pain during cystoscopy, It also found that 58.4% reported anxiety before cystoscopy, and 21.8% experienced embarrassment. These findings highlight how discomfort can deter participation. In cancer screening, pain plus embarrassment from intimate procedures (Pap smears, HPV tests, colonoscopy, and FIT kits) are strong deterrents.
HBM explains this as barriers outweighing percieved benefits, while PMT suggests that high threat plus low coping appraisal leads to avoidance. Biardeau et al. (2017) also found younger patients and those given detailed information sometimes reported higher anxiety, showing that distress can stem from expectations as much as the procedure itself.

{{RoundBoxTop|theme=3}}

Emma, 55, avoided her free bowel kit, calling it “gross” and “awkward.” Despite family history of cancer, months later it remained unopened. Embarrassment outweighed her knowledge of benefits, showing how discomfort blocks participation.

[[File:Bowel cancer Home Test Kit Instructions and test tubes in Australia, 2022.jpg|thumb|right|300px|Home bowel cancer screening kit and instructions]]

{{RoundBoxBottom}}

'''Stigma and shame'''

Stigma and shame, shaped by culture or religion, also deter screening{{f}}. Ahmed et al. (2022) found Caribbean women avoided breast and cervical screening due to modesty or stigma. Screenings often involve “taboo” body parts, amplifying embarrassment.
Stigma intersects with identity gender, age, religion and in some communities is wrongly linked to sexual activity or “bad morals.” Though inaccurate, this belief deters participation.
The TPB explains this through subjective norms: when communities see screening as shameful, this norm can override knowledge of benefits. HBM also frames shame as a barrier.

{{RoundBoxTop|theme=3}}

A migrant woman avoids a Pap smear because only male GPs bulk bill in her area. Reinforced by her husband’s views, stigma and financial barriers outweigh her friends’ reassurance, so she avoids screening.

{{RoundBoxBottom}}

==Positive emotions and motivation to screen==
'''Relief-seeking''' 

On the positive side, many find relief in cancer screening and use it to reduce uncertainty. A normal result provides peace of mind, often motivating repeat screening and encouraging others to participate. Relief can therefore create a positive cycle{{f}}.
However, relief also carries risks. Some interpret a clear result as proof they are safe, delaying follow-ups{{f}}. Marteau (1990) explained that while screening reduces psychological burden, it can also mask ongoing risk if results are misinterpreted.
HBM suggests relief increases perceived benefits, but false reassurance reduces susceptibility. PMT suggests relief lowers threat appraisal if not paired with strong efficacy messages.{{f}}

'''Hope, empowerment, and reassurance'''

Hope, empowerment, and reassurance shape screening. Feeling in control of one’s health reduces anxiety and increases uptake{{f}}. Autonomy, like accessing screening without referral, strengthens agency. Hope can also turn fear into action. For some, fear motivates, and seeking reassurance through screening reduces uncertainty.{{f}}
Health campaigns can foster empowerment by emphasising choice. Davison and Degner (1997) found participation {{vague}} reinforced feelings of control. Similarly, Affendi et al. (2018) showed self-efficacy predicts health behaviour. Confidence consistently predicts preventive action, aligning with HBM (self-efficacy) and TPB (perceived control).

'''Public Health Campaigns and Framing''' 

Public health campaigns strongly influence screening. Positive framing that fosters hope and empowerment is often more effective than fear appeals. Fear can motivate, but only when people feel able to respond otherwise, it drives avoidance (PMT).{{f}}
Gressard et al. (2017) found smokers initially knew little about lung cancer screening but showed interest when informed. However, fatalistic beliefs, distrust, and confusion limited uptake. This shows campaigns must avoid fuelling misconceptions and instead provide clear, supportive messages. Done well, they can transform fear into motivation and encourage participation.

Relief, hope, and empowerment especially when reinforced by positive campaigns can strongly encourage screening. Yet these same emotions, if misdirected, may create false reassurance. Effective interventions must balance reassurance with accurate communication about ongoing risk.

==Theoretical perspectives==
'''Health belief model (HBM)'''

[https://www.ncbi.nlm.nih.gov/books/NBK606120/ The Health Belief Model (HBM)] has long been used to explain health behaviours. Developed in the 1950s by psychologists in the United States Public Health Service (USPHS), it aimed to understand the low uptake of preventative measures such as screening (Alyafei &amp; Easton-Carr, 2024). Today, it remains a widely applied framework for health-related decision-making.
Its core constructs are:

•	'''Perceived susceptibility''' – belief about personal cancer risk.
•	'''Perceived severity''' – seriousness of cancer if undetected.
•	'''Perceived benefits''' – value of early detection (e.g., survival rates).
•	'''Perceived barriers''' – deterrents like pain, embarrassment, or stigma.
•	'''Self-efficacy''' – confidence in completing screening.
•	'''Cues to action''' – triggers such as reminders, GP advice, or campaigns.

Fear and anxiety interact with these constructs. Fear can heighten susceptibility and severity, while anxiety may raise barriers through discomfort or embarrassment. In contrast, reassurance strengthens perceived benefits and builds self-efficacy. For example, a woman may weigh her fear of discomfort (barrier) against the peace of mind she expects from knowing her results (benefit).{{f}}
Critics argue{{f}} HBM is overly cognitive and neglects emotions and social influences, giving it less of a “human feel.” While it cannot fully predict behaviour, it remains valuable for understanding how people approach cancer screening.

'''Protection motivation theory (PMT)'''

[https://open.ncl.ac.uk/theories/10/protection-motivation-theory/ Protection Motivation Theory (PMT)], proposed by Rogers (1975), explains health behaviour through two appraisals: threat appraisal (severity, vulnerability) and coping appraisal (response efficacy, self-efficacy, costs).
Core constructs include:

•	'''Perceived severity''' – seriousness of the threat (e.g., cancer).
•	'''Perceived vulnerability''' – likelihood of being affected.
•	'''Response efficacy''' – belief screening reduces risk.
•	'''Self-efficacy''' – confidence in completing screening.
•	'''Response costs''' – barriers such as pain, time, or embarrassment.

Fear and anxiety are central. Ruiter et al. (2001) showed fear appeals work only when coping appraisal is high. If people believe screening is effective and achievable, fear can motivate action. When coping is low, fear leads to denial, avoidance, or minimisation.
A classic example is the “Grim Reaper” campaign (1987), a confronting HIV/AIDS ad in Australia. It grabbed attention but highlighted the limits of fear appeals, people who didn’t see themselves at risk ignored it, while others felt stigmatised or more afraid. From a PMT perspective, the ad created high threat appraisal but little coping appraisal, showing fear alone isn’t enough.
Reviews suggest coping appraisal predicts behaviour more strongly than threat appraisal. Effective interventions must therefore combine realistic risk information with empowering, confidence-building messages.

'''Theory of planned behaviour (TPB)'''

[https://doi.org/10.5964/ejop.v16i3.3107 The Theory of Planned Behaviour (TPB)] explains behaviour through attitudes (beliefs about outcomes), subjective norms (social pressure), and perceived control (confidence and resources, similar to self-efficacy) (Ajzen, 1991). Together these shape intention, which predicts behaviour.
Emotions influence each factor. Fear and anxiety can create negative attitudes and avoidance, while hope and relief encourage positive attitudes. Stigma and shame act through norms, especially in communities where screening is seen as “taboo.” Empowerment strengthens control, lowering anxiety and supporting follow-through. For example, a woman may fear pain (attitude), feel cultural stigma (norms), but be reassured by an accessible home FIT kit (control).
Evidence shows TPB is useful but limited. It predicts about 19–27% of health behaviour (McEachan et al., 2011), leaving an “intention–behaviour gap.” Critics argue it overlooks habits and emotions (Sniehotta et al., 2014). Recent work shows norms interact with attitudes and control (La Barbera &amp; Ajzen, 2020, 2023).&lt;!-- 2 years? also i think you missed this one and the Ajzen one above in your reference list --&gt; Applications highlight its value: programs have improved screening attitudes, norms, and control when based on TPB (Huang et al., 2012).
Overall, TPB highlights how attitudes, norms, and control interact with emotions in screening choices.

'''Integration &amp; comparison'''

{| class=&quot;wikitable&quot;
|+ '''Table 2. Comparison of psychological theories and their relevance to cancer screening'''
! Model
! Key Constructs
! Role of Emotions
! Relevance to Screening
|-
| Health Belief Model (HBM)
| Perceived susceptibility, severity, benefits, barriers, self-efficacy, cues to action
| Fear increases susceptibility and severity; anxiety can heighten barriers; relief strengthens perceived benefits
| Explains why people weigh risks/benefits differently, leading some to avoid and others to attend screening
|-
| Protection Motivation Theory (PMT)
| Threat appraisal (severity, vulnerability) and coping appraisal (response efficacy, self-efficacy, costs)
| Fear appeals motivate only when coping appraisal is high; low efficacy leads to avoidance or denial
| Shows why fear-based campaigns succeed or fail, depending on whether people believe they can act effectively
|-
| Theory of Planned Behaviour (TPB)
| Attitudes, subjective norms, perceived behavioural control
| Emotions shape attitudes (fear vs relief), norms (stigma/shame), and control (empowerment/self-efficacy)
| Captures the role of cultural stigma, empowerment, and social pressure in screening choices
|}

Taken together, these models provide a fuller picture of how emotions shape cancer screening behaviour. HBM highlights how people weigh personal risk against barriers. PMT explains why fear appeals succeed or backfire depending on whether people feel capable of coping. TPB adds the influence of social norms and perceived control. Together, they show that fear, anxiety, and relief can either motivate or deter action, depending on context.

==Strategies for addressing emotional barriers==
'''Clear information &amp; normalisation''' 

Clear, simple explanations reduce uncertainty and anxiety about screening. When people know what will happen and what results mean, the process feels less threatening. Framing screening as routine, like a dental check-up, helps normalise it and reduce stigma. By combining clarity with normalisation, screening becomes less of a fearful unknown and more of a standard habit that supports health.{{f}}

'''Peer/community support''' 

Family, friends, and cultural groups strongly influence screening decisions. Seeing others screen, or hearing trusted stories, makes participation feel more acceptable. Shared experiences reduce embarrassment and help reshape social norms. Community programs that encourage open discussion, especially in groups where stigma is strong, show how collective support can turn screening from a private worry into a supported action.{{f}}

'''Positive campaign messaging''' 

Campaigns framed around hope, empowerment, and reassurance often work better than fear appeals. Fear motivates only if people feel capable of acting; otherwise, it creates avoidance. Positive framing builds confidence and shows screening as a step toward peace of mind and control. By balancing risk information with encouragement, campaigns can transform screening into an empowering choice, not just a fearful obligation.{{f}}

[[File:Doctor talking with a patient.jpg|thumb|right|300px]]

'''Accessibility &amp; ease''' 

Screening is more likely when it feels simple and convenient. Home kits, like the FIT test, allow privacy and control. Reminders texts, letters, GP prompts act as cues to action that keep it on people’s radar. Reducing costs, travel, and waiting times makes following through easier. When practical barriers are lowered, emotional ones like fear or embarrassment have less power to stop people.{{f}}

'''Case study/example program''' 

Australia’s cervical cancer campaigns highlight how well-designed strategies work. By promoting HPV testing as safe, routine, and empowering, while making it widely accessible, participation improved. Pairing positive framing with practical supports reduced stigma and encouraged women to see screening as a normal part of protecting their health.

== Quiz ==
&lt;quiz display=simple shuffle=none&gt;

{Which of the following is an example of an emotional barrier to cancer screening?
|type=&quot;()&quot;}
- Enjoyment of medical procedures
+ Fear of receiving a cancer diagnosis
- Confidence in early detection programs

{In the Health Belief Model, which factor refers to a person’s belief in their ability to take action?
|type=&quot;()&quot;}
+ Self-efficacy
- Perceived severity
- Social norms

{Relief after receiving a clear screening result can influence behaviour by:
|type=&quot;()&quot;}
+ Encouraging people to attend future screenings
- Making people less likely to trust doctors
- Reducing the accuracy of screening tests

{According to Protection Motivation Theory, fear will most likely motivate action when:
|type=&quot;()&quot;}
+ The person believes the recommended action will work and they can do it
- The person avoids thinking about the threat
- The threat is vague and the action feels difficult

{Which emotion can act as both a motivator and a barrier to cancer screening?
|type=&quot;()&quot;}
+ Anxiety
- Happiness
- Anger

&lt;/quiz&gt;

==Conclusion==
Fear and anxiety are double-edged, {{g}} they can motivate action but also create {{what}} avoidance. Relief, hope, and empowerment more consistently encourage {{what}} participation, especially when reinforced by supportive campaigns and accessible services.
Screening behaviour is shaped by these emotions in clear ways. Fear and anxiety influence uptake by either pushing people to avoid or to act. Relief motivates screening by reducing uncertainty, though it risks false reassurance. Anxiety can serve as both a barrier and a motivator, depending on coping resources. Finally, some individuals act more quickly because confidence, social support, or cultural norms make screening feel both acceptable and achievable.
Theories help explain these dynamics. The Health Belief Model highlights perceptions of risk, benefits, and barriers. Protection Motivation Theory shows how fear appeals only succeed when paired with strong coping efficacy. The Theory of Planned Behaviour captures the social side, where norms and perceived control shape intention. Together, they provide a fuller view of how emotions drive or deter screening.

'''Key Takeaway''' 
To improve screening uptake, campaigns must not just minimise fear but reframe emotions as sources of reassurance, empowerment, and motivation for action.

==See also==
[[Motivation and emotion/Book/2025/Pain avoidance motivation|Pain avoidance motivation: How does avoidance of physical pain shape motivated action?]]

[[Motivation and emotion/Book/2025/Positive emotion and approach motivation|The motivational power of positivity:How do positive emotional states enhance goal pursuit and achievement Behaviours?]]

[[Motivation and emotion/Book/2025/Coping with anticipatory stress|Coping with anticipatory stress: What strategies are effective for managing stress about upcoming events?]]

==References==
{{Hanging indent|1=

Ahmed, N. U., Brewster, C., Chang-Martinez, C., Thomas-DeVlugt, L., &amp; Rodriguez, A. (2022). Dignity, shame, stigma, or ignorance in avoidance of breast and cervical cancer screenings among women of Caribbean descent. Open Journal of Social Sciences, 10(5), 496–508. https://doi.org/10.4236/jss.2022.105032

Ajzen, I. (2019). The theory of planned behavior: Frequently asked questions. Europe’s Journal of Psychology, 16(3), 1–10. https://doi.org/10.5964/ejop.v16i3.3107

Alyafei, A., &amp; Easton-Carr, R. (2024). The health belief model of behavior change. In StatPearls. StatPearls Publishing. https://www.ncbi.nlm.nih.gov/books/NBK606120/

Australian Government Department of Health. (2025). Screening for cancer. https://www.health.gov.au/topics/cancer/screening-for-cancer

Australian Institute of Health and Welfare. (2022). BreastScreen Australia monitoring report 2022: Summary. https://www.aihw.gov.au/reports/cancer-screening/breastscreen-australia-monitoring-report-2022/summary

Australian Institute of Health and Welfare. (2025). National Bowel Cancer Screening Program monitoring report 2025: Summary. https://www.aihw.gov.au/reports/cancer-screening/nbcsp-monitoring-2025/contents/summary

Biardeau, X., Lam, O., Ba, V., Campeau, L., &amp; Corcos, J. (2017). Prospective evaluation of anxiety, pain, and embarrassment associated with cystoscopy and urodynamic testing in clinical practice. Canadian Urological Association Journal, 11(3–4), 104. https://doi.org/10.5489/cuaj.4127

Cancer Treatment Centers of America. (n.d.). Stage 1 lung cancer. https://www.cancercenter.com/cancer-types/lung-cancer/stages/stage-1-lung-cancer

Conner, M., &amp; Norman, P. (Eds.). (2015). Predicting and changing health behaviour: Research and practice with social cognition models (3rd ed.). Open University Press.

Davison, B. J., &amp; Degner, L. F. (1997). Empowerment of men newly diagnosed with prostate cancer. Cancer Nursing, 20(3), 187–196. https://journals.lww.com/cancernursingonline/fulltext/1997/06000/empowerment_of_men_newly_diagnosed_with_prostate.4.aspx

Ebell, M. H., Thai, T. N., &amp; Royalty, K. J. (2018). Cancer screening recommendations: An international comparison of high income countries. Public Health Reviews, 39, 7. https://doi.org/10.1186/s40985-018-0080-0

Furedi, F. (2007). The only thing we have to fear is the ‘culture of fear’ itself: How human thought and action are being stifled by a regime of uncertainty. Spiked. https://www.researchgate.net/publication/238082918

Furedi, F. (2018). How fear works: Culture of fear in the twenty-first century. Bloomsbury Publishing. https://books.google.com.au/books?id=P35ADwAAQBAJ

Gressard, L., DeGroff, A. S., &amp; Richards, T. B. (2017). A qualitative analysis of smokers’ perceptions about lung cancer screening. BMC Public Health, 17, 589. https://doi.org/10.1186/s12889-017-4496-0

Huang, C. M., Chien, L. Y., Cheng, C. F., &amp; Guo, J. L. (2012). Integrating life skills into a theory-based drug-use prevention program: Effectiveness among junior high students in Taiwan. Journal of School Health, 82(7), 328–335. https://doi.org/10.1111/j.1746-1561.2012.00706.x

Isa, A., Muhamad, N. A., Mustapha, N., Abdul Mutalip, M. H., Mohd Royali, M. S., Baharin, M. F., &amp; Sm, S. (2017). Association between self-efficacy and health behaviour in disease control: A systematic review. Global Journal of Health Science, 10(1), 18. https://doi.org/10.5539/gjhs.v10n1p18

Ireland, K., Hendrie, D., Ledwith, T., &amp; Singh, A. (2022). Strategies to address barriers and improve bowel cancer screening participation in Indigenous populations, particularly in rural and remote communities: A scoping review. Health Promotion Journal of Australia, 34(2). https://doi.org/10.1002/hpja.672

La Barbera, F., &amp; Ajzen, I. (2020). Control interactions in the theory of planned behavior: Rethinking the role of subjective norm. Europe’s Journal of Psychology, 16(3), 401–417. https://doi.org/10.5964/ejop.v16i3.2056

Marteau, T. M. (1990). Screening in practice: Reducing the psychological costs. BMJ: British Medical Journal, 301(6742), 26–28. https://doi.org/10.1136/bmj.301.6742.26

McEachan, R. R. C., Conner, M., Taylor, N. J., &amp; Lawton, R. J. (2011). Prospective prediction of health-related behaviours with the theory of planned behaviour: A meta-analysis. Health Psychology Review, 5(2), 97–144. https://doi.org/10.1080/17437199.2010.521684

National Breast Cancer Foundation. (n.d.). Breast cancer statistics. https://nbcf.org.au/about-breast-cancer/breast-cancer-stats/

National Cancer Institute. (n.d.). Cervical cancer—Cancer stat facts. https://www.cancer.gov/types/cervical/survival
National Cancer Institute. (n.d.). What screening statistics mean. https://www.cancer.gov/aboutcancer/screening/research/what-screening-statistics-mean

Open Lab. (n.d.). Protection motivation theory. Newcastle University. https://open.ncl.ac.uk/theories/10/protection-motivation-theory/

Ruiter, R. A. C., Abraham, C., &amp; Kok, G. (2001). Scary warnings and rational precautions: A review of the psychology of fear appeals. Psychology &amp; Health, 16(6), 613–630. https://doi.org/10.1080/08870440108405863

Sniehotta, F. F., Presseau, J., &amp; Araújo-Soares, V. (2014). Time to retire the theory of planned behaviour. Health Psychology Review, 8(1), 1–7. https://doi.org/10.1080/17437199.2013.869710

Zeliadt, S. B., Heffner, J. L., Sayre, G., et al. (2015). Attitudes and perceptions about smoking cessation in the context of lung cancer screening. JAMA Internal Medicine, 175(9), 1530–1537. https://doi.org/10.1001/jamainternmed.2015.3558

}}

==External links==
•	[https://www.betterhealth.vic.gov.au/health/conditionsandtreatments/cancer-screening Better Health Channel] – Cancer screening (Better Health Channel)
•	[https://www.cancer.org.au/cancer-information/causes-and-prevention/early-detection-and-screening Cancer Council Australia] – Early detection and screening (Cancer Council Australia)
•	[https://www.cancer.gov/about-cancer/screening/research/what-screening-statistics-mean National Cancer Institute] – What screening statistics mean (National Cancer Institute)

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      <comment>/* Coping With Occupations Violence */ {{ic|A better link is probably [[w:Social support|social support]] or possibly one of the chapters listed here: [[:Category:Motivation and emotion/Book/Social support]]}}</comment>
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__TOC__
== Overview ==
{{RoundBoxTop|theme=3}}
[[File:NounProject Abuse (38107).svg|thumb|'''Figure 1:''' an example of someone being verbally abused.]]

;Scenario

Emma is a 21-year-old person of colour who works in aged care. She has been working at a residential facility for the last six month. During a busy evening shift, a resident becomes frustrated about delay in care and begins shouting at Emma in front of other stuff and residents. The resident calls Emma names, incompetent, racial slurs, points fingers at her, and threatens to make s formal complaint to have her fired. Although the situation is eventually de-escalated by her supervisor, Emma feels shaken for the rest of her shift.  

{{RoundBoxBottom}}

* What is the definition of occupational violence (OV), why is it an important workplace and psychological issue.
* The relationship between OV and:
# emotional wellbeing 
# psychological distress
# motivation 
# job satisfaction
# coping 

* This chapter looks at both the employee experience and the organisational responses. 

{{RoundBoxTop}}

;Focus questions

{{ic|Add bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}}

What is OV, what form can it take and what are the risk factors? {{ic|This is too many questions in one; revise}}

what are the emotional and and psychological impacts of OV?

how can employee cope with experiences of OV.{{g}}

How can organisations prefect{{g}} OV and support employees who are affected?

{{RoundBoxBottom}}

== Understanding Occupational Violence ==
{{ic|Embed links to related Wikipedia articles or book chapters}}

* What is occupational violence{{g}}

# Defining OV according to search such as...
# Difference between very obvious OV and micro OV (e.g. micro violence)
# OV can be a single incident or repeated behaviour

* Forms of occupational violence

# verbal violence: threats, verbal abuse and intimidation
# Bullying and harassment: repeated harmful behaviour, such as physical assaults, aggression an intimidating behaviour
# Discrimination and exclusion: unfair treatment, favouritism, and social isolation
# Sexual violence/harassment: unwanted touches or advances, non-consensual sexual behaviour or conduct.

* What are the risks of occupational violence{{g}}

# OV can result from multiple individual, social and organisational factors{{vague}}.
# Workplace culture can either increase or reduce risks.
# Some employees can be more vulnerable to discrimination and harassment because of race, sick colour, cultural background, sexual orientation, gender and poor management.

== Emotional and Psychological Impacts of OV ==

{{ic|citations needed to theory and research}}

* Emotional impacts: employees who are victims of OV may experience emotional responses such as:

# Fear and anxiety,
# Anger and frustration
# Sadness
# Humiliation
# Shame
# Emotional exhaustion

* Mental well-being: victims of OV may also experience:

# Increased psychological distress
# Increased stress
# Feeling of helplessness and reduces psychological safety
# Long-term psychological effects following repeated exposure.

* Motivation and job satisfaction:

# Reduced motivation
# Reduced workplace engagement
# Lower job satisfaction
# Reduced sense of belonging

== Coping With Occupations Violence ==

{{ic|citations needed to theory and research}}

* Individual coping strategies and [[social support]] {{ic|A better link is probably [[w:Social support|social support]] or possibly one of the chapters listed here: [[:Category:Motivation and emotion/Book/Social support]]}}

# Problem-focused coping
# Emotional-focused coping such as seeking professional help outside of work.
# Seeking support from friends, family and trusted colleagues
# Developing strategies to manage workplace stress
# If available, accessing an employee assistance program

* Reporting and organisation support

* Reporting incidents to supervisors/management
* Workplace counselling and support services

== Preventing OV and Supporting Employees ==
{{ic|citations needed to theory and research}}

* Preventions

# Clear workplace policies and procedures
# Staff straining 
# Risk assessment 
# Appropriate supervision and staffing 
# Clear expectations around acceptable behaviour and explicitly outlined punishment for unacceptable behaviour. 
# Effective reporting systems. 

* Supporting employees  

# immediate support following an incident and preventing repeated exposure 
# counselling or employee assistance program for those affected. 
# Follow-up with effected employees and provide appropriate workplace adjustments

== Conclusion ==

* Summering{{sp}} the relationship between: 

# Occupational violence 
# Emotional violence
# Psychological wellbeing 
# Motivation 
# Job satisfaction 
# Coping 

* The importance of organisational responsibility. 
* There is need for prevention, support and effective coping strategies. 

== See also ==

# [[Motivation and emotion/Book/2024/Occupational violence, emotion, and coping for educators|Occupational Violence]] (Book chapter, 2024)
# [[wikipedia:Workplace_violence|Workplace Violence]] (Wikipedia)
# [[Motivation and emotion/Book/2019/Social support and emotion|Social support and emotion]] (Book chapter, 2019)

== References ==
{{Hanging indent|1=

Alameddine, M., Mourad, Y., &amp; Dimassi, H. (2015). A national study on nurses’ exposure to occupational violence in lebanon: Prevalence, consequences and associated factors. ''PLOS ONE'', ''10''(9), e0137105. https://doi.org/10.1371/journal.pone.0137105

Bakes‐Denman, L., Mansfield, Y., &amp; Meehan, T. (2020). Supporting mental health staff following exposure to occupational violence – staff perceptions of ‘peer’ support. ''International Journal of Mental Health Nursing'', ''30''(1). https://doi.org/10.1111/inm.12767

Greys González-González, Darling Rebolledo-Ríos, Ximena Osorio-Spuler, Rudner, N., &amp; Constanza Peña-Barra. (2025). Violence against nurses: Personal and institutional coping strategies—A scoping review. ''Behavioral Sciences'', ''15''(9), 1166–1166. https://doi.org/10.3390/bs15091166

Pariona-Cabrera, P., Bartram, T., Cavanagh, J., Halvorsen, B., Shao, B., &amp; Yang, F. (2023). The effects of workplace violence on the job stress of health care workers: Buffering effects of wellbeing HRM practices. ''International Journal of Human Resource Management'', ''35''(9), 1–27. https://doi.org/10.1080/09585192.2023.2237876

Pihl-Thingvad, J., Elklit, A., Brandt, L. L. P., &amp; Andersen, L. L. (2019). Occupational violence and PTSD-symptoms. ''Journal of Occupational &amp; Environmental Medicine'', ''61''(7), 572–583. [https://www-jstor-org.ezproxy.canberra.edu.au/stable/48510401 https://doi.org/10.1097/jom.0000000000001612]

Zhou, B., Marchand, A., &amp; Guay, S. (2017). I see so i feel: Coping with workplace violence among victims and witnesses. ''Work'', ''57''(1), 125–135. [[doi:10.3233/WOR-172538|https://doi.org/10.3233/wor-172538]]

}}

== External links ==

* [https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC4565636/ A National Study on Nurses’ Exposure to Occupational Violence in Lebanon: Prevalence, Consequences and Associated Factors] (2015)
* [https://www-jstor-org.ezproxy.canberra.edu.au/stable/48510401?seq=1 Occupational Violence and PTSD-Symptoms: A Prospective Study on the Indirect Effects of Violence Through Time Pressure and Nontraumatic Strains in the Occupational Context] (2019)

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== &lt;big&gt;Overview&lt;/big&gt; ==
{{robelbox|theme=7|title=Case study: Nikil|iconwidth=55px|icon=Search-icon-white-background.png}}

[[File:Case_study_magnifying_glass.png|left|340px|Looking closer at the case study! ]]

Nikil is a 21-year-old medical student in India who is a high-achieving student. He is the first in his family to attend a university. His family emphasizes that his success will bring honor and pride to his parents and community. He feels a great need to excel to repay his parents’ sacrifices and make use of his opportunity to gain higher socio-economic status. 

He often studies late into the night and skips meals, not because becoming a doctor is something he enjoys, but because he is afraid of disappointment and failure. He often ruminates heavily on his mistakes, compares his grades to others and has anxiety before exams. He often feels he must excel to be accepted. 

He began to find it hard to maintain a 97% average which he had throughout high school into university. Nikhil's current lifestyle left him feeling empty and fatigued, with decreased interest and creativity. Additionally, he overcriticized himself for not being perfect and it affected how he felt about himself. 

As he talked with his parents about how he was feeling, they helped him reflect on why he wanted to become a doctor, which helped him realise that this was exactly what he wanted to pursue. During his hospital rotation, he realised that his ability to empathise, think logically, and make a lasting impact on his client gave him immense satisfaction. He realised this is truly his career path. Once he realised this,  his studies became much more enjoyable; he was able to persist, committed, and develop healthy coping strategies, ultimately helping him to graduate successfully.

This case study shows Nikil is someone who has grit, particularly through his persistence and effort. However, support from his family and his own personal interest in becoming a doctor helped reinvigorate his passion and commitment to pursuing this career. {{RoundBoxBottom}}

Students around the world face new challenges, setbacks, disappointments, and difficulties every day. These setbacks can be especially challenging during the early educational years, when career success is often dependent on academic performance. A recent example of a setback faced by students everywhere is the [[COVID-19|Coronavirus (Covid-19) pandemic]] and the emergence of [[wikipedia:Artificial_intelligence_in_education|AI learning tools.]] This caused students, teachers and scientists around the globe to persevere through systemic-level disruptions by adapting and developing innovative ways to connect, learn, improve, and retain knowledge to facilitate academic achievement. Some students found these challenges especially difficult leading them to disengage and drop out, but others like Nikhil (who we will discuss) persisted and eventually found success. This begs the question: is academic achievement based solely on your [[Intelligence Quotient|IQ]] score, talent, and [[Psychological resilience|resilience]] or does it also require some good fashioned hardwork? This exact question led author and psychologist [https://angeladuckworth.com/ Angela Duckworth] to popularise the term &quot;[[wikipedia:Grit_(personality_trait)|grit]]&quot;, suggesting that persistent interest and sustained effort can pave the way for success rather than talent or skills alone.

{{RoundBoxTop|theme=15}}
'''Focus questions:''' 
* What is grit?
* How does grit influence academic achievement?
* What psychological theories explain grit?
* What does the empirical evidence say about grit? Any critiques?
* Can grit be fostered and if so, how can it be applied?

'''Reflection:'''

'''Think of a time when you faced a major academic or life challenge. What factors or setbacks helped or hindered your ability to continue during the challenging situation?'''
{{RoundBoxBottom}}

Throughout the chapter, referring back to this case study of Nikil below to help consolidate your learning.

{{RoundBoxTop|theme=1}}
[[File:Crystal Clear app ktip.svg|left|20px|]]  
'''Key concepts:'''
*Grit
*Academic Achievement
* Persistence
* Interest
*Intelligence
*Consciousness
*Self-regulation
{{RoundBoxBottom}}

== &lt;big&gt;Grit&lt;/big&gt; ==
[[File:Marathon runner.png|thumb|289x289px|A middle-aged man showing his perseverance and passion towards achieving his goal of winning a marathon.]]

Grit is often regarded as a conceptual topic without a definitive definition or measure, in order to quantify, measure and understand what laypeople and scientists regard grit to be lets look at a few sources which ain to define grit.

=== &lt;u&gt;&lt;big&gt;Defining grit&lt;/big&gt;&lt;/u&gt; ===
The word &quot;grit&quot; originates from the German word ''&quot;[https://www.collinsdictionary.com/dictionary/german-english/griess Griess],&quot;'' which according to the [[mwod:grit|Merriam-Webster dictionary]], means &quot;grit&quot;.

Furthermore the dictionary defintion for a person with grit is explained as two qualities: firmness of mind or spirit and unyielding courage in the face of hardship or danger. Otherwise, as a person with courage and is adapt to grinding, setbacks, or hardships through the firmness of their mind. 

Although this is the dictionary definition, the psychological definition is slightly different. [[wikipedia:Angela_Duckworth|Angela Lee Duckworth]] and colleagues popularised &quot;grit,&quot; to be simply defined as a personality trait of an individual who [https://dictionary.cambridge.org/dictionary/english/persevere\ perseveres] and has a [https://dictionary.cambridge.org/dictionary/english/passion passion] for their long-term [[Goal setting|goals]] (Lam &amp; Zhou, 2019; Lee, Kim &amp; Shin, 2025; Tugabirwe &amp; Rukundo, 2024; Jiang et al., 2019 )

[[File:Girl climbing mountain.png|thumb|256x256px|A girl through passion and perseverance, is climbing difficult and challenging mountain to achieve her long-term goal of climbing to the summit{{ic|how does this relate to academic achievement?}}]]

&lt;blockquote&gt;
''&quot;Grit is passion and perseverance for long-term goals.''

''One way to think about grit is to consider what grit isn’t. Grit isn’t talent.'' 

''Grit isn’t luck. Grit isn’t how intensely, for the moment, you want something.''

''Instead, grit is about having what some researchers call an &quot;ultimate concern”–a goal you care about so much that it organizes and gives meaning to almost everything you do. And grit is holding steadfast to that goal. Even when you fall down. Even when you screw up. Even when progress toward that goal is halting or slow.''

''Talent and luck matter to success. But talent and luck are no guarantee of grit. And in the very long run, I think grit may matter as least as much, if not more.&quot;''  

[https://angeladuckworth.com/qa/#faq-125 ''━'' ''Angela Duckworth'']&lt;/blockquote&gt;

The definition used by the American Psychological Association is,

&lt;blockquote&gt;''&quot;n. a personality trait characterized by perseverance and passion for achieving long-term goals. Grit entails working strenuously to overcome challenges and maintaining effort and interest over time despite failures, adversities, and plateaus in progress. Recent studies suggest this trait may be more relevant than intelligence in determining a person’s high achievement. For example, grit may be particularly important to accomplishing an especially complex task when there is a strong temptation to give up altogether.&quot;''

[https://dictionary.apa.org/grit ''━'' ''APA 2018'']&lt;/blockquote&gt;

=== &lt;u&gt;&lt;big&gt;Characterising grit&lt;/big&gt;&lt;/u&gt; ===
[[File:Elderly + award.png|thumb|283x283px|A person, despite age {{g}} achieved an award through their grit.]]

Grit is characterised as a hierarchical, non-cognitive dispositional or personality trait which means, an enduring characteristic and behaviours employed by the individual to uniquely adjust to life across different situations (APA, 2018; Barbouta, Barbouta &amp; Kotrotsiou, 2020; Clark, Dorio, Eldridge, Malecki &amp; Demaray, 2020; Clark &amp; Malecki, 2019; He et al., 2021; Helal &amp; Hassan 2025; Lam &amp; Zhou, 2019; Lee &amp; Sohn, 2017; Singh &amp; Chukkali, 2021).   

A gritty individual works tirelessly towards challenges, maintains effort, interest and stamina over extended periods despite failures, advesities and plateus (He et al., 2021; Lee, Kim &amp; Shin, 2025; Tugabirwe &amp; Rukundo, 2024). Grit is a malleable construct which can be learned and developed through coping skills and self-cultivation, social support, training, experiences and practicing endurance similar to how you would develop your muscles in the gym (Duckworth et al., 2007; Harpaz, Vaizman &amp; Yaffe, 2024; Singh &amp; Chukkali, 2021; Jiang et al., 2019 ). Specifically, Grit encompasses goal-directness, persistence, passion and commitment.  

According to a 2020 study there is a moderate positive correlation between grit and older participants (Barbouta, Barbouta &amp; Kotrotsiou, 2020). Perhaps, due to the increase time to experience different situations and circumstances could be accredited to why older people tend to have higher grit levels. This could also be a contributing reason as to why postgraduate students in the same study had a higher overall mean in academic score of 78.2 (SD of 10.0) compared to the undergraduate students (overall mean of 72.9, SD of 9.6) (Barbouta, Barbouta &amp; Kotrotsiou, 2020).  

==== &lt;big&gt;2 Facet of grit&lt;/big&gt; ====
[[File:Mollusk, shells and fossils prize winner.png|thumb|224x224px|A fossil hunter holding their winning ammonite fossil earned through his lifelong passion and commitment to finding, and refurbishing pieces of fossil history.]]Perseverance of effort (PE) is the ability to sustain energy and towards long term goals involving high mental stamina by overcoming adversities and distractions through sustained effort to accomplish a goal (Clark &amp; Malecki, 2019; Lee, Kim &amp; Shin, 2025; Jiang et al., 2019 ; Wolters &amp; Hussain, 2015).

Oftentimes, PE is compared to qualities of [[wikipedia:Conscientiousness|conscientiousness]] from the big five personality theory because of the overlapping themes of being responsible, diligent and goal-oriented (O’Connor &amp; Paunonen, 2007).

Consistency of interest (CI) is ability to adhere and maintain focus to goals which the idividual is passionate and accredits meaning and purpose towards for long periods to sustain their ultimate final long term goal( Clark &amp; Malecki, 2019; Lee, Kim &amp; Shin, 2025; Jiang et al., 2019 ). For example, an ultimate final goal could be completing an undergraduate degree with a high distinction.

=== &lt;big&gt;&lt;u&gt;Measures of grit&lt;/u&gt;&lt;/big&gt; ===
There are multiple scales which have been used to quanitify grit. These incluse the Original Grit scale, Short Grit scale, Triarchic model of grit scale, Multi-dimensional grit scale and the Academic grit scale.

===== Original grit scale (Grit-O) =====
[[File:Psychological Survey.png|thumb|292x292px|Psychological self-report survey measure ]]

As the name suggests this is the original first developed grit scale by Duckworth and collegues, asking demographic questions, the individual's level of academic performance satisfaction compared to their actual academic score (Barbouta, Barbouta &amp; Kotrotsiou, 2020). Nowadays this scale is commonly used.

===== Short grit scale (Grit-S) =====
The Short Grit Scale is an improved, model fit and overall a better measurement tool inspired by the Grit-O. This is currently the most used grit scale in wester and individualist countries. It is a twelve item  two factor hierachical scale maximized by the particular items which were most correlated in accordance with factor analysis.

===== Triarchic model of grit scale =====
The triachic model of grit by Datu and collegues in 2017 expanded upon the 2 factor hierachical structure and introduced the facet of situational adaptability, which gain acclaim.

===== Multi-dimensional scale of grit =====
With the growing need for cultural inclusion and generalisability with research the Multi-Dimensional Scale of Grit (MDSG) was designed by Singh and Chukkali in 2021 to allow the concept of grit to traverse the global scale and be more accessible to non-western and individualistic communities (Singh &amp; Chukkali, 2021). This 12 item Likert scale measure, particularly designed to be applicable to collectivist, religious and eastern countries where through religious and ancient literature have identifies similar elements such as “gumption&quot; and “titiksha” from Hindu holy books; yang in Taoist principles; “dukkha” from Buddhist literature and the Islamic perspectives’ emphasis on strength of character, constancy, steadfastness, work devotion determination (Singh &amp; Chukkali, 2021). Overall the scale tends to have good internal consistency, reliability, criterion and divergent validity, but more studies need to conducted to corroborate its generalizability with the wider community due to the gender, age and university humanity and social science focus (Singh &amp; Chukkali, 2021).

==== Academic grit scale (AGS) ====
Finally, the concept of domain-specific grit was explore through the academic grit scale. This scale has 10 items focusing on determination, resilience, and focus in the pursuit of challenging long-term goals within education (Clark &amp; Malecki, 2019).

[[File:Glossary icon.jpg|centre|93x93px|'''&lt;u&gt;Glossary&lt;/u&gt;''' ]]

'''Table 1.''' The 2 x 7 on the definition and theory adjasent to grit x key theoretical terms.
{| class=&quot;wikitable sortable&quot;
|+&lt;big&gt;Key terms often associated with grit:&lt;/big&gt;
!Key term
!Definition
!Theory
|-
|[https://dictionary.apa.org/lockes-theory-of-goal-setting Long-term goal oriented:]
|

* ''a'' ''person' who focused on the process of establishing specific, time-based behavior targets that are measurable, achievable, and realistic. Goal setting is effective only if the individual's are aware of what needs to be accomplished and accept the goal themselves  and believe in their attainability.''
|According to Locke theory of goal setting, specifies specific, challenging, sub-goals are better for performance to regulate energy expenditure, improve persistence, skill development with timely feedback on progression are pivotal to attaining long term goals, such as academic achievement.
Also in accordance with self-determination theory a individual is moer{{sp}} likely to achieve their long term goals if he motivation behind their drive is intrinsic to satidy their psychological needs for autonomy, competence and relatedness (Deci &amp; Ryan, 2000).
Furthermore, expectancy-value theory suggests a persons effort, persistence and choices are determined by the person self-efficacy to attain goal (Deci &amp; Ryan, 2000). 

This allows the individual to foster a growth mindset where their belief in their abilities help them to self-regulate, make informed choices and dedicate themselves to their goal (Deci &amp; Ryan, 2000).
|-
|[https://dictionary.apa.org/passion Passionate]:
|
*''an intense, driving, or overwhelming feeling or conviction. Passion is often contrasted with emotion, in that passion affects a person unwillingly.''
*''a strong enthusiasm for or devotion to an activity, object, concept, or the like.''   
|According to self-determination theory, there are two types of passion: harmonious which is the healthy form compared to the maladaptive form called obsessive (Deci &amp; Ryan, 2000). 
Harmonius{{sp}} passion allows for flexibility and immersive enagement{{sp}}  whereas obsessive passion can be rigid and impersonal Deci &amp; Ryan, 2000).
|-
|[https://dictionary.apa.org/persistence Perseverance/Persistence:] 
[https://dictionary.apa.org/effortfulness Effortfulness]
|
* ''Continuance or repetition of a particular behavior, process, or activity despite cessation of the initiating stimulus.''
* ''The quality or state of maintaining a course of action or keeping at a task and finishing it despite the obstacles (such as opposition or discouragement) or the effort involved.''
* ''exertion that demands attentional and other cognitive resources: a feature of many psychological tasks that can be judged reliably by participants.''
|According to Cloninger’s seven factor psychobiological model of personality expand further on persistence as the tendency to continue a task or activity regardless of frustration, dissatisfaction, or fatigue.
According to SDT the psychological needs to be competence, related and sutonomous can increase the volition of the peron to strive in their activities (Deci &amp; Ryan, 2000).
|-
|[https://psycnet.apa.org/doiLanding?doi=10.1037/edu0000699 Academic achievement]
|
* ''any identifiable success in the areas of scholarship or disciplined study.''
* ''in educational psychology, a level of proficiency in scholastic work in general or in a specific skill, such as arithmetic or reading. Evidence of future academic achievement is usually based on the results of standardized ability tests and assessment of performance by a teacher or other supervisor.''
|Achievement goal theory talks about there are 4 major categories of goals: approach or avoidant mastery of skills and understanding and approach or avoidant performance or competive{{sPP and peer validation based goals. the avoidant types of goals tend to have negative affect, drive and self-worth outcomes (Harwood &amp; Thrower, 2020).
|-
|[https://dictionary.apa.org/interest Interest:]
|
* ''an attitude characterized by a need or desire to give selective attention to something that is significant to the individual, such as an activity, goal, or research area.''
|
|-
|[https://dictionary.apa.org/resilience Resilience:]
|
*''the process and outcome of successfully adapting to difficult or challenging life experiences, especially through mental, emotional, and behavioral flexibility and adjustment to external and internal demands.''
* ''A number of factors contribute to how well people adapt to adversities, predominant among them (a) the ways in which individuals view and engage with the world, (b) the availability and quality of social resources, and (c) specific coping strategies. Psychological research demonstrates that the resources and skills associated with more positive adaptation (i.e., greater resilience) can be cultivated and practiced.''
|
|-
|[https://dictionary.apa.org/intelligence Intelligence]
|
* ''the ability to derive information, learn from experience, adapt to the environment, understand, and correctly utilize thought and reason.'' 
|
|}

== Grit &amp; academic achievement: ==
The association between grit and academic achievement using the measure discussed earlier try to empircally understand and predict success in academic settings.

==== &lt;big&gt;Foundational studies&lt;/big&gt; ====
Foundational studies by Duckworth and colleagues tried to predict success through academic engagement, self-efficacy, educational graduation, retention rates and Grade point averages over time (Wen et al., 2019 cited from Duckworth et al., 2007). Throughout the years two types of grit was identified.

===== General Grit =====
* An overarching dispositional trait where attitudes and behaviors stay consistent across different contexts (Clark &amp; Malecki, 2019).

===== Domain-specific Grit =====
* Grit-based attitudes and behaviors are only displayed when in a certain contexts or condition (Clark &amp; Malecki, 2019).
* For example, Academic grit is when a person shows grit during educational pursuits.

Overall domain-specific grit has shown a better predictor of academic achievement than general grit. (Clark &amp; Malecki, 2019).

==== &lt;big&gt;Recent studies&lt;/big&gt; ====
Although foundational studies highlighted a high correlation between grit and academic achievement, especially amongst primary to college students, the current data suggest differently.{{f}}

[[File:Contradicting research data plots.png|thumb|240x240px|Contradicting research data plots from different research articles]]

A 2019 meta-analysis of suggested the correlation between grit and academic achievement was small but significant with the mean coefficient of 0.16 (95% CI: 0.14, 0.18 Z=15.95, p &lt; .001) and mean average correlation of overall grit is 0.17 (Lam &amp; Zhou, 2019). Similarly a more recent 2022 meta-analysis suggested the overall grit level to academic achievement was weak to moderate (weighted correlation = 0.19). They also found, the effect size is similar to conscientiousness (r = .19) and subjective well-being (r = .16). The total estimated average weighted average of grit overall was 0.24 (95% CI: 0.213, 0.261) (Lam &amp; Zhou, 2019).

In accordance with longitudinal studies, they seem to support a reciprocal relationship of PE and academic achievement being mutually reinforcing to each other (Wen et al., 2019). This means PE predicts achievement and prior achievement contributes to PE’s development. Overall, PE has been discovered to be a better predictor for academic success than CI especially in standardised measures like the gpa and similar school grades systems (Lam &amp; Zhou, 2022). Many studies consistently show PE has higher correlations and reforcing relationship (r=0.21; R&lt;sup&gt;2&lt;/sup&gt;=2.3%; r= 0.508; r=0.425) to academic success whereas, CI has a weaker predictive and correlation to academic success (Clark, Dorio, Eldridge, Malecki &amp; Demaray, 2020; Clark &amp; Malecki, 2019; Lam &amp; Zhou, 2022; Jiang et al., 2019 ).

Also, a two-factor hierarchical structure in the AGS scale validation studies with samples from high-achieving adolescents, the national spelling bee child and adolescent finalists, Ivy League undergraduates, and West Point cadets showed to have strong internal consistency, test-retest reliability, consensual validity and high predictive validity (Clark &amp; Malecki, 2019). There is also evidence to suggest grit is a better predictor of academic achievement in kindergarden to year 12 students (r=0.17) comparatively to university students (r=0.14)(Lam &amp; Zhou, 2019; Lam &amp; Zhou, 2022).

==== &lt;big&gt;Critiques:&lt;/big&gt; ====
{| class=&quot;wikitable&quot;
|+Table 2. The 2 x 16 on the Strengths and Weaknesses of Grit x Theory Efficacy
!
!Strengths
!Limitations
!Sources
|-
|'''Scope'''
|Domain-specific
|Overlaps with Consciousness
|Clark, &amp; Malecki, 2019; Jiang, et al., 2019). 
----(Clark, &amp; Malecki, 2019; Lam &amp; Zhao, 2022; Martoyo &amp; Lindawati, 2023; Rimfeld, Kovas, Dale &amp; Plomin, 2016).
|-
|'''Predictive power'''
|Validity (incremental, can build upon itself)
|Weak Consistency of Interest
|(Clark, &amp; Malecki, 2019; Harpaz, Vaizman &amp; Yaffe, 2024). 
----(Abubakar, et al., 2021; Jiang, et al., 2019; Lam &amp; Zhao 2022)
|-
|'''New perspective'''
|Non cognitive focus (included cultural backgrounds)
|Method issues with reliability and correlation
|(Jiang, et al., 2019; Singh &amp; Chukkali, 2021)
----(Clark, &amp; Malecki, 2019; Clark, Dorio, Eldridge, Malecki, &amp; Demaray, 2020; Jiang, et al., 2019; Lam &amp; Zhou, 2019; Tannoubi et al., 2023).
|}

All of these contradictions and critiques makes it difficult to determine whether grit is the sole influencer of academic success as once believed.

== Alternative academic success influences ==
As an alternative to thinking grit is sole contributing factors to academic success, let us, think more broadly. 

===== Cognitive Ability (IQ) =====
Grit is distinct from cognitive ability/IQ. Grit has been shown{{f}} to outperform IQ as a predictor of academic achievement in samples of high-achieving students.

Although grit is a better predictor of academic success in high achieving samples; student samples of lower end of the IQ spectrum, from poor socioeconomic status has suggested different results (Lee &amp; Sohn, 2017; Segal &amp; Kalfon-Hakhmigari, 2025; Tugabirwe &amp; Rukundo, 2024). In a 2021 study looking at disadvantaged rural students, grit had an insignificant effect on school achievement for those with an IQ of 0.85 (Jiang, et al., 2019).

A 2025 study suggested, grit could moderately influence cognitive abilities towards high educational achievement. It said stem high school student with high levels of cognitive abilities were statistically significant (β = 0.14, SE = 0.03, t(640) = 5.08, p &lt; 0.001, 95% CI [0.09, 0.19]) suggesting 34.58% of variance in STEM (physics, computer science, achievement interaction between cognition and grit to strongly predict highschool success (Segal &amp; Kalfon-Hakhmigari, 2025){{rewrite}}. Surprisingly, this study suggested a greater association between CI (r = 0.10 to 0.15 (p &lt; 0.05) as opposed to PE (r = 0.08, p = 0.046) as previous studies suggested helping them to bridge gaps which would otherwise affect performance (Segal &amp; Kalfon-Hakhmigari, 2025). Another study looking at Indonesian students and GPA also found similar results (1.4% - 6.3%) and grit scores seemed to increase as they progressed through school from  first to second to third year  (Martoyo &amp; Lindawati, 2023). As well as, students with extremely high levels of cognition showed slightly lower levels of grit compared to student with high cognition (Segal &amp; Kalfon-Hakhmigari, 2025){{g}}.

===== Deliberate practice =====
Deliberate practice ($r = .19, p &lt; .01$) and conscientiousness ($r = .21, p &lt; .01$) in korean college students correlated positively with GPA, this highlighted the grit did not have a direct effect but mediatory one to achievement in academics (Lee &amp; Sohn, 2017).

===== Self-regulated learning =====
Self-regulated learning suggests a consistent association of PE with self-efficacy, cognitive, metacognitive, motivational, time and study environment management strategies, and procrastination and CI with study environment management strategies, and procrastination, with only PE showing any improvement to academic achievement through regression analysis (Wolters &amp; Hussain, 2015).

===== Research motivation =====
Research motivation based on their intelligence (r = 0.72, p &lt; 0.01) in postgraduate student was correlated with grit (r = 0.27, p &lt; 0.01) and academic achievement (r = 0.26, p &lt; 0.01). Although research motivation was the bigger predictor with an r value of 0.84 (p &lt; 0.01), making it a critical mediatory pathway.

===== Coping and self-cultivation skills =====
Academic grit and coping strategies which included self-efficacy, autonomic Help-Seeking Orientation and self-cultivation or personal growth characteristics in Anglo-Saxon (0.37) participant, explained 24-26% of variance (Harpaz, Vaizman &amp; Yaffe, 2024).

===== Social Support =====
Social support plays a critical role by enhancing correlation between grit and academic achievement. The first study did a regression analysis on korean student and receiving parental support (r= 0.267, p&lt; 0.01), friend support (r= 0.140, p&lt; 0.01), teacher support (r= 0.197, p&lt; 0.01), and grit (r= 0.367, p&lt; 0.01), as being correlated with academics (Lee, Kim &amp; Shin, 2025).

== Conclusion ==
Grit's relationship with academic achievement has evolved over time. Foundational studies identified two types of grit: general grit, a consistent trait across contexts, and domain-specific grit, which manifests in specific areas like academics. Although early research linked grit strongly to academic success among students, recent meta-analyses have shown only a small correlation, with prior academic performance being a better predictor than grit. Critically, grit overlaps with cognitive ability. For disadvantaged students, grit has shown limited impact. Moreover, factors such as cognitive ability, deliberate practice, self-regulated learning, research motivation, and social support emerge as significant influences on academic achievement, indicating that grit alone may not be the sole determinant of success. 

Gaps within the research are the subjective of causality and the mechanisms for grit as a concept has led to various methodological limitations and reduce the reliance on self-reports which are subject to a multitude of biases. The overall data lack generalisability at time due to the hyper restricted populations of the sample derived for the study, with studies focusing on western and students with high cognitive abilities. Other factors like burnout, career aspirations, non-educational responsibility, cognitive load, resource accessability weren't explored as well. 

Areas for future research should focus more on longitudinal and experimental studies testing and for confounding variable and overall clarifying the concept, its effect, inclusions and exclusion to have overall more replicable and accurate studies. Also, exploring the malleability of grit, its cross-cultural, gender, socioeconomic influences. As well as, looking at areas outside of academic achievement, such as sports and work.

Although the research on grit and academic achievement is conflicting and confusing, developing grit is a fantastic was to practice stamina and can be applicable to all facets of life{{rewrite}}.

{{robelbox|theme=11|title=Test yourself!|iconwidth=55px|icon=Search-icon-white-background.png}} 
&lt;quiz display=simple&gt;
{What is Grit?}
- Cognitive trait
+ non-cognitive trait
+ Perseverance of Effort and Consistency of Interest
- Adaptability and Commitment

{How does grit influence academic achievement?}
+ persist through setbacks and sustain effort toward goals
- try and persist until faced with a difficult challenge
- use brute force or rote learning to facilitate learning
+ self-regulated learning strategies or deliberate practice

{What psychological theories explain grit?}
+ Social-determination theory and Locke theory of goal setting
- Adaptability 2-factor theory and Interest &amp; persistence theory
+ Cloninger’s seven-factor psychobiological model of personality, Achievement goal theory
- Intellectual modification and Fixed Mindset theory

{What does the empirical evidence say about grit? Any critiques?}
- Grit is the sole predictor of academic success
+ The research on grit is confusing regarding it being the predictor of academic success

{Can grit be fostered?}
- Grit is viewed as a malleable which can be assisted using independant and fixed mindset
+ Grit is viewed as a malleable which can be assisted using coping strategies, growth mindset and support
&lt;/quiz&gt;{{RoundBoxBottom}}

{{robelbox|theme=11|title=Answers!|iconwidth=55px|icon=Search-icon-white-background.png}} 
What is Grit?
* non-cognitive trait
* Perseverance of Effort and Consistency of Interest

How does grit influence academic achievement?
* persist through setbacks and sustain effort toward goals
* self-regulated learning strategies or deliberate practice

What psychological theories explain grit?
* Social-determination theory and Locke theory of goal setting
* Cloninger’s seven-factor psychobiological model of personality, Achievement goal theory

What does the empirical evidence say about grit? Any critiques?
* The research on grit is confusing regarding it being the predictor of academic success

Can grit be fostered?
* Grit is viewed as a malleable which can be assisted using coping strategies, growth mindset and support{{RoundBoxBottom}}

== See also ==
* [[Motivation and emotion/Book/2021/Academic buoyancy|Academic buoyancy]] (Wikiversity)
* [[Motivation and emotion/Book/2021/Academic resilience|Academic resilience]] (Wikiversity)
* [[Motivation and emotion/Book/2020/Conscientiousness and motivation|Conscientiousness and motivation]] (Wikiversity)
* [[Motivation and emotion/Book/2020/Deliberate practice and mastery|Deliberate practice and mastery]] (Wikiversity)
* [[Motivation and emotion/Book/2019/Expectancy-value theory of achievement motivation|Expectancy-value theory of achievement motivation]] (Wikiversity)
* [[Motivation and emotion/Book/2020/Feedback and motivation in sport|Feedback and motivation in sport]] (Wikiversity)
* [[Motivation and emotion/Book/2024/Grit and conscientiousness|Grit and conscientiousness]]  (Wikiversity)
* [[Motivation and emotion/Book/2018/Growth mindset development|Growth mindset development]] (Wikiversity)
* [[Motivation and emotion/Book/2017/Hardiness|Hardiness]] (Wikiversity)
* [[Motivation and emotion/Book/2016/Long-term goal achievement|Long-term goal achievement]]  (Wikiversity)
* [[Motivation and emotion/Book/2021/Mental toughness|Mental toughness]] (Wikiversity)
* [[Motivation and emotion/Book/Chapters by year|Motivation and emotion book chapters]] (Wikiversity)
* [[Motivation and emotion/Book/2021/Perseverance|Perseverance]] (Wikiversity)
* [[Motivation and emotion/Book/2022/Self-efficacy and academic achievement|Self-efficacy and academic achievement]] (Wikiversity)
* [[Motivation and emotion/Book/2015/Willpower|Willpower]] (Wikiversity)

== References ==
{{Hanging indent|1=

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Barbouta, A., Barbouta, C., &amp; Kotrotsiou, S. (2020). Growth Mindset and Grit: How Do University Students' Mindsets and Grit Affect their Academic Achievement? International journal of caring sciences, 13(1), 654-664. https://www.internationaljournalofcaringsciences.org/docs/72.%20kotrotsiou%206-2-2020.pdf

Clark, K. N., &amp; Malecki, C. K. (2019). Academic Grit Scale: Psychometric properties and associations with achievement and life satisfaction. Journal of School Psychology, 72, 49-66. https://doi.org/10.1016/j.jsp.2018.12.001

Clark, K. N., Dorio, N. B., Eldridge, M. A., Malecki, C. K., &amp; Demaray, M. K. (2020). Adolescent academic achievement: A model of social support and grit. Psychology in the schools, 57(2), 204-221. https://doi.org/10.1002/pits.22318

Deci, E., &amp; Ryan, R. (2000). ''Self-Determination Theory - an overview {{!}} ScienceDirect Topics.'' Sciencedirect.com. https://www.sciencedirect.com/topics/social-sciences/self-determination-theory

Hamdy Helal, M., &amp; Abohashem Hassan, E. (2025). Research motivation as a mediating variable between system intelligence, academic grit, and academic achievement among postgraduate students, faculty of education, Zagazig University. BMC Psychology, 13(1), 70-78. https://doi.org/10.1186/s40359-025-02374-z

Harpaz, G., Vaizman, T., &amp; Yaffe, Y. (2024). University students' academic grit and academic achievements predicted by subjective well‐being, coping resources, and self‐cultivation characteristics. Higher education quarterly, 78(1), 192-211. https://doi.org/10.1111/hequ.12455

Harwood, C., &amp; Thrower, S. (2020). Achievement Goal Theory - an overview {{!}} ScienceDirect Topics. Www.sciencedirect.com. https://www.sciencedirect.com/topics/psychology/achievement-goal-theory

He, X., Wang, H., Chang, F., Dill, S.-E., Liu, H., Tang, B., &amp; Shi, Y. (2021). IQ, grit, and academic achievement: Evidence from rural China. International journal of educational development, 80, 102306. https://doi.org/10.1016/j.ijedudev.2020.102306

Jiang, W., Xiao, Z., Liu, Y., Guo, K., Jiang, J., &amp; Du, X. (2019). Reciprocal relations between grit and academic achievement: A longitudinal study. Learning and Individual Differences, 71, 13-22. https://doi.org/10.1016/j.lindif.2019.02.004

Lam, K. K. L., &amp; Zhou, M. (2019). Examining the relationship between grit and academic achievement within K‐12 and higher education: A systematic review. Psychology in the schools, 56(10), 1654-1686. https://doi.org/10.1002/pits.22302

Lam, K. K. L., &amp; Zhou, M. (2022). Grit and Academic Achievement: A Comparative Cross-Cultural Meta-Analysis. Journal of educational psychology, 114(3), 597-621. https://doi.org/10.1037/edu0000699

Lee, S., &amp; Sohn, Y. W. (2017). Effects of grit on academic achievement and career-related attitudes of college students in Korea. Social behavior and personality, 45(10), 1629-1642. https://doi.org/10.2224/sbp.6400

Lee, S., Kim, Y., &amp; Shin, J. (2025). Exploring the Interplay of Social Support, Grit, and Achievement in Korean Junior High School Students. Psychology in the schools, 62(7), 2300-2310. https://doi.org/10.1002/pits.23467

Martoyo, I., &amp; Lindawati, L. (2023). Grit, Student Academic Achievement and Factors Affecting It. Jurnal psikologi teori dan terapan (Online), 14(3), 262-269. https://doi.org/10.26740/jptt.v14n03.p262-269

‌O’Connor, M. C., &amp; Paunonen, S. V. (2007). Big Five personality predictors of post-secondary academic performance. Personality and Individual Differences, 43(5), 971–990. https://doi.org/10.1016/j.paid.2007.03.017

Rimfeld, K., Kovas, Y., Dale, P. S., &amp; Plomin, R. (2016). True Grit and Genetics: Predicting Academic Achievement From Personality. Journal of personality and social psychology, 111(5), 780-789. https://doi.org/10.1037/pspp0000089

Segal, H., &amp; Kalfon-Hakhmigari, M. (2025). Grit as a moderator of the association between cognitive abilities and STEM achievements in high school. International journal of STEM education, 12(1), 25-14. https://doi.org/10.1186/s40594-025-00536-4

Singh, S., &amp; Chukkali, S. (2021). Development and validation of multi-dimensional scale of grit. *Cogent psychology, 8*(1). https://doi.org/10.1080/23311908.2021.1923166

Tannoubi, A., Quansah, F., Magouri, I., Chalghaf, N., Bonsaksen, T., Srem-Sai, M., Hagan, J. E., Handrianto, C., Azaiez, F., &amp; Bragazzi, N. L. (2023). Modelling the associations between academic engagement, study process and grit on academic achievement of physical education and sport university students. BMC Psychology, 11(1), 1-9. https://doi.org/10.1186/s40359-023-01454-2

Tugabirwe, I., &amp; Rukundo, A. (2024). Grit Predicts Academic Achievement among Undergraduate Science Teachers at a University of Science and Technology. Qeios, 6(1). https://doi.org/10.32388/MMPITX.2

Wolters, C. A., &amp; Hussain, M. (2015). Investigating grit and its relations with college students’ self-regulated learning and academic achievement. *Metacognition and learning, 10*(3), 293-311. https://doi.org/10.1007/s11409-014-9128-9
}}

== External links ==
* [https://penntoday.upenn.edu/news/lesson-grit-angela-duckworth A lesson in grit from Angela Duckworth]  (Penn Today)
* [https://theconversation.com/do-we-actually-grow-from-adversity-122252 Do we actually grow from adversity?]  (The Conversation)
* [https://theconversation.com/grit-matters-when-a-child-is-learning-to-read-even-in-poor-south-african-schools-157982 Grit matters when a child is learning to read, even in poor South African schools] (The Conversation)
* [https://theconversation.com/grit-or-quit-how-to-help-your-child-develop-resilience-195195 Grit or quit? How to help your child develop resilience] (The Conversation)
* [https://www.bbc.com/worklife/article/20210601-grit-the-dark-side-of-deciding-to-tough-it-out Grit: The dark side of deciding to 'tough it out']  (ABC)
* [https://www.youtube.com/watch?v=W-ONEAcBeTk Grit: The Power of Passion and Perseverance | Angela Duckworth | Talks at Google] (YouTube)
* [https://www.youtube.com/watch?v=H14bBuluwB8 Grit: The Power of Passion and Perseverance | Angela Lee Duckworth | TED] (YouTube)
* [https://www.forbes.com/sites/angelicagutierrez/2025/07/10/grit-why-it-matters-and-how-to-develop-it/ Grit: Why It Matters And How To Develop It]  (Forbes)
* [https://theconversation.com/grit-and-relentless-perseverance-can-take-a-toll-on-brain-health-particularly-for-people-facing-social-stresses-like-racism-251585 ‘Grit’ and relentless perseverance can take a toll on brain health − particularly for people facing social stresses like racism] (The Conversation)
* [https://www.abc.net.au/news/2018-07-31/growth-mindset-grit-and-resilience-key-to-success/10055608 Growth mindset, grit and resilience are central to getting what you want, psychologists say] (ABC)
* [https://www.forbes.com/sites/joanmichelson2/2018/08/30/high-achievers-have-more-grit-than-talent-8-ways-you-can-too/ High Achievers Have More Grit Than Talent] (Forbes)
* [https://www.theguardian.com/society/2025/may/21/its-not-grit-that-children-lack-but-proper-support It’s not ‘grit’ that children lack, but proper support]  (The Guardian)
* [https://theconversation.com/psychological-grit-is-over-rated-as-the-key-to-retention-in-distance-education-a-south-african-study-debunks-the-myth-199022 Psychological grit is over-rated as the key to retention in distance education: a South African study debunks the myth]  (The Conversation)
* [https://www.youtube.com/watch?v=cgLG9bFYmZc Should Schools Be Teaching Kids ‘Grit’ to Fix Mental Health? | This Morning's View]  (YouTube)
* [https://theconversation.com/true-grit-we-measured-it-and-found-it-protected-doctors-from-career-burnout-170628 True grit – we measured it and found it protected doctors from career burnout] (The Conversation)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Achievement]]
[[Category:Motivation and emotion/Book/Grit] None</text>
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    <title>WikiJournal Preprints/Pentagram map</title>
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      <text bytes="62965" sha1="d99pd1pa63q6ylvb5ci0rly1zj4j6ok" xml:space="preserve">{{Article info
| last1 = Stiegler
| orcid1 = 0009-0001-5789-6923
| first1 = Jean-Baptiste
| affiliation1 = Université Paris-Saclay
| correspondence1 = jean-baptiste.stiegler@universite-paris-saclay.fr
| journal = WikiJournal of Science
| et_al = true
| w1 = Pentagram map
| from w1 = true
| keywords = Pentagram map, Dynamical system, Projective geometry, Moduli space, Integrable systems
| license = CC-BY-SA 4.0
| submitted = 2025-12-08
| abstract = In [[w:mathematics|mathematics]], the '''pentagram map''' is a [[w:Dynamical system#Discrete dynamical system|discrete dynamical system]] acting on [[w:polygons|polygons]] in the [[w:projective plane|projective plane]]. It defines a new polygon whose vertices are obtained as the intersection points of the shortest [[w:Diagonal|diagonals]] of the initial polygon. This is a [[w:Projective linear group|projectively]] [[w:Equivariant map|equivariant]] procedure, hence it [[w:Quotient space (topology)|descends]] to the [[w:moduli space|moduli space]] of polygons and defines another dynamical system (which is also referred to as the pentagram map). It was first introduced by [[w:Richard Schwartz (mathematician)|Richard Schwartz]] in 1992.{{Sfn|Schwartz|1992}}

The pentagram map on the moduli space is famous for its [[w:Completely integrable|complete integrability]] and its link with [[w:cluster algebra|cluster algebras]].{{sfn|Gekhtman|Izosimov|2025|p=14}}

It admits many generalizations in [[w:Projective space|projective spaces]] and other settings.
}}
== Introduction ==

=== Informal definition ===

==== On polygons ====
[[File:Pentagram pentagon nolabel big.svg|alt=|thumb|300x300px|The pentagram map applied on a [[w:Convex set|convex]] [[w:pentagon|pentagon]].]]
Initially, the pentagram map was defined for [[w:convex polygon|convex polygon]]s (with at least five sides) on the [[w:euclidean plane|Euclidean plane]]. Given such a polygon &lt;math&gt;P&lt;/math&gt; with &lt;math&gt;n&lt;/math&gt; sides, one can draw the &quot;shortest [[w:diagonal|diagonal]]s&quot;, meaning the [[w:Line segment|segments]] whose endpoints are a [[w:Vertex (geometry)|vertex]] and one of its second neighbors (as in Figure 1). The intersections of the shortest diagonals are then taken as the vertices of a new &lt;math&gt;n&lt;/math&gt;-gon &lt;math&gt;T(P)&lt;/math&gt;; this new polygon is the output of the pentagram map.{{Sfn|Berger|2005}}

The same construction can be done on [[w:Concave polygon|non-convex polygons]], but there are several complications. First, some consecutive short diagonals may not intersect, so one must extend the segments to [[w:Line (geometry)|lines]]. Second, the image &lt;math&gt;T(P)&lt;/math&gt; can fail to be a new &lt;math&gt;n&lt;/math&gt;-gon because some consecutive vertices could coincide. However, this [[w:Generic property|generically]] doesn't happen.{{Sfn|Ovsienko|Schwartz|Tabachnikov|p=411|2009}} Finally, it is possible that two diagonals are [[w:Parallel (geometry)|parallel]] and don't intersect on the [[w:euclidean plane|Euclidean plane]]. This is resolved by extending the Euclidean plane to the [[w:real projective plane|real projective plane]] by the addition of a [[w:line at infinity|line at infinity]], where the [[w:Vanishing point|intersection point]] lies (see Figure 3). Hence, the pentagram map is defined for generic polygons in the real projective plane.{{Sfn|Berger|2005|p=25}}

More generally, the construction of the pentagram map is well defined whenever the concepts of lines and their intersections make sense. This is encompassed by the notion of a general [[w:projective plane|projective plane]], of which the real projective plane is one example; but the pentagram map can also be considered over other [[w:Field (mathematics)|fields]], for instance the [[w:complex number|complex number]]s, which give the [[w:complex projective plane|complex projective plane]].{{Sfn|Weinreich|2022|loc=§3.1.1}}

==== On the moduli space of polygons ====
Since the pentagram map is constructed by drawing lines and marking their intersections, it [[w:Commutative property|commutes]] with any transformation that sends lines to lines. Such maps are called [[w:projective transformations|projective transformations]]. Hence, polygons can be identified [[w:up to|up to]] [[w:Perspectivity#Projectivity|projective transformations]]. This identification gives the [[w:Quotient space (topology)|quotient space]] (technically called a [[w:moduli space|moduli space]]) of [[w:Equivalence class|classes]] of polygons. 

The pentagram map on polygons induces another dynamical system on the moduli space,{{Sfn|Schwartz|1992|loc=§1 Projective geometry}} whose behavior differs quite a lot from the initial one.{{Efn|Compare the paragraph about the [[w:Pentagram map#Collapsing of convex polygons|collapsing of convex polygons]] and the one about [[w:Pentagram map#Complete integrability|complete integrability]].}} The dynamic is trivial for the classes of pentagons and hexagons, but this is no longer the case for polygons with more vertices.{{Efn|See the paragraph about [[w:Pentagram_map#Pentagons_and_hexagons|pentagons and hexagons]].}}

=== Historical elements ===
The pentagram map for general polygons was introduced in {{Harvard citation|Schwartz|1992}}, but the simplest case is the one of [[w:pentagons|pentagons]], hence the name &quot;[[w:pentagram|pentagram]]&quot;.{{Sfn|Marí-Beffa|2014|p=1}} Their study goes back to {{Harvard citation|Clebsch|1871}},{{Sfn|Izosimov|2022a|p=1085}} {{Harvard citation|Kasner|1928}}{{Sfn|Tabachnikov|2019}} and {{Harvard citation|Motzkin|1945}}.{{Sfn|Schwartz|2013|p=1}}

The pentagram map interacts with some classical configuration theorems of [[w:projective geometry|projective geometry]]. It provides results analogous to the ones of [[w:Pascal's theorem|Pascal's theorem]] and [[wikipedia:Brianchon's_theorem|Brianchon's theorem]].{{Sfn|Schwartz|Tabachnikov|2010}} Some specific configurations make [[w:Desargues' theorem|Desargues's theorem]] and [[w:Poncelet's porism|Poncelet's porism]] appear.{{Sfn|Berger|2005|loc=§4 and §5}}{{Efn|See the paragraph about [[w:Pentagram map#Poncelet polygons|Poncelet polygons]].}}

==Definitions and first properties==

=== Definition of the map ===
[[File:Pentagram pentagon label big.svg|alt=|thumb|300x300px|The pentagram map on a convex pentagon, with vertices labeled.]]
[[File:Pentagram on nonconvex pentagon.svg|alt=|thumb|300x300px|The pentagram map applied on a [[w:Self-intersecting polygon|self-intersecting]] (in particular, non-convex) pentagon. The vertex &lt;math&gt;w_2&lt;/math&gt; is on the [[w:line at infinity|line at infinity]], because it is the [[w:Vanishing point|intersection of two parallel lines]].]]
Let &lt;math&gt;n\geq 5&lt;/math&gt; be an integer. A polygon &lt;math&gt;P&lt;/math&gt; with &lt;math&gt;n&lt;/math&gt; sides, or &lt;math&gt;n&lt;/math&gt;-gon, is a tuple of [[w:Vertex (geometry)|vertices]] &lt;math&gt;(v_1,\dots,v_n)&lt;/math&gt; lying in some [[w:projective plane|projective plane]] &lt;math&gt;\mathbb P ^2&lt;/math&gt;,{{Efn|In the following, the figures represent polygons on the real plane, where the intuition is easier to grasp.}} where the indices are understood [[w:Modular arithmetic|modulo]] &lt;math&gt;n&lt;/math&gt;. The [[w:Dimension of an algebraic variety|dimension]] of the space of &lt;math&gt;n&lt;/math&gt;-gons is &lt;math&gt;2n&lt;/math&gt;.{{Sfn|Weinreich|2022|loc=definition 1.1}}

Suppose that the vertices are in sufficiently [[w:general position|general position]], meaning that no consecutive triple of points are [[w:Collinearity|collinear]].{{Sfn|Ovsienko|Schwartz|Tabachnikov|2013|p=1}} Taking the intersection of two consecutive &quot;shortest&quot; [[w:diagonal|diagonal]]s{{Efn|Meaning the line between a vertex &lt;math&gt;v_k&lt;/math&gt; and a &quot;second neighbour&quot; &lt;math&gt;v_{k\pm 2}&lt;/math&gt;.}} defines a new point&lt;math display=&quot;block&quot;&gt; w_k := \overline{v_{k-1} v_{k+1}} \cap \overline{v_{k} v_{k+2}}. &lt;/math&gt;This procedure defines a new &lt;math&gt;n&lt;/math&gt;-gon &lt;math&gt;T(P)=(w_1,\dots,w_n)&lt;/math&gt;, as in Figure 2.{{Sfn|Schwartz|1992|p=71}}

The labeling of the indices of &lt;math&gt;T(P)&lt;/math&gt; is not [[w:canonical|canonical]]. In most papers, a choice is made at the beginning of the paper and the formulas are tuned accordingly.{{Sfn|Izosimov|2016|loc=remark 1.5}}

The pentagram map on polygons is a [[w:birational map|birational map]] &lt;math&gt;T:(\mathbb P^2)^n&lt;/math&gt;{{nowrap|{{font|size=145%|⇢}}}}&lt;math&gt;(\mathbb P^2)^n&lt;/math&gt;. Indeed, each [[w:Homogeneous coordinates|coordinate]] of &lt;math&gt;w_k&lt;/math&gt; is given as a [[w:rational function|rational function]] of the coordinates of &lt;math&gt;v_{k-1},\dots,v_{k+2}&lt;/math&gt;, since it is defined as the intersection of lines passing by them. Moreover, the [[w:inverse map|inverse map]] is given by taking the intersections &lt;math&gt;\overline{w_{k-2} w_{k-1}} \cap \overline{w_{k} w_{k+1}} &lt;/math&gt;, which is rational for the same reason.{{Sfnp|Weinreich|2022|loc=definition 1.2}}

=== Moduli space ===
The pentagram map is defined by taking [[w:Line (geometry)|lines]] and intersections of them. The biggest [[w:Group (mathematics)|group]] which maps lines to lines is the one of [[w:projective transformations|projective transformations]], denoted by &lt;math&gt;\mathbb P \mathrm{GL}_{3}&lt;/math&gt;. Such a transformation &lt;math&gt;M&lt;/math&gt; [[w:Group action|acts]] on a polygon &lt;math&gt;P&lt;/math&gt; by sending it to &lt;math&gt;M \cdot P:=(Mv_1,\dots,Mv_n)&lt;/math&gt;. The pentagram map [[w:Commutative property|commutes]] with this action, and thereby induces another [[w:dynamical system|dynamical system]] on the [[w:moduli space|moduli space]] of projective [[w:equivalence classes|equivalence classes]] of polygons, whose [[w:Dimension of an algebraic variety|dimension]] is &lt;math&gt;2n-8&lt;/math&gt;.{{Sfn|Schwartz|1992|loc=§1 Projective geometry}}

===Twisted polygons===
[[File:Twisted heptagon.svg|alt=|thumb|300x300px|An example of twisted [[w:heptagon|heptagon]] on the real plane.]]
The pentagram map naturally generalizes to the larger space of twisted polygons (see example in Figure 4). For any integer &lt;math&gt;n\geq5&lt;/math&gt;, a twisted &lt;math&gt;n&lt;/math&gt;-gon &lt;math&gt;P&lt;/math&gt; is the data of:

* a [[w:Sequence#Indexing|bi-infinite sequence]] of points &lt;math&gt;(v_k)_{k\in\mathbb Z}&lt;/math&gt; in the projective plane (called the vertices),
* a [[w:projective transformation|projective transformation]] &lt;math&gt;M \in \mathbb P \mathrm{GL}_3&lt;/math&gt; (called the [[w:monodromy|monodromy]]),

such that for any &lt;math&gt;k \in \mathbb Z&lt;/math&gt;, the property &lt;math&gt;v_{k+n}=Mv_k&lt;/math&gt; is satisfied. The dimension of the space of twisted &lt;math&gt;n&lt;/math&gt;-gons is &lt;math&gt;2n+8&lt;/math&gt;.{{Sfn|Schwartz|2008}}

When &lt;math&gt;M&lt;/math&gt; is the [[w:Identity_element|identity]], this gives back the initial definition of polygons (which are said to be closed). The space of closed &lt;math&gt;n&lt;/math&gt;-gons is of [[w:codimension|codimension]] &lt;math&gt;8&lt;/math&gt; in the space of twisted ones.{{Sfn|Soloviev|2013|p=2816}}

The action of projective transformations over the space of closed polygons generalizes to the space of twisted ones (the monodromy is changed by [[w:Matrix similarity|conjugation]]). This provides again a moduli space, of dimension &lt;math&gt;2n&lt;/math&gt;.{{Sfn|Weinreich|2022|loc=definition 1.3}}

== Collapsing of convex polygons ==

=== Exponential shrinking ===
[[File:Pentagram map convex heptagon iterate.svg|alt=|thumb|300x300px|The pentagram map iterated on a convex [[w:heptagon|heptagon]], exhibiting the convergence.]]
Let &lt;math&gt;P&lt;/math&gt; be a closed [[w:Convex polygon#Strictly convex polygon|strictly convex polygon]] lying on the real plane. One of the first results proved by Richard Schwartz it that its iterates under the pentagram map shrink [[w:Exponential growth|exponentially fast]] to a point, as illustrated in Figure 5. This follows from two facts.
# The image of a strictly convex polygon is contained in its [[w:Interior (topology)|interior]], and is also strictly convex.{{Sfn|Glick|2020|p=2818}}
# There exists a constant &lt;math&gt;0&lt; \eta_P&lt;1&lt;/math&gt;, depending on &lt;math&gt;P&lt;/math&gt;, such that for any &lt;math&gt;N \in \mathbb N&lt;/math&gt;, the diameters of the iterates verify the inequality &lt;math display=&quot;inline&quot;&gt;\operatorname{diam}(T^N(P))\leq\eta_P^N \operatorname{diam}(P). &lt;/math&gt;{{Sfn|Schwartz|1992|loc=theorem 3.1}}

Hence, by [[w:Cantor's intersection theorem#Variant in complete metric spaces|Cantor's intersection theorem]], the sequence of polygons collapses toward a point.{{Sfn|Schwartz|1992|loc=§3 Convex polygons}}

The behavior on the moduli space is very different, since the dynamics is [[w:Recurrent point|recurrent]].{{Sfn|Schwartz|2001|loc=theorem 1.1}} It is even a [[w:quasiperiodic motion|quasiperiodic motion]],{{Sfn|Ovsienko|Schwartz|Tabachnikov|2009}} as discussed in [[w:Pentagram map#Complete integrability|the section about integrability]].

=== Coordinates of the limit point ===
The limit point coordinates were given in {{Harvard citation|Glick|2020}}. They satisfy some [[w:Degree of a polynomial|degree]] 3 [[w:polynomial equation|polynomial equations]], whose coefficients are [[w:rational function|rational function]]s in the coordinates of the vertices of the starting polygon. The proof relies on the fact that the limit point must be an [[w:eigenline|eigenline]] of a certain [[w:linear operator|linear operator]] of &lt;math&gt;\mathbb R^3&lt;/math&gt;, named Glick's operator.{{sfn|Glick|2020}} 

Moreover, the polygon stays convex under iteration of the inverse pentagram map [[w:If_and_only_if|if and only if]] Glick's operator (seen as a projective mapping) is affine. The set formed by such polygons is an algebraic subvariety of [[w:Codimension|codimension]] 2.{{sfn|Izosimov|2021}} 

Glick's operator was reinterpreted in {{Harvard citation|Aboud|Izosimov|2022}} as the infinitesimal monodromy of the polygon. The [[w:Pentagram map#The scaling symmetry|scaling symmetry]] is used to [[w:Deformation (mathematics)|deform]] a closed polygon &lt;math&gt;P&lt;/math&gt; into a family of twisted ones '''&lt;math&gt;(P_z)_{z\in \mathbb C^*}&lt;/math&gt;''' with monodromy &lt;math&gt;M_z&lt;/math&gt;. The infinitesimal monodromy is defined to be:{{sfn|Aboud|Izosimov|2022}}
&lt;math display=&quot;block&quot;&gt;\left.\frac{dM_z}{dz}\right|_{z=1}.&lt;/math&gt;

=== Generalization ===
The collapsing of polygons may also happen in some [[w:Pentagram map#Generalizations|generalization of the pentagram map]], when considering some specific configurations of polygons in the real plane. The coordinates of the collapse point are given by a formula analogous to the one for the original pentagram map.{{Sfn|Schwartz|2026a}}{{Sfn|Schwartz|2026b}}

== Periodic orbits on the moduli space ==
For some configurations of closed polygons, the iterate of the pentagram map will send &lt;math&gt;P&lt;/math&gt; to a projectively equivalent polygon (up to some shift of the indices). This means that, on the moduli space, the orbit of the class of &lt;math&gt;P&lt;/math&gt; is [[w:Periodic orbit|periodic]].

===Pentagons and hexagons===
[[File:penta hexagon.svg|300px|thumb|The outward hexagon is projectively equivalent to the inward one, with respect to their labeling.]]The following two facts are proved by checking [[w:cross-ratio|cross-ratio]] equalities, so they are true for polygons in any [[w:projective plane|projective plane]] (not just the [[w:Real projective plane|real one]]).{{Sfn|Schwartz|1992|loc=§2 Pentagons and hexagons}}

The pentagram map &lt;math&gt;T&lt;/math&gt; is the identity on the moduli space of [[w:pentagon|pentagon]]s.{{Sfn|Schwartz|1992|loc=theorem 2.1}}{{Sfn|Clebsch|1871}}{{Sfn|Motzkin|1945}} The second iterate &lt;math&gt;T^2&lt;/math&gt; is the identity on the space of labeled [[w:hexagon|hexagon]]s, up to a shift of labeling (see Figure 6).{{Sfn|Schwartz|1992|loc=theorem 2.3}} This phenomenon doesn't generalize to generic polygons with at least seven sides, for which the motion is [[w:Quasiperiodic motion|quasiperiodic]].{{Sfn|Tupan|2022}}

==== Generalization ====
The result about pentagons and hexagons generalizes to some [[w:Pentagram map#Generalizations|higher pentagram maps]] in &lt;math&gt;\mathbb P ^k&lt;/math&gt;, for polygons with &lt;math&gt;k+3&lt;/math&gt; or &lt;math&gt;2k+2&lt;/math&gt; sides. The proof uses a generalization of the [[w:Gale transform|Gale transform]].{{Sfn|Dirdak|2024}}

=== Poncelet polygons ===
A polygon is said to be Poncelet{{Efn|The name comes from [[w:Jean-Victor Poncelet|Jean-Victor Poncelet]] and [[w:Poncelet porism|his porism]].{{Sfn|Izosimov|2022a|p=1085}}}} if it is [[w:Inscribed figure|inscribed]] in a [[w:Conic section|conic]] and circumscribed about another one.{{Sfn|Schwartz|2015|loc=|p=433}}{{Efn|In particular, pentagons are Poncelet since [[w:five points determine a conic|five points determine a conic]].{{Sfn|Schwartz|2015|loc=|p=433}}}} For a convex Poncelet &lt;math&gt;n&lt;/math&gt;-gon &lt;math&gt;P&lt;/math&gt; lying on the [[w:real projective plane|real projective plane]], the polygon &lt;math&gt;T^2(P)&lt;/math&gt; is projectively equivalent to &lt;math&gt;P&lt;/math&gt;.{{Sfn|Schwartz|2015|loc=theorem 1.1}} 

In fact, when &lt;math&gt;n&lt;/math&gt; is odd, the converse is also true.{{Sfn|Izosimov|2022a|loc=corollary 1.1}} However, this converse statement is no longer true when the polygons are considered over the [[w:complex projective plane|complex projective plane]] since there are explicit counterexamples.{{Sfn|Izosimov|2022a|loc=remark 1.3}}

==Coordinates for the moduli space==
The moduli space can be described by different [[w:Coordinate_system|coordinate systems]]. The following ones give simple expressions for the dynamics, as presented in the next section.

=== Corner coordinates ===
[[File:Corner coordinates big.svg|thumb|300x300px|The geometric construction of the points defining the corner invariants.]]
Define the [[w:cross-ratio|cross-ratio]] of four [[w:Collinearity|collinear]] points to be

: &lt;math&gt; [a,b,c,d]=\frac{(a-b)(c-d)}{(a-c)(b-d)}. &lt;/math&gt;

The corner invariants are a system of coordinates on the space of twisted polygons, constructed by taking intersections as in Figure 7.{{Sfn|Schwartz|2001|loc=figure 2}} The left and right invariants are respectively defined{{Efn|The ordering of the vertices in the cross-ratios can differ from a paper to another one, which slightly changes the formulas in the following sections.}} as the following cross-ratios:

: &lt;math&gt;x_k:=[v_{k-2},v_{k-1},\overline{v_{k-2}v_{k-1}}\cap\overline{v_{k}v_{k+1}},\overline{v_{k-2}v_{k-1}}\cap\overline{v_{k+1}v_{k+2}}],&lt;/math&gt;

: &lt;math&gt;y_k:=[\overline{v_{k+1}v_{k+2}}\cap\overline{v_{k-2}v_{k-1}}, \overline{v_{k+1}v_{k+2}}\cap\overline{v_{k-1}v_{k}},v_{k+1},v_{k+2}].&lt;/math&gt;

Since the cross-ratio is [[w:Cross-ratio#Projective geometry|projective invariant]], the sequences &lt;math&gt;(x_k)_{k \in \mathbb Z}&lt;/math&gt; and &lt;math&gt;(y_k)_{k \in \mathbb Z}&lt;/math&gt; associated to a twisted &lt;math&gt;n&lt;/math&gt;-gon are &lt;math&gt;n&lt;/math&gt;-periodic.{{Sfn|Ovsienko|Schwartz|Tabachnikov|2010|p=415}}

The corner invariants are elements of &lt;math&gt;\mathbb{P}^1\smallsetminus\{0,1,\infty\}&lt;/math&gt;, and they realize an [[w:Isomorphism_of_varieties|isomorphism of varieties]] between the moduli space of twisted &lt;math&gt;n&lt;/math&gt;-gons and &lt;math&gt;(\mathbb{P}^1\smallsetminus\{0,1,\infty\})^{2n}&lt;/math&gt;.{{Sfn|Weinreich|2022|loc=theorem 3.6}}

===ab-coordinates===

There is a second set of coordinates for the moduli space of twisted &lt;math&gt;n&lt;/math&gt;-gons defined over any [[w:Field (mathematics)|field]] &lt;math&gt;F&lt;/math&gt; satisfying &lt;math&gt;\mathrm{SL}_3(F)\cong \mathbb P\mathrm{GL}_3(F)&lt;/math&gt;,{{Sfn|Weinreich|2022|loc=remark 3.8}} and such that &lt;math&gt;n&lt;/math&gt; is not divisible by &lt;math&gt;3&lt;/math&gt;.{{Sfn|Ovsienko|Schwartz|Tabachnikov|2010|loc=section 4.1}}

The vertices &lt;math&gt;v_k&lt;/math&gt; in the [[w:projective plane|projective plane]] &lt;math&gt;\mathbb P^2(F)&lt;/math&gt; can be [[w:Lift (mathematics)|lifted]] to [[w:Vector space|vectors]] &lt;math&gt;V_k&lt;/math&gt; in the [[w:affine space|affine space]] &lt;math&gt;F^3&lt;/math&gt; so that each consecutive triple of vectors spans a [[w:parallelepiped|parallelepiped]] having [[w:determinant|determinant]] equal to &lt;math&gt;1&lt;/math&gt;. This leads to the relation defining the &lt;math&gt;ab&lt;/math&gt;-coordinates:{{Sfn|Ovsienko|Schwartz|Tabachnikov|2010|loc=equation 4.1}}

: &lt;math&gt;V_{k+3} = a_k V_{k+2} + b_k V_{k+1} + V_k.&lt;/math&gt;

This bring out an analogy between twisted polygons and solutions of third order linear [[w:ordinary differential equations|ordinary differential equations]], normalized to have unit [[w:Wronskian|Wronskian]].{{Sfn|Ovsienko|Schwartz|Tabachnikov|2010|loc=remark 6.6}}

They are linked to the corner coordinates by:{{Sfn|Ovsienko|Schwartz|Tabachnikov|2010|loc=lemma 4.5}}
: &lt;math&gt;x_k=\frac{a_{k-2}}{b_{k-2}b_{k-1}},&lt;/math&gt;
: &lt;math&gt;y_k=-\frac{b_{k-1}}{a_{k-2}a_{k-1}}.&lt;/math&gt;

==Formulas on the moduli space==

===As a birational map ===
The pentagram map is a [[w:birational map|birational map]] on the moduli space, because it can be decomposed as the [[w:Function composition|composition]] of two [[w:Birational geometry|birational]] [[w:Involution (mathematics)|involutions]].{{Sfn|Schwartz|2008|loc=§1.2 The Pentagram Map}} The corner invariants change in the following way:{{Sfn|Ovsienko|Schwartz|loc=lemma 2.4|Tabachnikov|2010}}

: &lt;math&gt;x_k'=x_k\frac{1-x_{k-1} y_{k-1}}{1-x_{k+1}y_{k+1}},&lt;/math&gt;

: &lt;math&gt;y_k'=y_{k+1}\frac{1-x_{k+2} y_{k+2}}{1-x_k y_k}.&lt;/math&gt;

=== The scaling symmetry ===
The [[w:multiplicative group|multiplicative group]] &lt;math&gt;F\smallsetminus\{0\}&lt;/math&gt; [[w:One-parameter group|acts]] on the moduli space in the following way:

: &lt;math&gt;R_s\cdot(x_1,\dots,x_n,y_1,\dots,y_n)=(sx_1,\dots,sx_n,s^{-1}y_1,\dots,s^{-1}y_n),&lt;/math&gt;

where &lt;math&gt;R&lt;/math&gt; is called the scaling action and &lt;math&gt;s&lt;/math&gt; is the scaling parameter. This action commutes with the pentagram map on the moduli space (as presented in the previous formulas). This property is called the scaling symmetry, and is instrumental in proving the [[w:Pentagram map#Complete integrability|complete integrability]] of the dynamics.{{Sfn|Ovsienko|Schwartz|Tabachnikov|2010|loc=corollary 2.5}}

==Invariant structures==

===Monodromy invariants===

The monodromy invariants, introduced in {{Harvard citation|Schwartz|2008}}, are a collection of [[w:Function (mathematics)|functions]] on the [[w:moduli space|moduli space]] that are invariant under the pentagram map.{{Sfn|Schwartz|2008|loc=theorem 1.2}} The simplest examples of them are 
:&lt;math&gt; O_n= x_1x_2\cdots x_{n}, \quad E_n = y_1y_2\cdots y_n. &lt;/math&gt;
The other monodromy invariants can be retrieved through different points of view: through the [[w:Pentagram map#The scaling symmetry|scaling symmetry]], as [[w:Combinatorics|combinatorial]] objects, or as some [[w:determinant|determinant]]s.{{Sfn|Schwartz|Tabachnikov|2011|loc=§2 The Monodromy Invariants}} The one involving scaling symmetry is presented here.

Let &lt;math&gt;M\in \mathrm{GL}_3&lt;/math&gt; be a [[w:Lift (mathematics)|lift]] of the monodromy of a twisted &lt;math&gt;n&lt;/math&gt;-gon. The quantities

: &lt;math&gt;\Omega_1=\frac{\operatorname{trace}^3(M)}{\det(M)}, \quad \Omega_2=\frac{\operatorname{trace}^3(M^{-1})}{\det(M^{-1})},&lt;/math&gt;

are independent of the choice of lift and are invariant under [[w:Matrix similarity|conjugation]], so they are well defined for the projective class of the polygon. They are invariant under the pentagram map, since the monodromy matrix doesn't change.{{Sfn|Schwartz|Tabachnikov|2011|loc=|p=5}} Now, the quantities

: &lt;math&gt;\tilde{\Omega}_1=O_n^2E_n\Omega_1, \quad \tilde{\Omega}_2=O_nE_n^2\Omega_2,&lt;/math&gt;

have the same properties, but turn out to be polynomials in the corner invariants.{{Efn|Some papers consider the cube roots of this functions, but it doesn't change the following definitions of the monodromy invariants.}} They can be written as{{Sfn|Schwartz|Tabachnikov|2011|loc=|p=5}}

: &lt;math&gt;
\tilde{\Omega}_1=\biggl(\sum_{k=0}^{\lfloor n/2\rfloor}O_k\biggr)^3, \quad
\tilde{\Omega}_2=\biggl(\sum_{k=0}^{\lfloor n/2\rfloor}E_k\biggr)^3,
&lt;/math&gt;

where each &lt;math&gt;O_k&lt;/math&gt; and &lt;math&gt;E_k&lt;/math&gt; are [[w:homogeneous polynomial|homogeneous polynomial]]s respectively of weight &lt;math&gt;k&lt;/math&gt; and &lt;math&gt;-k&lt;/math&gt;,{{Sfn|Ovsienko|Schwartz|Tabachnikov|2013|p=11}} meaning they change under the [[w:Pentagram map#The scaling symmetry|rescaling action]] on variables by{{Sfn|Schwartz|Tabachnikov|2011|p=5}}

: &lt;math&gt; R_s(O_k)= s^k O_k, \quad R_s(E_k)= s^{-k} E_k. &lt;/math&gt;

The quantities &lt;math&gt;O_1,\dots,O_{\lfloor n/2 \rfloor},O_n, E_1,\dots,E_{\lfloor n/2 \rfloor},E_n,&lt;/math&gt; are unchanged by the dynamics, and are called the monodromy invariants. Moreover, they are [[w:algebraically independent|algebraically independent]].{{Sfn|Schwartz|2008|loc=theorem 1.2}}

==== Polygons on conics ====
Whenever &lt;math&gt;P&lt;/math&gt; is [[w:Inscribed figure|inscribed]] in a [[w:conic section|conic section]], one has &lt;math&gt;O_k(P)=E_k(P)&lt;/math&gt; for all &lt;math&gt;k&lt;/math&gt;.{{Sfn|Schwartz|Tabachnikov|2011|loc=theorem 1.1}} Moreover, if &lt;math&gt;P&lt;/math&gt; is circumscribed about another conic,{{Efn|See the paragraph about [[w:Pentagram map#Poncelet polygons|Poncelet polygons]].}} then its monodromy invariants are characterized by the pair of conics.{{Sfn|Schwartz|2015|loc=theorem 1.2}} For such odd-gons, the translation on the [[w:Jacobian variety|Jacobian variety]]{{Efn|See the paragraph about [[w:Pentagram map#Algebro-geometric integrability|algebraic integrability]].}} is restricted to the [[w:Prym variety|Prym variety]] (which is a half-dimensional torus in the Jacobian).{{Sfn|Izosimov|2016|loc=theorem 1.3}}

===Poisson bracket===

An invariant [[w:Poisson bracket|Poisson bracket]] on the space of twisted polygons was found in {{Harvard citation|Ovsienko|Schwartz|Tabachnikov|2010}}. The monodromy invariants [[w:Poisson bracket#Constants of motion|commute]] with respect to it:
&lt;math display=&quot;block&quot;&gt; \{O_i,O_j\}=\{O_i,E_j\}=\{E_i,E_j\}=0 &lt;/math&gt;for all &lt;math&gt;i,j&lt;/math&gt;.{{sfn|Ovsienko|Schwartz|Tabachnikov|2010|loc=theorem 1}}

The Poisson bracket is defined in terms of the corner coordinates by:
&lt;math display=&quot;block&quot;&gt; \begin{align}
 \{x_i,x_{i\pm1}\} &amp;= \mp x_i x_{i+1}, \\
 \{y_i,y_{i\pm 1}\} &amp;= \mp y_i y_{i+1},
\end{align}&lt;/math&gt;and &lt;math display=&quot;block&quot;&gt; \{x_i,x_j\} = \{y_i,y_j\} = \{x_i,y_j\} = 0&lt;/math&gt;for all other &lt;math&gt; i,j.&lt;/math&gt;{{sfn|Ovsienko|Schwartz|Tabachnikov|2010|loc=equation 2.16}}

=== The spectral curve ===

Let &lt;math&gt;\zeta&lt;/math&gt; be an element of the [[w:multiplicative group|multiplicative group]] and &lt;math&gt;P_\zeta&lt;/math&gt; be the polygon obtained by applying the [[w:Pentagram map#The scaling symmetry|rescaling action]] &lt;math&gt;R_\zeta&lt;/math&gt; on &lt;math&gt;P&lt;/math&gt;.  A [[w:Lax matrix|Lax matrix]] &lt;math&gt;\hat{T}(\zeta) \in \mathrm{GL}_3&lt;/math&gt; is a lift of the monodromy of &lt;math&gt;P_\zeta&lt;/math&gt; satisfying a [[w:Lax pair#Zero-curvature equation|zero-curvature equation]].{{Sfn|Weinreich|2022|loc=§5 The Lax representation}} Then, the spectral function is the [[w:Bivariate polynomial|bivariate]] [[w:characteristic polynomial|characteristic polynomial]]&lt;math display=&quot;block&quot;&gt; Q(\lambda,\zeta) := \det(\lambda\operatorname{Id}-\hat{T}(\zeta)),&lt;/math&gt;or some renormalization of it. The [[w:spectral curve|spectral curve]] is the [[w:Projective variety#projective completion|projective completion]] of the [[w:Algebraic curve|affine curve]] defined by the equation &lt;math&gt;Q(\lambda,\zeta)=0&lt;/math&gt;.{{Sfn|Weinreich|2022|loc=§6. The geometry of the spectral curve}} It is invariant under the pentagram map, and the monodromy invariants appear as the [[w:coefficient|coefficient]]s of &lt;math&gt;Q&lt;/math&gt;.{{Sfn|Soloviev|2013|loc=theorem 6.4}} Its [[w:geometric genus|geometric genus]] is &lt;math&gt;n-1&lt;/math&gt; if &lt;math&gt;n&lt;/math&gt; is odd, and &lt;math&gt;n-2&lt;/math&gt; if &lt;math&gt;n&lt;/math&gt; is even.{{Sfn|Weinreich|2022|p=|loc=theorem 6.4}}

It was first introduced in {{Harv|Soloviev|2013|ps=|p=}} for his proof of [[w:Pentagram map#Algebro-geometric integrability|algebro-geometric integrability]].{{sfn|Soloviev|2013}}

==Complete integrability==
The pentagram map on the moduli space has been proved to be a [[w:completely integrable|completely integrable]] [[w:discrete dynamical system|discrete dynamical system]], both in the [[w:Integrable system#Hamiltonian systems and Liouville integrability|Arnold-Liouville]]{{Efn|Over the [[w:real number|real number]]s.}} and the [[w:Integrable system#Complete integrability over the complex numbers|algebro-geometric]]{{Efn|Over [[w:algebraically closed field|algebraically closed field]]s of [[w:Characteristic (algebra)|characteristic]] different from 2.}} senses. In any case, this means that the moduli space is [[w:almost everywhere|almost everywhere]] [[w:Foliation|foliated]] by [[w:Torus#Flat torus|flat tori]] (or in the algebraic setting, [[w:Abelian variety|Abelian varieties]]), where the motion is a [[w:Translation (geometry)|translation]]. This [[w:Generic property|generically]] induces a [[w:quasiperiodic motion|quasiperiodic motion]] on the corresponding torus.{{Sfn|Ovsienko|Schwartz|Tabachnikov|2009}}

===Arnold–Liouville integrability===

The proof of the integrability of the pentagram map on a real twisted polygon was achieved in {{Harvard citation|Ovsienko|Schwartz|Tabachnikov|2010}}. This is done by noticing that the monodromy invariants &lt;math&gt;O_n&lt;/math&gt; and &lt;math&gt;E_n&lt;/math&gt; are [[w:Casimir invariant|Casimir invariant]]s for the Poisson bracket, meaning (in this context) that&lt;math display=&quot;block&quot;&gt; \{O_n,f\}=\{E_n,f\} = 0 &lt;/math&gt;for every smooth function &lt;math&gt;f&lt;/math&gt;.{{sfn|Ovsienko|Schwartz|Tabachnikov|2010|loc=theorem 1}} When &lt;math&gt;n&lt;/math&gt; is even, this is also true for the monodromy invariants &lt;math&gt;O_{\lfloor n/2 \rfloor }&lt;/math&gt; and &lt;math&gt;E_{\lfloor n/2 \rfloor }&lt;/math&gt;.{{sfn|Ovsienko|Schwartz|Tabachnikov|2010|loc=theorem 1}}

This allows to consider the Casimir [[w:level set|level set]], where each Casimir invariant has a specified value. Because of [[w:Sard's theorem|Sard's theorem]], any generic level set is a [[w:smooth manifold|smooth manifold]].{{Sfn|Schwartz|2017|p=44}} This family of level sets forms a [[w:foliation|foliation]] in [[w:Poisson manifold#Symplectic leaves|symplectic leaves]], on which the Poisson bracket gives rise to a [[w:symplectic form|symplectic form]].{{sfn|Ovsienko|Schwartz|Tabachnikov|2010|loc=corollary 2.13}}

Each of these symplectic leaves has an iso-monodromy [[w:foliation|foliation]], namely, a decomposition into the common level sets of the remaining monodromy functions. By using again [[w:Sard's theorem|Sard's theorem]], they are generically [[w:Symplectic manifold#Lagrangian submanifolds|Lagrangian manifolds]].{{Sfn|Schwartz|2017|p=45}} Moreover, they are compact.{{Sfn|Ovsienko|Schwartz|Tabachnikov|2010|loc=§3.3. Compactness of the level sets}} Since the monodromy invariants Poisson-commute and there are enough of them, the discrete [[w:Liouville–Arnold theorem|Liouville–Arnold theorem]] can be applied to prove that the level sets are [[w:Torus#Flat torus|flat tori]] over which the dynamics is a translation.{{sfn|Ovsienko|Schwartz|Tabachnikov|2010|p=412}}{{sfn|Kato|2017|loc=§5.6 Complete integrability of pentagram map}}

===Algebro-geometric integrability===

In {{Harvard citation|Soloviev|2013}}, it was shown that the pentagram map admits a [[w:Lax representation|Lax representation]] with a spectral parameter, which allows to prove its algebro-geometric integrability. This means that the space of polygons (either twisted or closed) is parametrized by its spectral data, consisting of [[w:Pentagram map#The spectral curve|its spectral curve]], with marked points and a [[w:Divisor (algebraic geometry)|divisor]] given by a [[w:Floquet theory|Floquet]]–[[w:Bloch's theorem|Bloch]] equation. This gives an embedding to the [[w:Jacobian variety|Jacobian variety]] through the [[w:Abel–Jacobi map|Abel–Jacobi map]], where the motion is expressed in terms of translation.{{sfn|Soloviev|2013|loc=theorems A, B and C}} The previously defined Poisson bracket is also retrieved.{{sfn|Soloviev|2013|loc=theorem D}} 

This integrability was generalized in {{Harvard citation|Weinreich|2022}} from the field of [[w:complex number|complex number]]s to any [[w:algebraically closed field|algebraically closed field]] of [[w:Characteristic (algebra)|characteristic]] different from 2. The translation on a torus is replaced by a translation on an [[w:Abelian variety|Abelian variety]] (in fact, a Jacobian variety again).{{sfn|Weinreich|2022|loc=theorem 1.4}}

=== Dimension of the invariant manifold ===

For twisted &lt;math&gt;n&lt;/math&gt;-gons, the [[w:dimension|dimension]] of the invariant manifolds (tori or Jacobian varieties) is{{Sfn|Ovsienko|Schwartz|Tabachnikov|2010|p=421}}

: &lt;math&gt;\begin{cases} 
n-1 &amp; \text{when }n \text{ is odd,}\\
n-2 &amp; \text{when }n \text{ is even.}
\end{cases}&lt;/math&gt;

Moreover, when &lt;math&gt;n&lt;/math&gt; is even, there are two isomorphic manifolds on which the iterates of the pentagram map alternate. But on each of them, the second iterate is a translation.{{Sfn|Weinreich|2022|loc=theorem 1.4}}

=== For closed polygons ===
There is no Poisson structure on the space of closed polygons.{{Sfn|Soloviev|2013|loc=corollary 4.1}} Nevertheless, the one from twisted polygons can be used to prove integrability.{{sfn|Ovsienko|Schwartz|Tabachnikov|2013|p=2153}}

Algebro-geometric integrability holds for closed polygons in a same manner as for the twisted ones.{{Sfn|Soloviev|2013|loc=theorem C}} However, Arnold-Liouville integrability is proved for real closed polygons only when they are convex. This is done by restricting the [[w:Hamiltonian vector field|Hamiltonian vector field]]s of monodromy functions to smaller dimensional tori, and showing that enough of them are still independent.{{sfn|Ovsienko|Schwartz|Tabachnikov|2013|loc=corollary 1.1}}

In both situation, the dimension of the invariant manifolds decreases by &lt;math&gt;3&lt;/math&gt; for closed &lt;math&gt;n&lt;/math&gt;-gons (compared to the twisted case), and is equal to{{Sfn|Soloviev|2013|loc=theorem C}}{{sfn|Ovsienko|Schwartz|Tabachnikov|2013|loc=theorem 1}}
:&lt;math&gt;\begin{cases} 
n-4 &amp; \text{when }n \text{ is odd,}\\
n-5 &amp; \text{when }n \text{ is even.}
\end{cases}&lt;/math&gt;

==Connections to other topics==

===The Boussinesq equation===

The [[w:Discretization|continuous limit]] of a polygon is a parametrized curve in the plane. When the time parameter is suitably chosen, the continuous limit of the pentagram map is the [[w:Boussinesq approximation (water waves)|Boussinesq equation]]. This [[w:partial differential equation|partial differential equation]] models water waves under some conditions, which is a classical example of [[w:integrable|integrable system]].{{Sfn|Ovsienko|Schwartz|Tabachnikov|2010|loc=theorem 5}}

Here is a description of the geometric action of the Boussinesq equation. Given a [[w:locally convex|locally convex]] curve &lt;math&gt; C:\mathbb R\to \mathbb R^2 &lt;/math&gt; and real numbers &lt;math&gt;x&lt;/math&gt; and &lt;math&gt;t&lt;/math&gt;, consider the [[w:chord (geometry)|chord]] connecting &lt;math&gt; C(x-t) &lt;/math&gt; to &lt;math&gt; C(x+t) &lt;/math&gt;. The [[w:Envelope (mathematics)|envelope]] of all these chords is a new curve &lt;math&gt; C_t(x) &lt;/math&gt;. When &lt;math&gt;t&lt;/math&gt; is extremely small, the curve &lt;math&gt; C_t(x) &lt;/math&gt; is a good model for the time &lt;math&gt;t&lt;/math&gt; evolution of the original curve &lt;math&gt; C_0(x) &lt;/math&gt; under the Boussinesq equation. This construction is also similar to the pentagram map. Moreover, the pentagram invariant bracket is a discretization of an invariant Poisson bracket associated to the Boussinesq equation.{{Sfn|Ovsienko|Schwartz|Tabachnikov|2010|loc=§6.4 Discretization}}

===Cluster algebras===

The pentagram map{{Sfn|Glick|2011}} and some of its generalizations{{Sfn|Gekhtman|Shapiro|Tabachnikov|Vainshtein|2012}}{{Sfn|Glick|Pylyavskyy|2016}} are identified as special cases of discrete dynamical systems powered by [[w:cluster algebra|cluster algebras]]. Using the results from {{Harvard citation|Goncharov|Kenyon|2013}}, this provides a link with the [[w:Poisson–Lie group|Poisson–Lie group]]s, [[w:dimer model|dimer model]]s and other so-called cluster-integrable systems.{{Sfn|Fock|Marshakov|2016}}{{Sfn|Izosimov|2022c}} These methods allow to retrieve the Poisson bracket and Hamiltonians used to prove complete integrability{{Sfn|Affolter|George|Ramassamy|2025|loc=§5 The pentagram map}} and provide [[w:Lax representation|Lax representation]]s.{{Sfn|Izosimov|2022b}}

=== Octahedron recurrence ===
Using a method to compute [[w:Determinant|determinants]] called [[w:Dodgson_condensation|Dodgson condensation]], {{Harvard citation|Schwartz|2008}} proves that the pentagram map satisfies a property called the &quot;octahedron recurrence&quot;.{{Sfn|Schwartz|2008|loc=§5 The Method of Condensation}} It is also shared by higher dimensional pentagram maps defined through cluster algebras mutations, referred as &quot;&lt;math&gt;T&lt;/math&gt;-systems&quot;.{{Sfn|Kedem|Vichitkunakorn|2015||loc=}}

Furthermore, the pentagram map (together with other dynamical systems defined through geometric constructions) verifies a generalization of the octahedron recurrence.{{Sfn|Affolter|de Tilière|Melotti|2025|loc=§9 The Pentagram Map}}

=== Singularity theory ===
The pentagram map exhibits a property called singularity confinement, which is a typical phenomenon in [[w:integrable system|integrable system]]s.{{Sfn|Grammaticos|Ramani|Papageorgiou|1991}} It states that if a polygon &lt;math&gt;P&lt;/math&gt; is [[w:Singular point of an algebraic variety|singular]] for the pentagram map &lt;math&gt;T&lt;/math&gt;, then there exists an integer &lt;math&gt;m&lt;/math&gt; such that &lt;math&gt;P&lt;/math&gt; not singular for the iterate map &lt;math&gt;T^m&lt;/math&gt;.{{Sfn|Glick|2012}}

Moreover, the pentagram map (along with some of its generalizations and other discrete dynamical systems) exhibit the Devron property.{{Efn|The name comes from an episode of [[w:Star Trek|Star Trek]].{{Sfn|Glick|2015|loc=§1 Introduction}}}} This means that if a polygon &lt;math&gt;P&lt;/math&gt; is singular for some iterate of the pentagram map &lt;math&gt;T^m&lt;/math&gt;, then it will also be singular for some iterate of the inverse map &lt;math&gt;T^{-m'}&lt;/math&gt;.{{Sfn|Glick|2015}}

== Generalizations ==
The definition of polygons still makes sense in any [[w:projective space|projective space]] &lt;math&gt;\mathbb P^d&lt;/math&gt; under the action of the [[w:Projective linear group|projective group]] &lt;math&gt;\mathbb P \mathrm{GL}_{d+1}&lt;/math&gt;, and even in other spaces with their associated groups.

The pentagram map can be generalized in many ways, and some of them are presented here. Not all of them are integrable.{{Sfn|Khesin|Soloviev|2015a|}} Some are [[w:discretization|discretization]]s of [[w:PDEs|PDEs]] from the [[w:KdV hierarchy|KdV hierarchy]], seen as higher dimensional version of [[w:Boussinesq approximation (water waves)|Boussinesq]] or [[w:Kadomtsev–Petviashvili equation|KP]] equations.{{Sfn|Marí-Beffa|2012}}{{Sfn|Wang|2023}} The description of all generalized pentagram maps in terms of [[w:cluster algebra|cluster algebra]]s is still an open question.{{Sfn|Gekhtman|Izosimov|2025|p=14}}

=== Polygons in general positions ===
Let &lt;math&gt;d \geq 2&lt;/math&gt; and &lt;math&gt;P&lt;/math&gt; be a twisted polygon of &lt;math&gt;\mathbb P^d&lt;/math&gt; in [[w:general position|general position]].

==== Short diagonal pentagram maps ====
The &lt;math&gt;k&lt;/math&gt;-th short diagonal hyperplane &lt;math&gt;H_k^{sh}&lt;/math&gt; is uniquely defined by passing through the vertices &lt;math&gt;v_k,v_{k+2},\dots,v_{k+2d-2}&lt;/math&gt;. [[w:Generic property#In algebraic geometry|Generically]], the intersection of &lt;math&gt;d&lt;/math&gt; consecutive [[w:Hyperplane|hyperplanes]] uniquely defines a new point

: &lt;math&gt;T_{sh}v_k:=H_k^{sh}\cap H_{k+1}^{sh}\cap \dots \cap H_{k+d-1}^{sh}.&lt;/math&gt;

Doing this for every vertex defines a new twisted polygon. This map, denoted by &lt;math&gt;T_{sh}&lt;/math&gt;, is again projectively equivariant.{{Sfn|Khesin|Soloviev|2013}}

==== Generalized pentagram maps ====
The previous procedure can be generalized. Let &lt;math&gt;I=(i_1,\dots,i_{d-1}),J=(j_1,\dots,j_{d-1})&lt;/math&gt; be two sets of integers, respectively called the jump tuple and the intersection tuple. Define &lt;math&gt;H_k^I&lt;/math&gt; to be the unique hyperplane passing through the vertices &lt;math&gt;v_k,v_{k+i_1},\dots,v_{k+i_1+\dots+i_{d-1}}&lt;/math&gt;. A new point is given by the intersection

: &lt;math&gt;T_{I,J}v_k:=H_k^I \cap H_{k+j_1}^I \cap \dots \cap H_{k+j_1+\dots +j_{d-1}}^I.&lt;/math&gt;

The map &lt;math&gt;T_{I,J}&lt;/math&gt; is called a generalized pentagram map.{{Sfn|Khesin|Soloviev|2015a}} The original pentagram map is recovered by considering &lt;math&gt;d=2,I=(2),J=(1)&lt;/math&gt;.

Integrability can be numerically tested by picking a random polygon &lt;math&gt;P&lt;/math&gt; with [[wikipedia:Rational_point|rational coordinates]] and studying the growth rate of the [[wikipedia:Height_function|height]] of its iterates. This is called the [[wikipedia:Integrable_system#Diophantine_integrability|diophantine integrability]] test, and some generalized pentagram maps don't seem to pass it.{{Sfn|Khesin|Soloviev|2015a|loc=§5 and §6}} However, it is conjectured that the maps &lt;math&gt;T_{I,I}&lt;/math&gt; are integrable for any &lt;math&gt;I&lt;/math&gt;.{{Sfn|Bolsinov|Matveev|Miranda|Tabachnikov|2018|loc=conjecture 4.13 (B. Khesin, F. Soloviev)}}

Some of these maps are [[w:discretization|discretization]]s of higher dimensional counterpart of the [[w:Boussinesq approximation (water waves)|Boussinesq equation]] in the [[w:KdV hierarchy|KdV hierarchy]].{{Sfn|Khesin|Soloviev|2015b|loc=theorem 4.1}}{{Sfn|Izosimov|2022b|loc=theorem 4.1}}

==== Dented pentagram maps ====
Fix an integer &lt;math&gt;m\in \{1,\dots ,d-1\}&lt;/math&gt;. Consider the jump tuple &lt;math&gt;I_m:=(1,\dots,1,2,1,\dots,1)&lt;/math&gt;, where the &lt;math&gt;2&lt;/math&gt; is at the &lt;math&gt;m&lt;/math&gt;-th place, and the intersection tuple &lt;math&gt;J:=(1,\dots,1)&lt;/math&gt;. The dented pentagram map is &lt;math&gt;T_m :=T_{I_m,J}&lt;/math&gt;. They are proved to be integrable.{{Sfn|Khesin|Soloviev|2015b|loc=theorem 2.14}}

For an integer &lt;math&gt;p \geq 2&lt;/math&gt;, the deep dented pentagram map (of depth &lt;math&gt;p&lt;/math&gt;) &lt;math&gt;T_m^p&lt;/math&gt; is the same map as before, but the number &lt;math&gt;2&lt;/math&gt; in the definition of &lt;math&gt;I_m&lt;/math&gt; is replaced by &lt;math&gt;p&lt;/math&gt;. This kind of pentagram maps are integrable too.{{Sfn|Khesin|Soloviev|2015b|loc=theorem 6.2}}

=== Corrugated polygons ===
A twisted polygon &lt;math&gt;P&lt;/math&gt; lying in &lt;math&gt;\mathbb P^d&lt;/math&gt; is said to be corrugated if for any &lt;math&gt;k\in \mathbb Z&lt;/math&gt;, the vertices &lt;math&gt;v_k,v_{k+1},v_{k+d},v_{k+d+1}&lt;/math&gt; span a projective two-dimensional plane. Such polygons are not in [[w:general position|general position]]. A new point is defined by

: &lt;math&gt;T_\text{cor}v_k:=\overline{v_k v_{k+d}}\cap \overline{v_{k+1} v_{k+d+1}}.&lt;/math&gt;

The map &lt;math&gt;T_\text{cor}&lt;/math&gt; yields a new corrugated polygon. This dynamics is [[w:Integrable system#Hamiltonian systems and Liouville integrability|completely Liouville-integrable]].{{Sfn|Gekhtman|Shapiro|Tabachnikov|Vainshtein|2012|loc=theorem 4.4}}

In fact, they can be retrieved as some dented pentagram map applied on corrugated polygons.{{Sfn|Khesin|Soloviev|2015b|loc=theorem 5.3}}

=== Grassmannian polygons ===
Let &lt;math&gt;d \geq 3, m \geq 1&lt;/math&gt; be integers. The pentagram map can also be generalized to the [[w:Grassmannian|Grassmannian]] space &lt;math&gt;\mathrm{Gr}(m,md)&lt;/math&gt;, which consists of &lt;math&gt;m&lt;/math&gt;-[[w:Dimension (vector space)|dimensional]] [[w:linear subspace|linear subspace]]s of an &lt;math&gt;md&lt;/math&gt;-dimensional [[w:vector space|vector space]]. When &lt;math&gt;m=1&lt;/math&gt;, the linear subspaces are [[w:Vector space#vector line|lines]], which retrieves the definition of [[w:projective space|projective space]]s &lt;math&gt;\mathbb P^d&lt;/math&gt;.{{Sfn|Felipe|Marí-Beffa|2019|loc=§2 definitions and notations}}

A point &lt;math&gt;v\in\operatorname{Gr}(m,md)&lt;/math&gt; is represented by an &lt;math&gt;md \times m&lt;/math&gt; matrix &lt;math&gt;X_v&lt;/math&gt; such that its columns form a [[w:Basis (linear algebra)|basis]] of &lt;math&gt;v&lt;/math&gt;. Consider the [[w:Group action|action]] of the [[w:general linear group|general linear group]] &lt;math&gt;\mathrm{GL}_{md}&lt;/math&gt; by multiplication on the left of &lt;math&gt;X_v&lt;/math&gt;. This defines an action on the Grassmannian, even though it is not [[w:Faithful action|faithful]].{{Efn|Because there can be many lifts for &lt;math&gt;v&lt;/math&gt;, and because some matrices act trivially.}} Hence, the polygons of &lt;math&gt;\mathrm{Gr}(m,md)&lt;/math&gt; and their moduli spaces are defined as before, after the change of underlying group.{{Sfn|Felipe|Marí-Beffa|2019|loc=§2 definitions and notations}}

Depending on the parity of &lt;math&gt;d&lt;/math&gt;, one can define linear subspaces spanned by some &lt;math&gt;X_{v_k}&lt;/math&gt;'s such that taking their intersection generically defines a new point &lt;math&gt;v\in\mathrm{Gr}(m,md)&lt;/math&gt;.{{Sfn|Felipe|Marí-Beffa|2019|loc=sections 4 and 5}} This generalization of the pentagram map is integrable in a [[w:noncommutative|noncommutative]] sense.{{Sfn|Ovenhouse|2020}}

=== Over rings ===
The pentagram map admits a generalization by considering [[w:Projective space#Generalizations|projective planes]] over [[w:stably finite ring|stably finite ring]]s, instead of [[w:Field (mathematics)|field]]s. In particular, this retrieves the pentagram map over Grassmannians. Again, it admits a [[w:Lax representation|Lax representation]].{{Sfn|Hand|Izosimov|2025}}

== Acknowledgments ==
The author thanks the four referees and an anonymous Wikipedia contributor for their thorough reviews. The author also thanks every [[xtools:articleinfo/en.wikipedia.org/Pentagram_map|contributors of the original Wikipedia article]], in particular Richard Schwartz who expanded it in 2011. The work of the author was supported in part by the French National Research Agency under the project DynAtrois (ANR-24-CE40-1163).

== References ==
{{reflist|25em}}

===Notes===
{{notelist}}

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'''NVO987 – Art History'''

I am an independent researcher and editor working under the name NVO987.

My research focuses on modern and contemporary art, visual culture, colour theory, colour perception, and algorithmic image culture.

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* [[wikidata:Q141299513|Children's Color Acquisition Across Cultural Environments in the Age of Algorithms]]

== Research and Learning ==

This user page presents research interests and learning resources related to art history, visual culture, colour, perception, culture, and technology.

== NVO987 ==

NVO987 is the working name used for research and editorial activities in art history and visual culture.</text>
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      <text bytes="43293" sha1="2v9t0mrj8exxov842ctbwf45wwumt5n" xml:space="preserve">[[File:Pharoah - James VI and I - Trump.png|thumb|Religious and media leaders from the time of the Pharaohs convinced common folk to give increasing shares of what they produced to elites.]]
:''This book uses dates in [[:w:ISO 8601|ISO 8601]], YYYY-MM-DD, when convenient.'' 

== Invitation to edit this book ==

You, dear reader, are invited to contribute questions, ideas and citations to support or refute claims made in this book possibly adding chapters. Wikiversity like other Wikimedia Foundation Projects invites humans to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] while writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]]. Others are invited to change or revert what you wrote. What stays tends to be written from a neutral point of view citing credible sources. If someone reverts your edit or you have a question, take it to the ''[[Wikiversity:FAQ|''''“Discuss”'''' page]]'' associated with the specific Wikiversity page most related to your concerns. 

Those who teach media literacy are encouraged to invite their students to debate and revise the contents of this book. Doing so would build on a tradition of [[:w:Wikipedia:Student assignments|instructors requiring students to edit wikipedia article(s).]]  Editing [[:w:Wikipedia|Wikipedia]] and other [[:w:Wikimedia Foundation|Wikimedia Foundation]] projects like this book is itself an exercise in media literacy: 

:''Central tenets of media literacy might include writing from a neutral point of view citing credible sources and engaging others, some of whom may disagree, in civil, supportive conversations about what can and cannot be said based on a reasonable evaluation of the available evidence. Wikimedia rules invite contributors to do just that, encouraging them to “be bold but not reckless,” contributing revisions written from a neutral point of view, citing credible sources -- and raising other questions and concerns on the ''''“Discuss”'''' page associated with the specific Wikiversity page most related to your concerns, as mentioned above.''&lt;ref&gt;For more on this, see Graves (2024).&lt;/ref&gt; 
== Text and self-help book and point of discuss ==

This book is intended both as a text and self-help book and as a point of discussion considering four levels of media literacy: 

:1. '''Think before you share''': [[Facebook whistleblower Frances Haugen says|Facebook whistleblower Frances Haugen said]], &quot;The shortest path to a click is anger or hate.&quot; The social psychology behind this phenomenon exploited also by legacy media has contributed to [[Media Literacy and You/Media consolidation, social media, and political polarization|the dramatic increase in political polarization and violence worldwide]], especially since the end of the [[w:Fairness doctrine|Fairness doctrine]] in 1987. To counter this, DiResta (2024, p. 335) recommends, &quot;Think before you share.&quot;
:2. '''Look for information to contradict preconceptions''' (Disconfirmation bias): [[w:Information is a public good: Designing experiments to improve government#Previous research|Virtually everyone]] (a) thinks they know more than they do ([[w:Overconfidence effect|overconfidence effect]]), and (b) prefers information and sources consistent with preconceptions ([[w:Confirmation bias|confirmation bias]]). The major media everywhere exploit this to please those who control most of the money for the media. Humans can counter this by searching for sources to help us understand our designated enemies. If we cannot explain circumstances under which we could see ourselves doing what we see our designated enemies doing, we haven't looked hard enough. 
:3. '''Talk''': Push ourselves to have friendly supportive conversations with others with whom we may vehemently disagree with the goals of agreeing to disagree agreeably and building collaboration on areas of common concern.&lt;ref&gt;Graves and Bailey (2025).&lt;/ref&gt;  
:4. '''Teach''': Humans who develop skills in the first three levels can leverage that knowledge in helping others acquire those skills. If each one teaches two&lt;ref&gt;&quot;[[:w:Each one teach one|Each one teach one]]&quot; is an African-American proverb from the time of legalized slavery. However, if each one teaches only one, the growth in literacy will only be linear. Having &quot;each one teaching two&quot;, on average, unleashes the power of doubling and [[:w:exponential growth|exponential growth]], which has the potential of educating the entirety of humanity in a reasonable period of time -- namely after 33 doublings starting from one.&lt;/ref&gt; in a certain period of time, that time period becomes a [[:w:Doubling time|doubling time]]. Ten doublings is a thousand -- actually 1,024 to be precise.&lt;ref&gt;2 time 2 = 4 times 2 = 8 times 2 = 16 times 2 = 32 times 2 = 64 times 2 = 128 times 2 = 256 times 2 = 512 times 2 = 1024: That's 10 doublings, as anyone with a modest understanding of modern digital [[:w:computer|computer]]s will tell you.&lt;/ref&gt; Twenty doublings become a million. Thirty doublings become a billion. Three more doublings become 8 billion, the [[:w:World population|world population]] as of approximately 2022-11-15.&lt;ref&gt;This book uses dates in [[:w:ISO 8601|ISO 8601]], YYYY-MM-DD, when convenient.&lt;/ref&gt; Many organizations, including several United Nations agencies, already have active [[w:media literacy|media literacy]] programs that have already trained many.&lt;ref&gt;''[[Wikibooks:Antiracist Activism for Teachers and Students]]'' includes a chapter on [[Wikibooks:Antiracist Activism for Teachers and Students/Points to Consider for Teaching Anti-racism/Media Literacy In Schools|Media Literacy In Schools]].&lt;/ref&gt; This book is being written hoping to increase the effectiveness and accelerate the rate of growth in media literacy and thereby accelerate progress against many of the most pressing issues facing humanity today.

Much of this book is a [[w:Monograph|research monograph]] summarizing research that seems to have been underreported by the major media to avoid offending people who control most of the money for the media. These research results seem to be central to major political divisions. Each chapter ends in exercises to help the reader practice media literacy skills and have fun doing it. Remember: 

:''I am entitled to my [[Wiktionary:cockamamie|cockamamie]] ideas, and you are entitled to yours.''

Humor is important but must be offered in a way that does not offend others. If others are offended, they may be less interested in dialogue. The term &quot;cockamamie&quot; is used here, hoping that this style of [[w:Self-deprecation|self-deprecation]] might be more inviting for dialogue.

''Never say, &quot;You're wrong.&quot; Instead, ask, &quot;May I offer a contrary perspective?&quot; Or &quot;May I share with you another view that I've heard?&quot;''

Much of the information in this book seems to have been largely overlooked and perhaps suppressed, apparently because it would either offend people who control substantial portions of the money for the media our would increase the cost of producing news; see the brief discussion of conflicts of interest by the major media in the next &quot;Key claims&quot; section.

==Key claims==

* ''Primary drivers of every major conflict include differences between the media or difference in interpretation that the different parties find credible''.
:-- This works, because everything we think we know is coded in systems of connections between neurons in our brains. These systems are more unique than fingerprints and evolve over time. The words we use do not mean the same to two different humans nor even to the same human at different points in time. In many cases these differences are inconsequential. ''Sometimes they are fatal.''&lt;ref&gt;Graves and Bailey (2026).&lt;/ref&gt;
:-- ''[[w:Social constructionism|Show me someone who knows the truth]], and I will show you someone who is dangerous'' -- especially during war or any other situation where humans may be moved to violence mandated by their belief system.&lt;ref&gt;[[w:Collateral damage|Collateral damage]] that &quot;they&quot; commit proves to &quot;us&quot; that &quot;they&quot; are subhuman or at best criminally misled and must be resisted by any means necessary. By contrast, collateral damage that &quot;we&quot; commit is unfortunate but necessary.&lt;/ref&gt;
* The major media everywhere have [[w:Conflict of interest|conflicts of interest ]] in honestly reporting on [[v:Information is a public good per communications prof Pickard|anything that might offend anyone who controls large portions of the money for the media]].&lt;ref&gt;Pickard and Graves (2025), accessed 2026-02-08; Pickard (2020).&lt;/ref&gt; [[v:Media Reform Coalition challenges anti-democratic media bias in the UK|British journalist and media reform advocate Dan Hind]] said that the content produced by the [[w:BBC|BBC]] was frivolous, soap opera stuff, because leading media personalities know very little about issues of substance and believe &quot;they might get in trouble if&quot; they produced anything serious. Similar analyses seem to apply to the major media everywhere&lt;ref&gt;Hind and Graves (2025), accessed 2026-02-09.&lt;/ref&gt; but may not apply to non-profit and local media, which seem more likely to produce [[w:Investigative journalism|investigative]] / [[v:Dean Starkman and the watchdog that didn't bark|accountability journalism]]:&lt;ref&gt;Usher and Kim-Leffingwell (2022); see also Starkman and Graves (2025), accessed 2026-02-09.&lt;/ref&gt; [[w:Watchdog journalism|Watchdogs]] tend to protect the people who feed them. Argentine journalist [[w:Horacio Verbitsky|Horacio Verbitsky]] said, &quot;Journalism is disseminating information that someone does not want known; the rest is [[w:propaganda|propaganda]].&quot;&lt;ref&gt;p. 16 in Verbitsky (1997); English translation from [[Wikiquote:Horacio Verbitsky]], accessed 2026-02-09.&lt;/ref&gt;
* The major media everywhere create the stage upon which politicians read their lines. 
:-- Their selection of acceptable topics for news and entertainment create and maintain the &quot;[[w:Overton window|Overton window]]&quot;, which is the range of acceptable political discourse. For example, in early 1964, US President [[w:Lyndon B. Johnson|Lyndon Johnson]] understood that he could lose the 1964 presidential election that year if he were seen to be soft on communism. His response was to clandestinely provoke an attack on US naval vessels in the Gulf of Tonkin, which he could then denounce as &quot;unprovoked&quot;. During a dark and stormy night 1964-08-04 the [[w:USS Maddox (DD-731)|USS ''Maddox'']] and [[w:USS Turner Joy|''Turner Joy'']] spent a couple of hours &quot;defending themselves&quot; against radar snow, then [[w:Gulf of Tonkin incident|reported that they had sunk two attacking North Vietnamese torpedo boats]]; subsequent investigations found no evidence of the reported attacks. That incident was used to justify the [[w:Gulf of Tonkin Resolution|Gulf of Tonkin Resolution]], with only two dissenting votes in the US Congress: Those two dissenters were defeated in their next reelection campaigns, illustrating the point that the major media create the environment in which many politicians cannot get elected without betraying the nation. 
:-- Nick Hart,&lt;ref name=Hart&gt;&lt;!--Nick Hart--&gt;{{cite Q|Q135663983}}&lt;/ref&gt; President and CEO of the Data Foundation,&lt;ref&gt;&lt;!--Data Foundation--&gt;{{cite Q|Q134705118}}&lt;/ref&gt; noted that President Trump in his first term signed the [[w:Foundations for Evidence-Based Policymaking Act|Foundations for Evidence-Based Policymaking Act]], which was bipartisan legislation ostensibly mandating evidence-informed public policy.&lt;ref&gt;Hart mentioned the [[w:Foundations for Evidence-Based Policymaking Act|Foundations for Evidence-Based Policymaking Act]] when he was interviewed for [[Evidence-informed public policy|&quot;Media &amp; Democracy&quot; 2025-07-31]].&lt;/ref&gt; The evidence is clear:

::''The US Congress is effectively not allowed to consider solid research suppressed by the major media.'' 

* The development of technology is never neutral in its impact on inequality but is driven to benefit people with power.&lt;ref&gt;Acemoglu and Johnson (2023)&lt;/ref&gt;. 
:-- [[Media Literacy and You/The impact of the media on political economy since the time of the Pharaohs|Improvements in agricultural technology from pre-history to the time of King James of the King James bible were managed to benefit elites.]] Then pamphlets and newspapers began to appear, the head of state stopped granting as many monopolies, and commoners began getting permission to become entrepreneurs. That transformed economic stagnation into growth in GDP per capita adjusted for inflation, initiating the [[w:Industrial Revolution|Industrial Revolution]], as documented in the chapter below on [[/The impact of the media on political economy since the time of the Pharaohs/]]. It also led to increasing inequality until organized labor got enough political power to demand and get a bigger share of the fruits of their labors. 
:--[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|In the US those benefits peaked during the Great Depression]], when the standard conservative mantra that blames the poor for their poverty did not sell newspapers. US President Franklin Roosevelt taxed the ultra-wealthy like they had never been taxed before or since, and dramatically reduced inequality, which continued to decline until increasing concentration of ownership of the media ushered in a new era of increasing inequality starting with the presidency of Ronald Reagan. 
:-- [[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future#Role of the media|Acemoglu and Johnson insist that technology, including artificial intelligence, can be developed to benefit all. However, but it will not happen without action by the poor and middle class as follows]]: 
:# Alter the narrative, 
:# Build countervailing powers [like organized labor], and 
:# Develop technical, regulatory, and policy solutions to tackle specific aspects of technology’s social bias.&lt;ref&gt;Acemoglu and Johnson (2023, ch. 11).&lt;/ref&gt;
:-- For more on this, see, e.g., the chapter on [[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Fox, the Great Depression, the Great Recession, and our future]]. 

=== The value of noncommercial news outlets ===

Some of the problems with the media and their contributions to increasing political polarization and violence are documented in the research summary on &quot;[[Information is a public good: Designing experiments to improve government]]&quot; and in the podcast series available on Wikiversity under &quot;[[:Category:Media reform to improve democracy]]&quot; with leading experts discussing their recommendations. One of the most compelling of the references discussed in that podcast series is Usher and Kim-Leffingwell (2022), who tallied all the federal prosecutions for political corruption in each of the 94 [[w:United States federal judicial district|US federal court district]]s between 2003 and 2019. During that period, the number of journalists in the US fell by a factor of roughly 3 -- between 60 and 70 percent. They found no statistically significant impact on federal prosecutions for political corruption of that decline in the number of journalists. 

However, each member of the [[w:Institute for Nonprofit News|Institute for Nonprofit News]] (INN) in a federal court district in one year was associated with on average 1.4 additional prosecutions for political corruption the following year. 

This suggests that the major media outlets that had so dramatically reduced their staffs had not substantively reduced the amount of investigative journalism they did. If we assume that the people prosecuted for political corruption also control substantive advertising budgets, then the major media outlets have conflicts of interest in honestly reporting on such. They may report on it if some other organization like a member of INN does the research and they are threatened with a loss of audience from not reporting on it. 

:'''''Major point''''': You and I benefit, the vast majority of humans on earth benefit, from news reports presumably published by members of INN that contributed to those on average 1.4 additional prosecutions for political corruption estimated by Usher and Kim-Leffingwell (2022). We benefit even if we never heard about the news reports that contributed to those prosecutions. We benefit even if we have never heard of the news outlets that presumably did the investigative journalism behind those additional prosecutions. Why? Because on average those news reports likely deterred other incidents of political corruption, which likely contributed to broadly shared economic growth and the development of new technology that ultimately benefit the vast majority of humanity. Other aspects of this are documented in the research on the impact of [[w:news desert|news desert]]s, which we summarize next.

=== Costs increase in news deserts===

There's a growing body of research describing what happens when local newspapers die. 

Perhaps most important, a 2018 research report by Gao et al. reported that the death of a local newspaper was followed by … increases in local tax revenue, averaging $85 per human per year.&lt;ref name = Gao2018&gt;Gao et al. (2018).&lt;/ref&gt; That $85 was roughly 13 hundredths of a percent of the 2019 US GDP. That's mentioned in the 2025-07-17 interview with [[Democratic delusions: Fix the media to fix democracy|Natalie Fenton about her new book, ''Democratic Delusions, How the Media Hollows out democracy and What We Can Do About It'']].

One of the most spectacular example of the cost of a news desert is the [[w:City of Bell scandal|Scandal of Bell, California]]. Their local newspaper died around 1999. Roughly a decade later the city was nearly bankrupt in spite of having property tax rates among the highest in the nation. An investigation by the ''[[w:Los Angeles Times|Los Angeles Times]]'' documented that the city manager had a compensation package worth $1.5 million a year, well over double that of the President of the United States. Other senior city officials were similarly well-remunerated. Some of the city officials went to jail over that. Did the city manager decide after 1999, &quot;Wow: The watchdog is dead. Let's have a party&quot;? 

Malfeasance also increases in business as pollution and workplace accidents increase as does the cost of capital, because investors know their money is not as secure without a local newspaper. That leads to a reduction in investments in new products, services and processes -- slowing economic growth. See &quot;[[Local newspapers limit malfeasance]]&quot;, esp. Kim et al. (2021). 

And executive compensation in increases in nonprofits, so less of what people donate goes to the charitable purpose for which they donated, according to Felix et al. (2024). Also, voter participation and split-ticket voting decline, per Benton (2019) and other references discussed in &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. And the ultra-right does better, as noted in [[News from Germany 1900-1945 and implications for today]] and the section on &quot;[[Information is a public good: Designing experiments to improve government#Previous research|Previous research]]&quot; in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;.&lt;ref&gt;Flößer (2024).&lt;/ref&gt; 

The 0.13 percent of GDP savings estimated by Gao et al. (2018) is roughly $120 per human per year. With over 300 million humans in the U.S, that is roughly $40 billion nationwide. 

{| class=&quot;wikitable&quot;
|+ Table 1. Costs increase in news deserts
|- 
! Entity !! What !!Source
|-
| local government || costs incr. 0.13% of GDP || Gao et al. (2018)
|- 
| local businesses || pollution &amp; workplace accidents incr., innovation &amp; econ growth decr. || Kim et al. (2021)
|- 
| nonprofits || exec. compensation incr. || Felix et al. (2024) 
|- 
| rowspan=2 | elections
| voter participation &amp; split-ticket voting decl. || Benton (2019)
|-
| Ultra-right does better || Flößer (2024)
|}

=== Government subsidies for news === 

John (1995) documented how in the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;This is discussed in the 2025-06-08 [[Media concentration per Columbia History Professor Richard John|interview with him]], available on Wikiversity under [[:Category:Media reform to improve democracy]], accessed 2026-04-30.&lt;/ref&gt; This encouraged literacy and limited political corruption, both of which helped [[The Great American Paradox|the early United States stay together and grow]]  while contemporary [[w:New Spain|New Spain]] / [[w:Mexico|Mexico]], fractured, shrank, and stagnated economically. As documented with Figure 1 in the chapter below on [[/The impact of the media on political economy since the time of the Pharaohs/]], that growth catapulted the young United States into its current position of dominance in the international political economy, a position it has been losing since at least 1990 -- or since the Reagan Revolution began in 1981, according to the analysis in the chapter below on [[/Fox, the Great Depression, the Great Recession, and our future/]]. Other countries now have stronger democracies due in part to government subsidies for media in the range of 0.05 and 0.25 percent of GDP with a firewall that limits political interference in the content, according to Neff and Pickard (2024). Table 1 in &quot;[[Information is a public good: Designing experiments to improve government]] compares media subsidies in various places with &quot;other points of reference&quot;.  

McChesney and Nichols (2010, pp. 310-311, note 88) suggested that the relatively high rate of economic growth of the economy in the early US was due in part to postal subsidies under the US [[w:Postal Service Act|Postal Service Act]] of 1792.&lt;ref&gt;See also the Wikiversity article on &quot;[[The Great American Paradox]]&quot;, accessed 2026-04-30.&lt;/ref&gt; They estimated those subsidies at 0.21 percent of GDP. To improve the current political economy of the US, they recommended subsidies of 0.15 percent of GDP distributed to local news nonprofits on the basis of local elections.&lt;ref&gt;McChesney and Nichols (2021, 2022).&lt;/ref&gt; The Wikipedia article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot; documents how some jurisdictions can devote that much money to local news nonprofits by matching what they spend on accounting, advertising, and public relations.&lt;ref&gt;See the section on &quot;[[Information is a public good: Designing experiments to improve government#Sampling units / experimental polities|Sampling units / experimental polities]]&quot; in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;, accessed 2026-04-30.&lt;/ref&gt;  

Pickard (2023) describes three basic strategies for confronting concentrated commercial media power: (1) break them up, (2) regulate them, and (3) create non-commercial, public alternatives. A fourth possibility might be [[w:externality|a graduated tax on income and wealth]] in proportion to the threat that major corporations pose to democracy. 

One class of noncommercial alternatives that Pickard mentions is local multimedia / Public Media Centers (PMCs) with management split between local journalists and boards, e.g., selected at random from registered voters. A key here is to have the boards selected in a way that cannot be influenced by people with power, whether business or political elites. Picard recommends considering '''six discrete layers''' when discussing PMCs, each of which, he says, must be radically democratised: 
# funding, 
# governance, 
# ascertainment (to determine a community’s ''critical information needs''), 
# infrastructure (including universal broadband service), 
# algorithmic (e.g., not allowing companies like Google and Facebook to suppress indexing information the might challenge their hegemony of those markets, [[w:Deep web|treating them like pedophilia and the Islamic State]]), 
# engagement, involving local communities in making their own news and in communicating their own stories; this is paramount to building trust and the grassroots-level support that this new local journalistic model requires.

All this needs to be managed in ways that provide substantive support to news deserts and underserved communities that have long been subjected to various kinds of informational redlining. This might be done by including the proposed PMCs within local libraries staffed by professional journalists, who provide training in media literacy in local schools for children and supervise students producing school newspapers. PMCs could host regular, e.g., monthly events, where local residents could share their concerns with journalist, who would use that input to help prioritize different issues for news coverage. Journalist could also coach local residents in how to research issues and collaborate with journalists in producing news reports that may be better researched and more relevant to local concerns than could be produced without such collaboration.

Management of such PMCs might be split between journalists on staff and boards of, e.g., six members selected at random from voter registration rolls serving staggered terms of one year with a new member rotated in every 2 months.  

Another alternative that could be done in parallel with local PMCs calls for 200 journalists in each US Congressional district funded at $10 billion annually in 2022 dollars, which is just a little under 4 hundredths of one percent of GDP; if such allocations are expressed as fractions of a percent of GDP, they would grow naturally with the economy. (The nominal GDP for the US was roughly $26.1 trillion in 2022.&lt;ref&gt;Johnston and Williamson (2026).&lt;/ref&gt; For 2026 it is estimated at $32.4 trillion.&lt;ref&gt;[[w:United States|United States]], accessed 2026-04-30.&lt;/ref&gt;) 

A similar model is the [[w:BBC|BBC]]’s Local Democracy Reporting Service (LDRS), in which the BBC funds journalists to cover the work of local councils and other local public bodies, funded at £8 million per year, which is a little under 2 hundredths of a percent of the [[w:United Kingdom|UK]]'s GDP of £7.27 trillion.&lt;ref&gt;[[w:United Kingdom|United Kingdom]], accessed 2026-04-30.&lt;/ref&gt; 

Pickard (2023) ended by saying, &quot;Today we face a crossroads: technocracy and oligarchy from above or radical democracy and structural reform from below. ... [T]his is not just a journalism crisis: it is a
democracy crisis.&quot;

==Table of Contents==
*[[/Introduction/]] including an exercise, asking all to discuss perceptions of the settlement of ''[[w:Dominion Voting Systems v. Fox News Network|Dominion Voting Systems v. Fox News Network]]'' in a friendly supportive manner with humans with whom they may vehemently disagree, because the alternative could be killing humans over misunderstandings. 

===Part I. The media and political economy===
# [[/The impact of the media on political economy since the time of the Pharaohs/]] describes how religious leaders in hierarchical societies prior to [[w:James VI and I|King James of the King James bible]] convinced commoners to live in poverty while giving increasing shares of what they produced so religious and secular elites could live in opulence. During the reign of King James, pamphlets and newspapers began to compete with the church for helping commoners understand their roles in society. This produced the Industrial Revolution and modern democracies. Media consolidation since World War II slowed, then reversed this trend. 
# [[/Fox, the Great Depression, the Great Recession, and our future/]] describes the unprecedented performance of the US political economy during the presidency of Franklin Roosevelt (FDR), insisting that much of what FDR achieved can be replicated, giving a media system that supports honest discussion of the available evidence. 
# [[/Media consolidation, social media, and political polarization/]] (Combine from McChesney and Nichols discussing the [[w:Postal Service Act|US Postal Service Act]] of 1792 with [[Media concentration per Columbia History Professor Richard John]], the section on &quot;[[v:Information is a public good: Designing experiments to improve government#Threats from social media|Threats from social media]]&quot; in &quot;[[Information is a public good: Designing experiments to improve government]], and the comments by [[v:Facebook whistleblower Frances Haugen says|Facebook whistleblower Frances Haugen that, &quot;the shortest path to a click is anger or hate.&quot;]].

===Part II. The media and war===
# [[/Deterrence without threat/]]: The historical record is clear: Nations that have prepared for war often got war, not peace. This happens for at least two reasons: First, some leaders cannot resist the temptation to use force inappropriately, sometimes clandestinely provoking others to do things that are then denounced as &quot;unprovoked&quot;; sometimes the media environment pushes them to do such. Alternatively, potential adversaries may believe -- or claim -- that you are actually preparing a first strike, and they must move preemptively or lose their ability to retaliate adequately. We can avoid these possibilities with three supportive policies: [a] Legislation that ''prohibits'' projecting force beyond our own borders. [b] Civilian-based defense training in nonviolent noncooperation like what helped Denmark survive Nazi occupation with minimal damage. And [c] a media system that penalizes rather than encourages a bellicose foreign policy.  
# [[/Responding to a nuclear attack/]]: The ''worst'' response to a nuclear attack would be a nuclear response: The death toll from the 1945 [[w:Atomic bombings of Hiroshima and Nagasaki|Atomic bombings of Hiroshima and Nagasaki]] was estimated at between 150,000 and a quarter of a million. By contrast, simulations of nuclear wars of different magnitudes estimated that between 4 and 95 percent of humanity around the world would starve to death if they did not die of something else sooner. The range depends on whether the war was &quot;limited&quot;, e.g., between India and Pakistan, and massive between the US and Russia. (Also add material from [[Nuclear weapons and effective defense]]). 
# [[/Threats from excessive government secrecy/]] (draft in [https://sanjosepeace.org/restrict-secrecy-more-than-data-collection/ &quot;Restrict secrecy more than data collection&quot;], adding material from [https://kkfi.org/program-episodes/does-us-government-secrecy-threaten-national-security/ Connelly (2023) ''The Declassification Engine: What History Reveals About America's Top Secrets''], [[Wikipedia:Moynihan Commission on Government Secrecy]] and [[1998 Embassy bombings and September 11]].
# [[/Shouting fire in a crowded theater/|Shouting ''fire'' in a crowded theater]]: Legal concerns about &quot;[[w:Shouting fire in a crowded theater|Shouting ''fire'' in a crowded theater]]&quot; date, at least in large part, from the [[w:Supreme Court of the United States|US Supreme Court]] decisions in ''[[w:Schenck v. United States|Schenck v. United States]]'' (1919) and ''[[w: Brandenburg v. Ohio| Brandenburg v. Ohio]]'' (1969). In ''Schenck'' the Court ruled that the government had a right to imprison Schenck and others, because their distribution of fliers encouraging draft resistance presented a [[w:clear and present danger|clear and present danger]] to the efficacy of ongoing military activities during [[w:World War I|World War I]], then in progress. The Court in ''Brandenburg'' held that the government cannot punish inflammatory speech ''unless that speech is &quot;directed to inciting or producing imminent lawless action and is likely to incite or produce such action&quot;.'' Some could argue that many uses of military force by the US and Israel since 1948 have violated international law, encouraged by biases in the major US media &quot;directed to inciting or producing imminent lawless action&quot;, though it may not be feasible to convince a court of that. Still, it might be useful to simulate such a case in a mock trial like the 1966 [[w:Russell Tribunal|Russell Tribunal]].&lt;ref&gt;Andersen (2006) provides such documentation for several such uses of force. Johnson (2026) ''How to Sell a Genocide: The Media's Complicity in the Destruction of Gaza'' organizes evidence supporting such claims for the current [[w:Gaza war|Gaza war]], which began with [[w:October 7 attacks|Palestinian attacks 2023-10-07]]. See also Andersen (2026). Might, e.g., Palestinians -- or at least Palestinian Americans -- be able to sue the [[w:Anti-Defamation League|Anti-Defamation League]] (ADL), the [[w:AIPAC|American Israel Public Affairs Committee]] (AIPAC), and all the major media outlets in the US for inciting genocide in the current [[w:Gaza war|Gaza war]]? That history includes routine suppression of coverage by the major media especially in the US of routine denial of equal protection of Israeli laws to non-Jews in Israel and under Israeli occupation, including suppression of Israeli violence against nonviolent protestors peaceably assembling and petitioning for a redress of grievances combined with over reporting of Palestinian violence and unquestioning coverage of fraudulent claims of Palestinian violence by Israel and supporters. The suppressions included underreporting of Palestinian nonviolence such as the [[w:2018–2019 Gaza border protests|(2018-2019) Great March of Return]], and suppression of the grievances inspiring such nonviolence such as indefinite detention without charges of thousands of Palestinians, including children, routine destruction of Palestinian property by settlers, confiscation of Palestinian property at gunpoint, closing [[w:Gaza Strip|Gaza]] to international trade, and maintaining Gaza on starvation rations. These routine biases in reporting have been encouraged by charges that more honest reporting would be &quot;[[w:Antisemitism|antisemetic]],  according to the ADL and AIPAC. This denial of coverage thereby encouraged Israel to increase the rate of such violations until the [[w:October 7 attacks|2023-10-07 attacks on Israel from Gaza]] unleashed Israeli &quot;retaliations&quot; way out of proportion to the alleged provocation. Sucharov (2022) reported that 69% of American Jews opposed privileging Jews over non-Jews in Israel. Their support of Israel in the current Gaza war is consistent with the media biases documented by Johnson (2026) and others including Andersen (2006, 2026). Regarding whether Israel could achieve anything positive from this war, Samuelson (2025) is skeptical. He summarized quantitative analyses of 60 previous insurgencies. The results including the observation that it is exceedingly difficult to defeat an insurgency without responding to the grievances that support it without force ratios far beyond Israel's resources.&lt;/ref&gt;

===Part III. Climate, immigrants, education, public health, and criminal justice===
# [[/Global warming/]] [Summarize research especially on conflicts of interest of major media in honestly reporting on this issue and the research on global warming itself and activities of groups concerned about this issue. Decompose into global population times CO2 equivalents per human.] 
# [[/Immigrants/]] [Summarize research documenting that [[w:Sanctuary city|sanctuary cities tend to have higher median incomes and no more crime than non-sanctuary jurisdictions]], and some studies report less crime. Moreover economists have documented that immigrants tend to be more entrepreneurial, overrepresented in patent applications, and generally increasing the rate of economic growth. See, e.g., Aghion et al. (2022) ''The power of creative destruction''; Aghion shared the 2025 Nobel Memorial Prize in Economics with two others.] 
# [[/Education/]] (draft in [[Invest in children]].) 
# [[/Public health/]] [Draft in [[UN public health data]] to be revised to be consistent with Bezruchka (2023, 2025).]
# [[/Substance abuse and addictive behavior/]] (Research cited in &quot;[[Wikipedia:War on drugs]]&quot; insists that the US and the world would have fewer problems with substance abuse and addiction problems with 100 percent public funding for treatment programs and complete decriminalization of possession and use of retail quantities of addictive substances. We would also likely have fewer problems with immigrants, as that would make it harder for the US to intervene in the internal affairs of foreign countries funded off the books, as exposed in the [[w:Iran–Contra affair|Iran–Contra affair]]. See [[w:Alfred W. McCoy|Alfred W. McCoy]] (1972; 3rd ed. 2003) ''The politics of heroin''. Journalist [[w:Gary Webb|Gary Webb]] published similar claims that the US intervention in Nicaragua in the Iran-Contra Affair was funded in part by drug money. The story was officially retracted by the ''San José Mercury News'', and Webb allegedly killed himself with 2 bullets to the head.
# [[/Criminal justice/]] (The section on &quot;[[w:United States incarceration rate#Editorial policies of major media|Editorial policies of major media]]&quot; in &quot;[[Wikipedia:United States incarceration rate]]&quot; cites research claiming that within the range range of experience in the US political economy since 1925, the incarceration rate is uncorrelated with crime: It's a function of the public's perception of crime, and that's a function of the media. That suggest that the US would be safer and more prosperous if incarceration policies were driving more by research than by editorial policies of the media. For example, there is also research that says that incarcerees who receive visits are less likely to recidivate, but that evidence is overlooked when convicts are incarcerated substantial distance from their family and friends and when the cost of phone services is substantially higher for incarcerees than among the general pubic. Also, it's known that better educated incarcerees are less likely to recidivate, but it's difficult and maybe impossible for many incarcerees to obtain education in prison.) 
# [[/Empower women and girls/]] [Cite research claiming that a primary restraint on population growth is empowering women and girls. Empowering women and girls is not just a matter of equity: It is also a means to reduce the threats of global warming, of increasing exposure to animal diseases and other problems that come with unrestrained population growth.]

=== Continuation ===

* [[/The evolving media literacy movement/]] to invite others to keep this book current with the evolving understanding of media literacy, how to encourage and promote it and the benefits of doing so.

==See also==

* [[Wikibooks:Antiracist Activism for Teachers and Students/Points to Consider for Teaching Anti-racism/Media Literacy In Schools]]

==Notes==
{{reflist}}
	
==Bibliography==

* &lt;!--Daron Acemoğlu and Simon Johnson (2023) Power and Progress--&gt;{{cite Q|Q125292212}}
* &lt;!--Robin Andersen (2006)  A century of media, a century of war--&gt;{{cite Q|Q138795568}}
* &lt;!--Robin Andersen (2026-06-02)  The Complicit Lens: US Media Coverage of Israel’s Genocide in Gaza--&gt;{{cite Q|Q138796307}}
* &lt;!--Perry Bacon Jr. (2022-10-17) &quot;America Should Spend Billions to Revive Local News&quot;--&gt;{{cite Q|Q139594786}}
* &lt;!-- Joshua Benton (9 April 2019). &quot;When local newspapers shrink, fewer people bother to run for mayor&quot;. Nieman Foundation for Journalism --&gt;{{cite Q|Q63127216}}
* &lt;!--Stephen Bezruchka (2023) Inequality Kills Us All--&gt;{{cite Q|Q136047815}}
* &lt;!--Stephen Bezruchka (2025) ''Born Sick in the USA''--&gt;{{cite Q|Q138749292}} 
* &lt;!--Renée DiResta (2024) Invisible Rulers: The People Who Turn Lies into Reality--&gt;{{cite Q|Q135107164}}
* &lt;!--Robert Felix, Joshua A. Khavis, and Mikhail Pevzner (2024) &quot;The effects of local newspaper closures on nonprofits’ executive compensation&quot;--&gt;{{cite Q|Q132730972}}
* &lt;!--Maxim Flößer (2024-03-06) &quot;Keine Lokalzeitung -- mehr AfD&quot;, Kontext--&gt;{{cite Q|Q125287792}}
* &lt;!--Pengjie Gao, Chang Lee, and Dermot Murphy (2018) &quot;Financing Dies in Darkness? The Impact of Newspaper Closures on Public Finance&quot;--&gt;{{cite Q|Q55670016}}
* &lt;!--Spencer Graves (2024) &quot;Wikipedia: The most democratic force on earth--&gt;{{cite Q|Q137796922}}
* &lt;!--Spencer Graves and Bryan Bailey (2025)  &quot;We have to talk&quot;, blog at PeaceWorksKC.org--&gt;{{cite Q|Q136126262}}
* [[d:Q138038060|Dan Hind and Spencer Graves (2025) &quot;Media Reform Coalition challenges anti-democratic media bias in the UK&quot; on Wikiversity]].
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Adam H. Johnson (2026-04-21) How to Sell a Genocide: The Media's Complicity in the Destruction of Gaza--&gt;{{cite Q|Q140073447}}
* &lt;!--Louis Johnston and Samuel H. Williamson, &quot;What Was the U.S. GDP Then?&quot; MeasuringWorth, 2026--&gt;{{cite Q|Q56881105}}
* &lt;!-- Min Kim, Derrald Stice, Han Stice, and Roger M. White (2021)  &quot;Stop the presses! Or wait, we might need them: Firm responses to local newspaper closures and layoffs&quot;--&gt;{{cite Q|Q132459373}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2021). &quot;The Local Journalism Initiative: a proposal to protect and extend democracy&quot;. Columbia Journalism Review, 30 November 2021 --&gt;{{cite Q|Q109978060}}
* &lt;!-- Robert W. McChesney; John Nichols (2022), To Protect and Extend Democracy, Recreate Local News Media (PDF), FreePress.net (updated 25 January 2022) --&gt;{{cite Q|Q109978337|access-date=2024-06-23}}
* &lt;!--Alfred W. McCoy (2003-05-01)  The politics of heroin : CIA complicity in the global drug trade : Afghanistan, Southeast Asia, Central America, Colombia--&gt;{{cite Q|Q141317509}} 
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* [[d:Q131398359|Victor Pickard (2020) ''Democracy without journalism? : confronting the misinformation society'' (Oxford U. Pr.)]].
* &lt;!-- Victor Pickard (2023-05-12) &quot;Another Media System is Possible: Ripping Open the Overton Window, from Platforms to Public Broadcasting&quot;--&gt;{{cite Q|Q131398460}}
* &lt;!--Doug Samuelson (2025)  Assessing Israel’s Approach in Gaza--&gt;{{cite Q|Q138843324}} 
* [[d:Q138037937|Dean Starkman and Spencer Graves (2025) &quot;Dean Starkman and the watchdog that didn't bark anglais&quot; on Wikiversity]].
* &lt;!--Mira Sucharov (2022)  Do American Jews Really Know What 'Zionist' Means?--&gt;{{cite Q|Q125903777}}
* [[d:Q134715465|Nikki Usher and Sanghoon Kim-Leffingwell (2022) &quot;How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption&quot;, ''SSRN Electronic Journal'']].
* [[d:Q61013892|Horacio Verbitsky (1997) ''Un mundo sin periodistas'' (in Spanish: A world without journalists; Editorial Sudamericana)]].

[[Category:Communication]]
[[Category:Political science]]
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      <text bytes="43562" sha1="t4j2ti5r9qqug5hn8l75q3vzn3n3u7k" xml:space="preserve">[[File:Pharoah - James VI and I - Trump.png|thumb|Religious and media leaders from the time of the Pharaohs convinced common folk to give increasing shares of what they produced to elites.]]
:''This book uses dates in [[:w:ISO 8601|ISO 8601]], YYYY-MM-DD, when convenient.'' 

== Invitation to edit this book ==

You, dear reader, are invited to contribute questions, ideas and citations to support or refute claims made in this book possibly adding chapters. Wikiversity like other Wikimedia Foundation Projects invites humans to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] while writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]]. Others are invited to change or revert what you wrote. What stays tends to be written from a neutral point of view citing credible sources. If someone reverts your edit or you have a question, take it to the ''[[Wikiversity:FAQ|''''“Discuss”'''' page]]'' associated with the specific Wikiversity page most related to your concerns. 

Those who teach media literacy are encouraged to invite their students to debate and revise the contents of this book. Doing so would build on a tradition of [[:w:Wikipedia:Student assignments|instructors requiring students to edit wikipedia article(s).]]  Editing [[:w:Wikipedia|Wikipedia]] and other [[:w:Wikimedia Foundation|Wikimedia Foundation]] projects like this book is itself an exercise in media literacy: 

:''Central tenets of media literacy might include writing from a neutral point of view citing credible sources and engaging others, some of whom may disagree, in civil, supportive conversations about what can and cannot be said based on a reasonable evaluation of the available evidence. Wikimedia rules invite contributors to do just that, encouraging them to “be bold but not reckless,” contributing revisions written from a neutral point of view, citing credible sources -- and raising other questions and concerns on the ''''“Discuss”'''' page associated with the specific Wikiversity page most related to your concerns, as mentioned above.''&lt;ref&gt;For more on this, see Graves (2024).&lt;/ref&gt; 
== Text and self-help book and point of discuss ==

This book is intended both as a text and self-help book and as a point of discussion considering four levels of media literacy: 

:1. '''Think before you share''': [[Facebook whistleblower Frances Haugen says|Facebook whistleblower Frances Haugen said]], &quot;The shortest path to a click is anger or hate.&quot; The social psychology behind this phenomenon exploited also by legacy media has contributed to [[Media Literacy and You/Media consolidation, social media, and political polarization|the dramatic increase in political polarization and violence worldwide]], especially since the end of the [[w:Fairness doctrine|Fairness doctrine]] in 1987. To counter this, DiResta (2024, p. 335) recommends, &quot;Think before you share.&quot;
:2. '''Look for information to contradict preconceptions''' (Disconfirmation bias): [[w:Information is a public good: Designing experiments to improve government#Previous research|Virtually everyone]] (a) thinks they know more than they do ([[w:Overconfidence effect|overconfidence effect]]), and (b) prefers information and sources consistent with preconceptions ([[w:Confirmation bias|confirmation bias]]). The major media everywhere exploit this to please those who control most of the money for the media. Humans can counter this by searching for sources to help us understand our designated enemies. If we cannot explain circumstances under which we could see ourselves doing what we see our designated enemies doing, we haven't looked hard enough. 
:3. '''Talk''': Push ourselves to have friendly supportive conversations with others with whom we may vehemently disagree with the goals of agreeing to disagree agreeably and building collaboration on areas of common concern.&lt;ref&gt;Graves and Bailey (2025).&lt;/ref&gt;  
:4. '''Teach''': Humans who develop skills in the first three levels can leverage that knowledge in helping others acquire those skills. If each one teaches two&lt;ref&gt;&quot;[[:w:Each one teach one|Each one teach one]]&quot; is an African-American proverb from the time of legalized slavery. However, if each one teaches only one, the growth in literacy will only be linear. Having &quot;each one teaching two&quot;, on average, unleashes the power of doubling and [[:w:exponential growth|exponential growth]], which has the potential of educating the entirety of humanity in a reasonable period of time -- namely after 33 doublings starting from one.&lt;/ref&gt; in a certain period of time, that time period becomes a [[:w:Doubling time|doubling time]]. Ten doublings is a thousand -- actually 1,024 to be precise.&lt;ref&gt;2 time 2 = 4 times 2 = 8 times 2 = 16 times 2 = 32 times 2 = 64 times 2 = 128 times 2 = 256 times 2 = 512 times 2 = 1024: That's 10 doublings, as anyone with a modest understanding of modern digital [[:w:computer|computer]]s will tell you.&lt;/ref&gt; Twenty doublings become a million. Thirty doublings become a billion. Three more doublings become 8 billion, the [[:w:World population|world population]] as of approximately 2022-11-15.&lt;ref&gt;This book uses dates in [[:w:ISO 8601|ISO 8601]], YYYY-MM-DD, when convenient.&lt;/ref&gt; Many organizations, including several United Nations agencies, already have active [[w:media literacy|media literacy]] programs that have already trained many.&lt;ref&gt;''[[Wikibooks:Antiracist Activism for Teachers and Students]]'' includes a chapter on [[Wikibooks:Antiracist Activism for Teachers and Students/Points to Consider for Teaching Anti-racism/Media Literacy In Schools|Media Literacy In Schools]].&lt;/ref&gt; This book is being written hoping to increase the effectiveness and accelerate the rate of growth in media literacy and thereby accelerate progress against many of the most pressing issues facing humanity today.

Much of this book is a [[w:Monograph|research monograph]] summarizing research that seems to have been underreported by the major media to avoid offending people who control most of the money for the media. These research results seem to be central to major political divisions. Each chapter ends in exercises to help the reader practice media literacy skills and have fun doing it. Remember: 

:''I am entitled to my [[Wiktionary:cockamamie|cockamamie]] ideas, and you are entitled to yours.''

Humor is important but must be offered in a way that does not offend others. If others are offended, they may be less interested in dialogue. The term &quot;cockamamie&quot; is used here, hoping that this style of [[w:Self-deprecation|self-deprecation]] might be more inviting for dialogue.

''Never say, &quot;You're wrong.&quot; Instead, ask, &quot;May I offer a contrary perspective?&quot; Or &quot;May I share with you another view that I've heard?&quot;''

Much of the information in this book seems to have been largely overlooked and perhaps suppressed, apparently because it would either offend people who control substantial portions of the money for the media our would increase the cost of producing news; see the brief discussion of conflicts of interest by the major media in the next &quot;Key claims&quot; section.

==Key claims==

* ''Primary drivers of every major conflict include differences between the media or difference in interpretation that the different parties find credible''.
:-- This works, because everything we think we know is coded in systems of connections between neurons in our brains. These systems are more unique than fingerprints and evolve over time. The words we use do not mean the same to two different humans nor even to the same human at different points in time. In many cases these differences are inconsequential. ''Sometimes they are fatal.''&lt;ref&gt;Graves and Bailey (2026).&lt;/ref&gt;
:-- ''[[w:Social constructionism|Show me someone who knows the truth]], and I will show you someone who is dangerous'' -- especially during war or any other situation where humans may be moved to violence mandated by their belief system.&lt;ref&gt;[[w:Collateral damage|Collateral damage]] that &quot;they&quot; commit proves to &quot;us&quot; that &quot;they&quot; are subhuman or at best criminally misled and must be resisted by any means necessary. By contrast, collateral damage that &quot;we&quot; commit is unfortunate but necessary.&lt;/ref&gt;
* The major media everywhere have [[w:Conflict of interest|conflicts of interest ]] in honestly reporting on [[v:Information is a public good per communications prof Pickard|anything that might offend anyone who controls large portions of the money for the media]].&lt;ref&gt;Pickard and Graves (2025), accessed 2026-02-08; Pickard (2020).&lt;/ref&gt; [[v:Media Reform Coalition challenges anti-democratic media bias in the UK|British journalist and media reform advocate Dan Hind]] said that the content produced by the [[w:BBC|BBC]] was frivolous, soap opera stuff, because leading media personalities know very little about issues of substance and believe &quot;they might get in trouble if&quot; they produced anything serious. Similar analyses seem to apply to the major media everywhere&lt;ref&gt;Hind and Graves (2025), accessed 2026-02-09.&lt;/ref&gt; but may not apply to non-profit and local media, which seem more likely to produce [[w:Investigative journalism|investigative]] / [[v:Dean Starkman and the watchdog that didn't bark|accountability journalism]]:&lt;ref&gt;Usher and Kim-Leffingwell (2022); see also Starkman and Graves (2025), accessed 2026-02-09.&lt;/ref&gt; [[w:Watchdog journalism|Watchdogs]] tend to protect the people who feed them. Argentine journalist [[w:Horacio Verbitsky|Horacio Verbitsky]] said, &quot;Journalism is disseminating information that someone does not want known; the rest is [[w:propaganda|propaganda]].&quot;&lt;ref&gt;p. 16 in Verbitsky (1997); English translation from [[Wikiquote:Horacio Verbitsky]], accessed 2026-02-09.&lt;/ref&gt;
* The major media everywhere create the stage upon which politicians read their lines. 
:-- Their selection of acceptable topics for news and entertainment create and maintain the &quot;[[w:Overton window|Overton window]]&quot;, which is the range of acceptable political discourse. For example, in early 1964, US President [[w:Lyndon B. Johnson|Lyndon Johnson]] understood that he could lose the 1964 presidential election that year if he were seen to be soft on communism. His response was to clandestinely provoke an attack on US naval vessels in the Gulf of Tonkin, which he could then denounce as &quot;unprovoked&quot;. During a dark and stormy night 1964-08-04 the [[w:USS Maddox (DD-731)|USS ''Maddox'']] and [[w:USS Turner Joy|''Turner Joy'']] spent a couple of hours &quot;defending themselves&quot; against radar snow, then [[w:Gulf of Tonkin incident|reported that they had sunk two attacking North Vietnamese torpedo boats]]; subsequent investigations found no evidence of the reported attacks. That incident was used to justify the [[w:Gulf of Tonkin Resolution|Gulf of Tonkin Resolution]], with only two dissenting votes in the US Congress: Those two dissenters were defeated in their next reelection campaigns, illustrating the point that the major media create the environment in which many politicians cannot get elected without betraying the nation. 
:-- Nick Hart,&lt;ref name=Hart&gt;&lt;!--Nick Hart--&gt;{{cite Q|Q135663983}}&lt;/ref&gt; President and CEO of the Data Foundation,&lt;ref&gt;&lt;!--Data Foundation--&gt;{{cite Q|Q134705118}}&lt;/ref&gt; noted that President Trump in his first term signed the [[w:Foundations for Evidence-Based Policymaking Act|Foundations for Evidence-Based Policymaking Act]], which was bipartisan legislation ostensibly mandating evidence-informed public policy.&lt;ref&gt;Hart mentioned the [[w:Foundations for Evidence-Based Policymaking Act|Foundations for Evidence-Based Policymaking Act]] when he was interviewed for [[Evidence-informed public policy|&quot;Media &amp; Democracy&quot; 2025-07-31]].&lt;/ref&gt; The evidence is clear:

::''The US Congress is effectively not allowed to consider solid research suppressed by the major media.'' 

* The development of technology is never neutral in its impact on inequality but is driven to benefit people with power.&lt;ref&gt;Acemoglu and Johnson (2023)&lt;/ref&gt;. 
:-- [[Media Literacy and You/The impact of the media on political economy since the time of the Pharaohs|Improvements in agricultural technology from pre-history to the time of King James of the King James bible were managed to benefit elites.]] Then pamphlets and newspapers began to appear, the head of state stopped granting as many monopolies, and commoners began getting permission to become entrepreneurs. That transformed economic stagnation into growth in GDP per capita adjusted for inflation, initiating the [[w:Industrial Revolution|Industrial Revolution]], as documented in the chapter below on [[/The impact of the media on political economy since the time of the Pharaohs/]]. It also led to increasing inequality until organized labor got enough political power to demand and get a bigger share of the fruits of their labors. 
:--[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|In the US those benefits peaked during the Great Depression]], when the standard conservative mantra that blames the poor for their poverty did not sell newspapers. US President Franklin Roosevelt taxed the ultra-wealthy like they had never been taxed before or since, and dramatically reduced inequality, which continued to decline until increasing concentration of ownership of the media ushered in a new era of increasing inequality starting with the presidency of Ronald Reagan. 
:-- [[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future#Role of the media|Acemoglu and Johnson insist that technology, including artificial intelligence, can be developed to benefit all. However, but it will not happen without action by the poor and middle class as follows]]: 
:# Alter the narrative, 
:# Build countervailing powers [like organized labor], and 
:# Develop technical, regulatory, and policy solutions to tackle specific aspects of technology’s social bias.&lt;ref&gt;Acemoglu and Johnson (2023, ch. 11).&lt;/ref&gt;
:-- For more on this, see, e.g., the chapter on [[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Fox, the Great Depression, the Great Recession, and our future]]. 

=== The value of noncommercial news outlets ===

Some of the problems with the media and their contributions to increasing political polarization and violence are documented in the research summary on &quot;[[Information is a public good: Designing experiments to improve government]]&quot; and in the podcast series available on Wikiversity under &quot;[[:Category:Media reform to improve democracy]]&quot; with leading experts discussing their recommendations. One of the most compelling of the references discussed in that podcast series is Usher and Kim-Leffingwell (2022), who tallied all the federal prosecutions for political corruption in each of the 94 [[w:United States federal judicial district|US federal court district]]s between 2003 and 2019. During that period, the number of journalists in the US fell by a factor of roughly 3 -- between 60 and 70 percent. They found no statistically significant impact on federal prosecutions for political corruption of that decline in the number of journalists. 

However, each member of the [[w:Institute for Nonprofit News|Institute for Nonprofit News]] (INN) in a federal court district in one year was associated with on average 1.4 additional prosecutions for political corruption the following year. Since federal prosecutions for political corruption averaged roughly 10 per federal court district per year during that period. each member of INN in a federal court district one year was associated with a 14 percent increase in federal prosecutions the following year.

This suggests that the major media outlets that had so dramatically reduced their staffs had not substantively reduced the amount of investigative journalism they did. If we assume that the people prosecuted for political corruption also control substantive advertising budgets, then the major media outlets have conflicts of interest in honestly reporting on such. They may report on it if some other organization like a member of INN does the research and they are threatened with a loss of audience from not reporting on it. 

:'''''Major point''''': You and I benefit, the vast majority of humans on earth benefit, from news reports presumably published by members of INN that contributed to those on average 1.4 additional prosecutions for political corruption estimated by Usher and Kim-Leffingwell (2022). We benefit even if we never heard about the news reports that contributed to those prosecutions. We benefit even if we have never heard of the news outlets that presumably did the investigative journalism behind those additional prosecutions. Why? Because on average those news reports likely deterred other incidents of political corruption, which likely contributed to broadly shared economic growth and the development of new technology that ultimately benefit the vast majority of humanity. Other aspects of this are documented in the research on the impact of [[w:news desert|news desert]]s, which we summarize next.

=== Costs increase in news deserts===

There's a growing body of research describing what happens when local newspapers die. 

Perhaps most important, a 2018 research report by Gao et al. reported that the death of a local newspaper was followed by … increases in local tax revenue, averaging $85 per human per year.&lt;ref name = Gao2018&gt;Gao et al. (2018).&lt;/ref&gt; That $85 was roughly 13 hundredths of a percent of the 2019 US GDP. That's mentioned in the 2025-07-17 interview with [[Democratic delusions: Fix the media to fix democracy|Natalie Fenton about her new book, ''Democratic Delusions, How the Media Hollows out democracy and What We Can Do About It'']].

One of the most spectacular example of the cost of a news desert is the [[w:City of Bell scandal|Scandal of Bell, California]]. Their local newspaper died around 1999. Roughly a decade later the city was nearly bankrupt in spite of having property tax rates among the highest in the nation. An investigation by the ''[[w:Los Angeles Times|Los Angeles Times]]'' documented that the city manager had a compensation package worth $1.5 million a year, well over double that of the President of the United States. Other senior city officials were similarly well-remunerated. Some of the city officials went to jail over that. Did the city manager decide after 1999, &quot;Wow: The watchdog is dead. Let's have a party&quot;? 

Malfeasance also increases in business as pollution and workplace accidents increase as does the cost of capital, because investors know their money is not as secure without a local newspaper. That leads to a reduction in investments in new products, services and processes -- slowing economic growth. See &quot;[[Local newspapers limit malfeasance]]&quot;, esp. Kim et al. (2021). 

And executive compensation in increases in nonprofits, so less of what people donate goes to the charitable purpose for which they donated, according to Felix et al. (2024). Also, voter participation and split-ticket voting decline, per Benton (2019) and other references discussed in &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. And the ultra-right does better, as noted in [[News from Germany 1900-1945 and implications for today]] and the section on &quot;[[Information is a public good: Designing experiments to improve government#Previous research|Previous research]]&quot; in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;.&lt;ref&gt;Flößer (2024).&lt;/ref&gt; 

The 0.13 percent of GDP savings estimated by Gao et al. (2018) is roughly $120 per human per year. With over 300 million humans in the U.S, that is roughly $40 billion nationwide. 

{| class=&quot;wikitable&quot;
|+ Table 1. Costs increase in news deserts
|- 
! Entity !! What !!Source
|-
| local government || costs incr. 0.13% of GDP || Gao et al. (2018)
|- 
| local businesses || pollution &amp; workplace accidents incr., innovation &amp; econ growth decr. || Kim et al. (2021)
|- 
| nonprofits || exec. compensation incr. || Felix et al. (2024) 
|- 
| rowspan=2 | elections
| voter participation &amp; split-ticket voting decl. || Benton (2019)
|-
| Ultra-right does better || Flößer (2024)
|}

=== Government subsidies for news === 

John (1995) documented how in the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;This is discussed in the 2025-06-08 [[Media concentration per Columbia History Professor Richard John|interview with him]], available on Wikiversity under [[:Category:Media reform to improve democracy]], accessed 2026-04-30.&lt;/ref&gt; This encouraged literacy and limited political corruption, both of which helped [[The Great American Paradox|the early United States stay together and grow]]  while contemporary [[w:New Spain|New Spain]] / [[w:Mexico|Mexico]], fractured, shrank, and stagnated economically. As documented with Figure 1 in the chapter below on [[/The impact of the media on political economy since the time of the Pharaohs/]], that growth catapulted the young United States into its current position of dominance in the international political economy, a position it has been losing since at least 1990 -- or since the Reagan Revolution began in 1981, according to the analysis in the chapter below on [[/Fox, the Great Depression, the Great Recession, and our future/]]. Other countries now have stronger democracies due in part to government subsidies for media in the range of 0.05 and 0.25 percent of GDP with a firewall that limits political interference in the content, according to Neff and Pickard (2024). Table 1 in &quot;[[Information is a public good: Designing experiments to improve government]] compares media subsidies in various places with &quot;other points of reference&quot;.  

McChesney and Nichols (2010, pp. 310-311, note 88) suggested that the relatively high rate of economic growth of the economy in the early US was due in part to postal subsidies under the US [[w:Postal Service Act|Postal Service Act]] of 1792.&lt;ref&gt;See also the Wikiversity article on &quot;[[The Great American Paradox]]&quot;, accessed 2026-04-30.&lt;/ref&gt; They estimated those subsidies at 0.21 percent of GDP. To improve the current political economy of the US, they recommended subsidies of 0.15 percent of GDP distributed to local news nonprofits on the basis of local elections.&lt;ref&gt;McChesney and Nichols (2021, 2022).&lt;/ref&gt; The Wikipedia article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot; documents how some jurisdictions can devote that much money to local news nonprofits by matching what they spend on accounting, advertising, and public relations.&lt;ref&gt;See the section on &quot;[[Information is a public good: Designing experiments to improve government#Sampling units / experimental polities|Sampling units / experimental polities]]&quot; in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;, accessed 2026-04-30.&lt;/ref&gt;  

Pickard (2023) describes three basic strategies for confronting concentrated commercial media power: (1) break them up, (2) regulate them, and (3) create non-commercial, public alternatives. A fourth possibility might be [[w:externality|a graduated tax on income and wealth]] in proportion to the threat that major corporations pose to democracy. 

One class of noncommercial alternatives that Pickard mentions is local multimedia / Public Media Centers (PMCs) with management split between local journalists and boards, e.g., selected at random from registered voters. A key here is to have the boards selected in a way that cannot be influenced by people with power, whether business or political elites. Picard recommends considering '''six discrete layers''' when discussing PMCs, each of which, he says, must be radically democratised: 
# funding, 
# governance, 
# ascertainment (to determine a community’s ''critical information needs''), 
# infrastructure (including universal broadband service), 
# algorithmic (e.g., not allowing companies like Google and Facebook to suppress indexing information the might challenge their hegemony of those markets, [[w:Deep web|treating them like pedophilia and the Islamic State]]), 
# engagement, involving local communities in making their own news and in communicating their own stories; this is paramount to building trust and the grassroots-level support that this new local journalistic model requires.

All this needs to be managed in ways that provide substantive support to news deserts and underserved communities that have long been subjected to various kinds of informational redlining. This might be done by including the proposed PMCs within local libraries staffed by professional journalists, who provide training in media literacy in local schools for children and supervise students producing school newspapers. PMCs could host regular, e.g., monthly events, where local residents could share their concerns with journalist, who would use that input to help prioritize different issues for news coverage. Journalist could also coach local residents in how to research issues and collaborate with journalists in producing news reports that may be better researched and more relevant to local concerns than could be produced without such collaboration.

Management of such PMCs might be split between journalists on staff and boards of, e.g., six members selected at random from voter registration rolls serving staggered terms of one year with a new member rotated in every 2 months.  

Another alternative that could be done in parallel with local PMCs calls for 200 journalists in each US Congressional district funded at $10 billion annually in 2022 dollars, which is just a little under 4 hundredths of one percent of GDP; if such allocations are expressed as fractions of a percent of GDP, they would grow naturally with the economy. (The nominal GDP for the US was roughly $26.1 trillion in 2022.&lt;ref&gt;Johnston and Williamson (2026).&lt;/ref&gt; For 2026 it is estimated at $32.4 trillion.&lt;ref&gt;[[w:United States|United States]], accessed 2026-04-30.&lt;/ref&gt;) 

A similar model is the [[w:BBC|BBC]]’s Local Democracy Reporting Service (LDRS), in which the BBC funds journalists to cover the work of local councils and other local public bodies, funded at £8 million per year, which is a little under 2 hundredths of a percent of the [[w:United Kingdom|UK]]'s GDP of £7.27 trillion.&lt;ref&gt;[[w:United Kingdom|United Kingdom]], accessed 2026-04-30.&lt;/ref&gt; 

Pickard (2023) ended by saying, &quot;Today we face a crossroads: technocracy and oligarchy from above or radical democracy and structural reform from below. ... [T]his is not just a journalism crisis: it is a
democracy crisis.&quot;

==Table of Contents==
*[[/Introduction/]] including an exercise, asking all to discuss perceptions of the settlement of ''[[w:Dominion Voting Systems v. Fox News Network|Dominion Voting Systems v. Fox News Network]]'' in a friendly supportive manner with humans with whom they may vehemently disagree, because the alternative could be killing humans over misunderstandings. 

===Part I. The media and political economy===
# [[/The impact of the media on political economy since the time of the Pharaohs/]] describes how religious leaders in hierarchical societies prior to [[w:James VI and I|King James of the King James bible]] convinced commoners to live in poverty while giving increasing shares of what they produced so religious and secular elites could live in opulence. During the reign of King James, pamphlets and newspapers began to compete with the church for helping commoners understand their roles in society. This produced the Industrial Revolution and modern democracies. Media consolidation since World War II slowed, then reversed this trend. 
# [[/Fox, the Great Depression, the Great Recession, and our future/]] describes the unprecedented performance of the US political economy during the presidency of Franklin Roosevelt (FDR), insisting that much of what FDR achieved can be replicated, giving a media system that supports honest discussion of the available evidence. 
# [[/Media consolidation, social media, and political polarization/]] (Combine from McChesney and Nichols discussing the [[w:Postal Service Act|US Postal Service Act]] of 1792 with [[Media concentration per Columbia History Professor Richard John]], the section on &quot;[[v:Information is a public good: Designing experiments to improve government#Threats from social media|Threats from social media]]&quot; in &quot;[[Information is a public good: Designing experiments to improve government]], and the comments by [[v:Facebook whistleblower Frances Haugen says|Facebook whistleblower Frances Haugen that, &quot;the shortest path to a click is anger or hate.&quot;]].

===Part II. The media and war===
# [[/Deterrence without threat/]]: The historical record is clear: Nations that have prepared for war often got war, not peace. This happens for at least two reasons: First, some leaders cannot resist the temptation to use force inappropriately, sometimes clandestinely provoking others to do things that are then denounced as &quot;unprovoked&quot;; sometimes the media environment pushes them to do such. Alternatively, potential adversaries may believe -- or claim -- that you are actually preparing a first strike, and they must move preemptively or lose their ability to retaliate adequately. We can avoid these possibilities with three supportive policies: [a] Legislation that ''prohibits'' projecting force beyond our own borders. [b] Civilian-based defense training in nonviolent noncooperation like what helped Denmark survive Nazi occupation with minimal damage. And [c] a media system that penalizes rather than encourages a bellicose foreign policy.  
# [[/Responding to a nuclear attack/]]: The ''worst'' response to a nuclear attack would be a nuclear response: The death toll from the 1945 [[w:Atomic bombings of Hiroshima and Nagasaki|Atomic bombings of Hiroshima and Nagasaki]] was estimated at between 150,000 and a quarter of a million. By contrast, simulations of nuclear wars of different magnitudes estimated that between 4 and 95 percent of humanity around the world would starve to death if they did not die of something else sooner. The range depends on whether the war was &quot;limited&quot;, e.g., between India and Pakistan, and massive between the US and Russia. (Also add material from [[Nuclear weapons and effective defense]]). 
# [[/Threats from excessive government secrecy/]] (draft in [https://sanjosepeace.org/restrict-secrecy-more-than-data-collection/ &quot;Restrict secrecy more than data collection&quot;], adding material from [https://kkfi.org/program-episodes/does-us-government-secrecy-threaten-national-security/ Connelly (2023) ''The Declassification Engine: What History Reveals About America's Top Secrets''], [[Wikipedia:Moynihan Commission on Government Secrecy]] and [[1998 Embassy bombings and September 11]].
# [[/Shouting fire in a crowded theater/|Shouting ''fire'' in a crowded theater]]: Legal concerns about &quot;[[w:Shouting fire in a crowded theater|Shouting ''fire'' in a crowded theater]]&quot; date, at least in large part, from the [[w:Supreme Court of the United States|US Supreme Court]] decisions in ''[[w:Schenck v. United States|Schenck v. United States]]'' (1919) and ''[[w: Brandenburg v. Ohio| Brandenburg v. Ohio]]'' (1969). In ''Schenck'' the Court ruled that the government had a right to imprison Schenck and others, because their distribution of fliers encouraging draft resistance presented a [[w:clear and present danger|clear and present danger]] to the efficacy of ongoing military activities during [[w:World War I|World War I]], then in progress. The Court in ''Brandenburg'' held that the government cannot punish inflammatory speech ''unless that speech is &quot;directed to inciting or producing imminent lawless action and is likely to incite or produce such action&quot;.'' Some could argue that many uses of military force by the US and Israel since 1948 have violated international law, encouraged by biases in the major US media &quot;directed to inciting or producing imminent lawless action&quot;, though it may not be feasible to convince a court of that. Still, it might be useful to simulate such a case in a mock trial like the 1966 [[w:Russell Tribunal|Russell Tribunal]].&lt;ref&gt;Andersen (2006) provides such documentation for several such uses of force. Johnson (2026) ''How to Sell a Genocide: The Media's Complicity in the Destruction of Gaza'' organizes evidence supporting such claims for the current [[w:Gaza war|Gaza war]], which began with [[w:October 7 attacks|Palestinian attacks 2023-10-07]]. See also Andersen (2026). Might, e.g., Palestinians -- or at least Palestinian Americans -- be able to sue the [[w:Anti-Defamation League|Anti-Defamation League]] (ADL), the [[w:AIPAC|American Israel Public Affairs Committee]] (AIPAC), and all the major media outlets in the US for inciting genocide in the current [[w:Gaza war|Gaza war]]? That history includes routine suppression of coverage by the major media especially in the US of routine denial of equal protection of Israeli laws to non-Jews in Israel and under Israeli occupation, including suppression of Israeli violence against nonviolent protestors peaceably assembling and petitioning for a redress of grievances combined with over reporting of Palestinian violence and unquestioning coverage of fraudulent claims of Palestinian violence by Israel and supporters. The suppressions included underreporting of Palestinian nonviolence such as the [[w:2018–2019 Gaza border protests|(2018-2019) Great March of Return]], and suppression of the grievances inspiring such nonviolence such as indefinite detention without charges of thousands of Palestinians, including children, routine destruction of Palestinian property by settlers, confiscation of Palestinian property at gunpoint, closing [[w:Gaza Strip|Gaza]] to international trade, and maintaining Gaza on starvation rations. These routine biases in reporting have been encouraged by charges that more honest reporting would be &quot;[[w:Antisemitism|antisemetic]],  according to the ADL and AIPAC. This denial of coverage thereby encouraged Israel to increase the rate of such violations until the [[w:October 7 attacks|2023-10-07 attacks on Israel from Gaza]] unleashed Israeli &quot;retaliations&quot; way out of proportion to the alleged provocation. Sucharov (2022) reported that 69% of American Jews opposed privileging Jews over non-Jews in Israel. Their support of Israel in the current Gaza war is consistent with the media biases documented by Johnson (2026) and others including Andersen (2006, 2026). Regarding whether Israel could achieve anything positive from this war, Samuelson (2025) is skeptical. He summarized quantitative analyses of 60 previous insurgencies. The results including the observation that it is exceedingly difficult to defeat an insurgency without responding to the grievances that support it without force ratios far beyond Israel's resources.&lt;/ref&gt;

===Part III. Climate, immigrants, education, public health, and criminal justice===
# [[/Global warming/]] [Summarize research especially on conflicts of interest of major media in honestly reporting on this issue and the research on global warming itself and activities of groups concerned about this issue. Decompose into global population times CO2 equivalents per human.] 
# [[/Immigrants/]] [Summarize research documenting that [[w:Sanctuary city|sanctuary cities tend to have higher median incomes and no more crime than non-sanctuary jurisdictions]], and some studies report less crime. Moreover economists have documented that immigrants tend to be more entrepreneurial, overrepresented in patent applications, and generally increasing the rate of economic growth. See, e.g., Aghion et al. (2022) ''The power of creative destruction''; Aghion shared the 2025 Nobel Memorial Prize in Economics with two others.] 
# [[/Education/]] (draft in [[Invest in children]].) 
# [[/Public health/]] [Draft in [[UN public health data]] to be revised to be consistent with Bezruchka (2023, 2025).]
# [[/Substance abuse and addictive behavior/]] (Research cited in &quot;[[Wikipedia:War on drugs]]&quot; insists that the US and the world would have fewer problems with substance abuse and addiction problems with 100 percent public funding for treatment programs and complete decriminalization of possession and use of retail quantities of addictive substances. We would also likely have fewer problems with immigrants, as that would make it harder for the US to intervene in the internal affairs of foreign countries funded off the books, as exposed in the [[w:Iran–Contra affair|Iran–Contra affair]]. See [[w:Alfred W. McCoy|Alfred W. McCoy]] (1972; 3rd ed. 2003) ''The politics of heroin''. Journalist [[w:Gary Webb|Gary Webb]] published similar claims that the US intervention in Nicaragua in the Iran-Contra Affair was funded in part by drug money. The story was officially retracted by the ''San José Mercury News'', and Webb allegedly killed himself with 2 bullets to the head.
# [[/Criminal justice/]] (The section on &quot;[[w:United States incarceration rate#Editorial policies of major media|Editorial policies of major media]]&quot; in &quot;[[Wikipedia:United States incarceration rate]]&quot; cites research claiming that within the range range of experience in the US political economy since 1925, the incarceration rate is uncorrelated with crime: It's a function of the public's perception of crime, and that's a function of the media. That suggest that the US would be safer and more prosperous if incarceration policies were driving more by research than by editorial policies of the media. For example, there is also research that says that incarcerees who receive visits are less likely to recidivate, but that evidence is overlooked when convicts are incarcerated substantial distance from their family and friends and when the cost of phone services is substantially higher for incarcerees than among the general pubic. Also, it's known that better educated incarcerees are less likely to recidivate, but it's difficult and maybe impossible for many incarcerees to obtain education in prison.) 
# [[/Empower women and girls/]] [Cite research claiming that a primary restraint on population growth is empowering women and girls. Empowering women and girls is not just a matter of equity: It is also a means to reduce the threats of global warming, of increasing exposure to animal diseases and other problems that come with unrestrained population growth.]

=== Continuation ===

* [[/The evolving media literacy movement/]] to invite others to keep this book current with the evolving understanding of media literacy, how to encourage and promote it and the benefits of doing so.

==See also==

* [[Wikibooks:Antiracist Activism for Teachers and Students/Points to Consider for Teaching Anti-racism/Media Literacy In Schools]]

==Notes==
{{reflist}}
	
==Bibliography==

* &lt;!--Daron Acemoğlu and Simon Johnson (2023) Power and Progress--&gt;{{cite Q|Q125292212}}
* &lt;!--Robin Andersen (2006)  A century of media, a century of war--&gt;{{cite Q|Q138795568}}
* &lt;!--Robin Andersen (2026-06-02)  The Complicit Lens: US Media Coverage of Israel’s Genocide in Gaza--&gt;{{cite Q|Q138796307}}
* &lt;!--Perry Bacon Jr. (2022-10-17) &quot;America Should Spend Billions to Revive Local News&quot;--&gt;{{cite Q|Q139594786}}
* &lt;!-- Joshua Benton (9 April 2019). &quot;When local newspapers shrink, fewer people bother to run for mayor&quot;. Nieman Foundation for Journalism --&gt;{{cite Q|Q63127216}}
* &lt;!--Stephen Bezruchka (2023) Inequality Kills Us All--&gt;{{cite Q|Q136047815}}
* &lt;!--Stephen Bezruchka (2025) ''Born Sick in the USA''--&gt;{{cite Q|Q138749292}} 
* &lt;!--Renée DiResta (2024) Invisible Rulers: The People Who Turn Lies into Reality--&gt;{{cite Q|Q135107164}}
* &lt;!--Robert Felix, Joshua A. Khavis, and Mikhail Pevzner (2024) &quot;The effects of local newspaper closures on nonprofits’ executive compensation&quot;--&gt;{{cite Q|Q132730972}}
* &lt;!--Maxim Flößer (2024-03-06) &quot;Keine Lokalzeitung -- mehr AfD&quot;, Kontext--&gt;{{cite Q|Q125287792}}
* &lt;!--Pengjie Gao, Chang Lee, and Dermot Murphy (2018) &quot;Financing Dies in Darkness? The Impact of Newspaper Closures on Public Finance&quot;--&gt;{{cite Q|Q55670016}}
* &lt;!--Spencer Graves (2024) &quot;Wikipedia: The most democratic force on earth--&gt;{{cite Q|Q137796922}}
* &lt;!--Spencer Graves and Bryan Bailey (2025)  &quot;We have to talk&quot;, blog at PeaceWorksKC.org--&gt;{{cite Q|Q136126262}}
* [[d:Q138038060|Dan Hind and Spencer Graves (2025) &quot;Media Reform Coalition challenges anti-democratic media bias in the UK&quot; on Wikiversity]].
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Adam H. Johnson (2026-04-21) How to Sell a Genocide: The Media's Complicity in the Destruction of Gaza--&gt;{{cite Q|Q140073447}}
* &lt;!--Louis Johnston and Samuel H. Williamson, &quot;What Was the U.S. GDP Then?&quot; MeasuringWorth, 2026--&gt;{{cite Q|Q56881105}}
* &lt;!-- Min Kim, Derrald Stice, Han Stice, and Roger M. White (2021)  &quot;Stop the presses! Or wait, we might need them: Firm responses to local newspaper closures and layoffs&quot;--&gt;{{cite Q|Q132459373}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2021). &quot;The Local Journalism Initiative: a proposal to protect and extend democracy&quot;. Columbia Journalism Review, 30 November 2021 --&gt;{{cite Q|Q109978060}}
* &lt;!-- Robert W. McChesney; John Nichols (2022), To Protect and Extend Democracy, Recreate Local News Media (PDF), FreePress.net (updated 25 January 2022) --&gt;{{cite Q|Q109978337|access-date=2024-06-23}}
* &lt;!--Alfred W. McCoy (2003-05-01)  The politics of heroin : CIA complicity in the global drug trade : Afghanistan, Southeast Asia, Central America, Colombia--&gt;{{cite Q|Q141317509}} 
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* [[d:Q131398359|Victor Pickard (2020) ''Democracy without journalism? : confronting the misinformation society'' (Oxford U. Pr.)]].
* &lt;!-- Victor Pickard (2023-05-12) &quot;Another Media System is Possible: Ripping Open the Overton Window, from Platforms to Public Broadcasting&quot;--&gt;{{cite Q|Q131398460}}
* &lt;!--Doug Samuelson (2025)  Assessing Israel’s Approach in Gaza--&gt;{{cite Q|Q138843324}} 
* [[d:Q138037937|Dean Starkman and Spencer Graves (2025) &quot;Dean Starkman and the watchdog that didn't bark anglais&quot; on Wikiversity]].
* &lt;!--Mira Sucharov (2022)  Do American Jews Really Know What 'Zionist' Means?--&gt;{{cite Q|Q125903777}}
* [[d:Q134715465|Nikki Usher and Sanghoon Kim-Leffingwell (2022) &quot;How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption&quot;, ''SSRN Electronic Journal'']].
* [[d:Q61013892|Horacio Verbitsky (1997) ''Un mundo sin periodistas'' (in Spanish: A world without journalists; Editorial Sudamericana)]].

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    <title>Universal Information Hydrodynamics</title>
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{| class=&quot;wikitable&quot; style=&quot;background:#f9f9f9;{{Text default color}}; border:1px solid #aaa; padding:5px; width:100%;&quot;
|-
| '''Disclosure:''' This learning resource was created by [[w:User:Feuras|J. R. Dunkley]] ([https://orcid.org/0009-0001-6699-375X ORCID: 0009-0001-6699-375X]), who is the developer of the Universal Information Hydrodynamics framework. All claims are sourced to DOI-registered preprints and openly available code archives. Perspective: the author's own research. Readers are encouraged to engage critically and discuss on the [[Talk:Universal Information Hydrodynamics|talk page]].
|}

'''Universal Information Hydrodynamics''' ('''UIH''') is a theoretical framework in [[w:Mathematical physics|mathematical physics]] that unifies reversible quantum dynamics and irreversible thermodynamic response within a single geometric structure known as [[w:Metriplectic system|metriplectic geometry]].&lt;ref name=&quot;UIH&quot;/&gt; The framework is built on the [[w:Fisher information metric|Fisher information metric]], [[w:Symplectic geometry|symplectic geometry]], and convex free energy functionals.

This learning project introduces the mathematical foundations and physical motivations of UIH, intended for advanced undergraduate or postgraduate students with background in differential geometry, statistical mechanics, and quantum mechanics.

== Learning Objectives ==

Upon completing this resource, students should be able to:

# Compute the [[w:Fisher information metric|Fisher information metric]] for parametric families and interpret it as a measure of statistical distinguishability.
# Explain how [[w:Metriplectic system|metriplectic geometry]] unifies Hamiltonian mechanics and gradient flow dynamics within a single bracket structure.
# State the '''Converse Madelung Question''' and describe the information-theoretic conditions that distinguish quantum fluids from classical ones.&lt;ref name=&quot;CMQ&quot;/&gt;
# Derive the UIH evolution equation &lt;math&gt;\frac{dF}{dt} = \{F, H\} + (F, S)&lt;/math&gt; and identify the roles of each term.
# Analyse the '''Emergent Fisher Halo''' construction and its relationship to the [[w:Galaxy rotation problem|galaxy rotation problem]].&lt;ref name=&quot;EFH&quot;/&gt;

== Prerequisites ==

Students should be familiar with:
* [[w:Differential geometry|Differential geometry]] - manifolds, metrics, connections
* [[w:Fisher information|Fisher information]] and the [[w:Fisher information metric|Fisher information metric]]
* [[w:Statistical mechanics|Statistical mechanics]] - free energy, entropy, Boltzmann distributions
* [[w:Quantum mechanics|Quantum mechanics]] - the [[w:Schrödinger equation|Schrödinger equation]], wavefunctions, probability densities
* [[w:Symplectic geometry|Symplectic geometry]] - Hamiltonian mechanics, Poisson brackets
* [[w:Madelung equations|Madelung equations]] - hydrodynamic formulation of quantum mechanics

== Syllabus ==

{| class=&quot;wikitable&quot; style=&quot;width:100%;&quot;
|-
! style=&quot;width:5%;&quot; | #
! style=&quot;width:30%;&quot; | Topic
! style=&quot;width:50%;&quot; | Description
! style=&quot;width:15%;&quot; | Status
|-
| 1
| '''[[/Overview|Overview]]'''
| The central idea: how UIH organises physical dynamics into a metriplectic geometry with reversible and irreversible components expressed through information-geometric objects.
| Complete
|-
| 2
| '''[[/Fisher Information Metric|Fisher Information Metric]]'''
| Deep dive into the Fisher information metric: definition, derivation, worked examples for Gaussian and exponential families, the Cramér–Rao connection, and its role as the geometric substrate for irreversible dynamics in UIH.
| Pending
|-
| 3
| '''[[/Metriplectic Structure|Metriplectic Structure]]'''
| The geometric framework: Poisson brackets, metric brackets, the metriplectic evolution equation, comparison with pure Hamiltonian and pure gradient flow systems, and worked bracket computations.
| Pending
|-
| 4
| '''[[/Converse Madelung Question|The Converse Madelung Question]]'''
| Full walkthrough of the first companion paper: the Madelung transformation, the converse question, information-theoretic axioms distinguishing quantum fluids, and the role of Fisher geometry.
| Pending
|-
| 5
| '''[[/Converse Madelung Answer|The Converse Madelung Answer]]'''
| Full walkthrough of the second companion paper: the necessary and sufficient conditions, the Fisher metriplectic encoding, and the synthesis into the UIH framework.
| Pending
|-
| 6
| '''[[/Emergent Fisher Halos|Emergent Fisher Halos]]'''
| Application to astrophysics: the Fisher halo construction, vacuum information geometry, galactic rotation curves, and comparison with dark matter models.
| Pending
|-
| 7
| '''[[/Hypocoercive Renormalisation|Hypocoercive Renormalisation]]'''
| Open quantum systems: hypocoercivity, renormalisation group flows, universal behaviours in dissipative systems, and the UIH classification scheme.
| Pending
|-
| 8
| '''[[/Exercises|Exercises]]'''
| Problem sets with guided solutions covering all topics in the learning project.
| Pending
|}

== Overview ==

UIH organises physical dynamics into a '''metriplectic geometry''' - a structure that simultaneously encodes:

# A '''symplectic (reversible)''' component governing Hamiltonian evolution, and
# A '''metric (irreversible)''' component governing dissipative processes.

The key insight is that both components can be expressed in terms of information-geometric objects. The irreversible drift is always a '''Fisher gradient flow''' - a steepest descent on a statistical manifold equipped with the Fisher information metric, driven by a convex free energy functional. The reversible component is an antisymmetric channel that performs no thermodynamic work.

This decomposition is local: it applies at each point of the underlying manifold, giving the framework its &quot;hydrodynamic&quot; character.

=== The UIH Evolution Equation ===

The evolution of an observable &lt;math&gt;F&lt;/math&gt; on the state space is governed by:

:&lt;math&gt;\frac{dF}{dt} = \{F, H\} + (F, S)&lt;/math&gt;

where:
* &lt;math&gt;\{F, H\}&lt;/math&gt; is the [[w:Poisson bracket|Poisson bracket]] with the energy &lt;math&gt;H&lt;/math&gt; - this generates reversible, entropy-conserving dynamics
* &lt;math&gt;(F, S)&lt;/math&gt; is the '''metric bracket''' with the entropy &lt;math&gt;S&lt;/math&gt; - this generates irreversible, energy-conserving dissipation
* The metric bracket is constructed from the [[w:Fisher information metric|Fisher information metric]] and a convex [[w:Helmholtz free energy|free energy functional]]

{| class=&quot;wikitable&quot; style=&quot;width:100%; text-align:center;&quot;
|-
! Property
! Poisson bracket &lt;math&gt;\{F, G\}&lt;/math&gt;
! Metric bracket &lt;math&gt;(F, G)&lt;/math&gt;
|-
| '''Symmetry'''
| Antisymmetric: &lt;math&gt;\{F,G\} = -\{G,F\}&lt;/math&gt;
| Symmetric: &lt;math&gt;(F,G) = (G,F)&lt;/math&gt;
|-
| '''Conserves'''
| Entropy: &lt;math&gt;\{S, H\} = 0&lt;/math&gt;
| Energy: &lt;math&gt;(H, S) = 0&lt;/math&gt;
|-
| '''Generates'''
| Reversible (Hamiltonian) evolution
| Irreversible (dissipative) evolution
|-
| '''Geometric origin'''
| [[w:Symplectic geometry|Symplectic structure]]
| [[w:Fisher information metric|Fisher information metric]]
|-
| '''Thermodynamic work'''
| Performs work
| No thermodynamic work (pure dissipation)
|}

''For detailed derivations, see the individual topic pages linked in the Syllabus above.''

== Companion Papers ==

The UIH framework was developed across a series of companion papers:

{| class=&quot;wikitable&quot; style=&quot;width:100%;&quot;
|-
! Paper
! Topic
! Key Result
! Subpage
|-
| '''The Converse Madelung Question''' (2025)&lt;ref name=&quot;CMQ&quot;/&gt;
| Quantum–fluid equivalence
| Information-theoretic axioms distinguishing quantum fluids from classical ones
| [[/Converse Madelung Question|Read more →]]
|-
| '''The Converse Madelung Answer''' (2025)&lt;ref name=&quot;CMA&quot;/&gt;
| Fisher metriplectic conditions
| Necessary and sufficient conditions via the Fisher information metric
| [[/Converse Madelung Answer|Read more →]]
|-
| '''Universal Information Hydrodynamics''' (2025)&lt;ref name=&quot;UIH&quot;/&gt;
| Framework synthesis
| Local metriplectic geometry unifying reversible and irreversible dynamics
| [[/Overview|Read more →]]
|-
| '''Emergent Fisher Halos''' (2025)&lt;ref name=&quot;EFH&quot;/&gt;
| Astrophysical application
| Galactic rotation curves from vacuum information geometry
| [[/Emergent Fisher Halos|Read more →]]
|-
| '''Hypocoercive Renormalisation''' (2025)&lt;ref name=&quot;HR&quot;/&gt;
| Open quantum systems
| RG classification of universal dissipative behaviours
| [[/Hypocoercive Renormalisation|Read more →]]
|}

== Code and Data ==

All numerical checks and computational verification for the UIH framework are openly available.

* '''UIH Code Archive''': [https://doi.org/10.5281/ZENODO.17651171 DOI: 10.5281/zenodo.17651171] - Python verification scripts for the main UIH results
* '''Source repository''': [https://github.com/feuras/uhi_archive github.com/feuras/uhi_archive]

The archive includes verification scripts covering:

{| class=&quot;wikitable&quot;
|-
! Script
! Verification Target
|-
| GKLS diagonal-to-Markov
| Lindblad generator structure
|-
| Fokker–Planck limits
| Classical reduction of quantum master equations
|-
| Fisher metriplectic checks
| Bracket symmetry and conservation laws
|-
| Coherence elimination
| Decoherence channel properties
|-
| K-tomography
| State reconstruction from measurement data
|-
| Density block unification
| Block-diagonal structure of density matrices
|}

== Further Reading ==

* [[w:Fisher information|Fisher information]] - Wikipedia article on the foundational concept
* [[w:Metriplectic system|Metriplectic system]] - Wikipedia article on the geometric structure
* [[w:Madelung equations|Madelung equations]] - the hydrodynamic formulation of quantum mechanics
* [[w:Information geometry|Information geometry]] - the broader mathematical field
* [[w:Symplectic geometry|Symplectic geometry]] - the mathematical framework for Hamiltonian mechanics
* [[w:Hypocoercivity|Hypocoercivity]] - the analytic framework for dissipative systems
* [[w:Galaxy rotation problem|Galaxy rotation problem]] - the astrophysical context for Emergent Fisher Halos

== External Links ==

* [https://jrdunkley.com J. R. Dunkley - Personal website]
* [https://orcid.org/0009-0001-6699-375X ORCID: 0009-0001-6699-375X]
* [https://www.wikidata.org/wiki/Q136913087 Wikidata: Universal Information Hydrodynamics (Q136913087)]
* [https://www.wikidata.org/wiki/Q136892720 Wikidata: J. R. Dunkley (Q136892720)]

== References ==

&lt;references&gt;
&lt;ref name=&quot;CMQ&quot;&gt;J. R. Dunkley (2025). &quot;The Converse Madelung Question&quot;. ''arXiv preprint''. [https://arxiv.org/abs/2511.03552 arXiv:2511.03552]. DOI: [https://doi.org/10.48550/ARXIV.2511.03552 10.48550/ARXIV.2511.03552].&lt;/ref&gt;
&lt;ref name=&quot;CMA&quot;&gt;J. R. Dunkley (2025). &quot;The Converse Madelung Answer&quot;. ''Zenodo Preprint''. DOI: [https://doi.org/10.5281/ZENODO.17643885 10.5281/ZENODO.17643885].&lt;/ref&gt;
&lt;ref name=&quot;UIH&quot;&gt;J. R. Dunkley (2025). &quot;Universal Information Hydrodynamics&quot;. ''Zenodo Preprint''. DOI: [https://doi.org/10.5281/ZENODO.17651781 10.5281/ZENODO.17651781].&lt;/ref&gt;
&lt;ref name=&quot;EFH&quot;&gt;J. R. Dunkley (2025). &quot;Emergent Fisher Halos from Information Geometry&quot;. ''Zenodo Preprint''. DOI: [https://doi.org/10.5281/ZENODO.17701223 10.5281/ZENODO.17701223].&lt;/ref&gt;
&lt;ref name=&quot;HR&quot;&gt;J. R. Dunkley (2025). &quot;Hypocoercive Renormalisation&quot;. ''Zenodo Preprint''. DOI: [https://doi.org/10.5281/ZENODO.17751078 10.5281/ZENODO.17751078].&lt;/ref&gt;
&lt;/references&gt;

[[Category:Physics]]
[[Category:Mathematical physics]]
[[Category:Information theory]]
[[Category:Quantum mechanics]]
[[Category:Differential geometry]]
[[Category:Original research]]
[[Category:Learning projects]]</text>
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    <title>User talk:Regliste</title>
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      <contributor>
        <username>Regliste</username>
        <id>3029369</id>
      </contributor>
      <comment>/* Email bounced */ Reply</comment>
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      <text bytes="4297" sha1="4p5voseyze5yniutud4jhe83i96u0jh" xml:space="preserve">==Welcome==
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:Thanks @[[User:Jtneill|Jtneill]] :) [[User:Regliste|Regliste]] ([[User talk:Regliste|discuss]] • [[Special:Contributions/Regliste|contribs]]) 17:14, 3 May 2026 (UTC)

== Email bounced ==

Hi, I tried to email you several times regarding your [[WikiJournal Preprints/Pentagram map|pentagram map]] to see if you have finished your revisions (as well as on [[WikiJournal Preprints/Kinematics of the cuboctahedron|Kinematics of the cuboctahedron]]) but your email bounced. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 17:15, 10 August 2026 (UTC)

:Hi @[[User:OhanaUnited|OhanaUnited]], I'm sorry to hear about that, I don't know what happened with my email address. I'll try to write you an email, if it doesn't work well we can continue the discussion here?
:I'm over for the pentagram map article. I'd just want to add an &quot;acknowledgment&quot; section, should I do it now? [[User:Regliste|Regliste]] ([[User talk:Regliste|discuss]] • [[Special:Contributions/Regliste|contribs]]) 22:24, 13 August 2026 (UTC)
::Hello @[[User:OhanaUnited|OhanaUnited]],
::I don't know if you received my email from the 20 of August, but I haven't receive a reply from you. I'm done with the pentagram map article, just need to add the acknowledgment section. Should I do it before or after publishing ?
::Sorry for hurrying you, but I have a conference soon and I would prefer the paper to be officially published soon, if possible...
::Best regards, [[User:Regliste|Regliste]] ([[User talk:Regliste|discuss]] • [[Special:Contributions/Regliste|contribs]]) 10:22, 6 September 2026 (UTC)
:::I added an [[WikiJournal Preprints/Pentagram map#Acknowledgments|acknowledgments]] section, if it's too early I can remove it to put it later. [[User:Regliste|Regliste]] ([[User talk:Regliste|discuss]] • [[Special:Contributions/Regliste|contribs]]) 14:04, 6 September 2026 (UTC)</text>
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    <title>Bully Metric Metonic cycle</title>
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      <text bytes="90594" sha1="r99vi5qza58z6jcw9vp7gk2cklfywd5" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| '''Figure 5d''': The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in '''Figure 5d''', the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

The table in '''Figure 5e''' illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ '''Figure 5e''': New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 ECFD B855}} || {{nowrap|8209 ED00 B6FC}} || {{nowrap|8209 ED03 B5AC}} || {{nowrap|8209 ED06 B45E}} || {{nowrap|8209 ED09 B30D}} || {{nowrap|8209 ED0C B1B3}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 ECFD BB9F}} || {{nowrap|8209 ED00 BA41}} || {{nowrap|8209 ED03 B8ED}} || {{nowrap|8209 ED06 B79F}} || {{nowrap|8209 ED09 B650}} || {{nowrap|8209 ED0C B4FB}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 ECFD BEE9}} || {{nowrap|8209 ED00 BD88}} || {{nowrap|8209 ED03 BC2F}} || {{nowrap|8209 ED06 BADE}} || {{nowrap|8209 ED09 B991}} || {{nowrap|8209 ED0C B840}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 ECFD C232}} || {{nowrap|8209 ED00 C0D0}} || {{nowrap|8209 ED03 BF72}} || {{nowrap|8209 ED06 BE1E}} || {{nowrap|8209 ED09 BCD0}} || {{nowrap|8209 ED0C BB81}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 1}} || {{nowrap|8209 ECFD C579}} || {{nowrap|8209 ED00 C418}} || {{nowrap|8209 ED03 C2B7}} || {{nowrap|8209 ED06 C15E}} || {{nowrap|8209 ED09 C00E}} || {{nowrap|8209 ED0C BEC1}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 29}} || {{nowrap|8209 ECFD C8BC}} || {{nowrap|8209 ED00 C75F}} || {{nowrap|8209 ED03 C5FD}} || {{nowrap|8209 ED06 C4A0}} || {{nowrap|8209 ED09 C34C}} || {{nowrap|8209 ED0C C1FE}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 ECFD CBFD}} || {{nowrap|8209 ED00 CAA4}} || {{nowrap|8209 ED03 C943}} || {{nowrap|8209 ED06 C7E2}} || {{nowrap|8209 ED09 C68A}} || {{nowrap|8209 ED0C C53A}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 ECFD CF3B}} || {{nowrap|8209 ED00 CDE7}} || {{nowrap|8209 ED03 CC89}} || {{nowrap|8209 ED06 CB27}} || {{nowrap|8209 ED09 C9CA}} || {{nowrap|8209 ED0C C877}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 ECFD D278}} || {{nowrap|8209 ED00 D127}} || {{nowrap|8209 ED03 CFCE}} || {{nowrap|8209 ED06 CE6D}} || {{nowrap|8209 ED09 CD0D}} || {{nowrap|8209 ED0C CBB5}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 ECFD D5B5}} || {{nowrap|8209 ED00 D467}} || {{nowrap|8209 ED03 D312}} || {{nowrap|8209 ED06 D1B4}} || {{nowrap|8209 ED09 D052}} || {{nowrap|8209 ED0C CEF6}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 ECFD D8F4}} || {{nowrap|8209 ED00 D7A6}} || {{nowrap|8209 ED03 D656}} || {{nowrap|8209 ED06 D4FC}} || {{nowrap|8209 ED09 D39B}} || {{nowrap|8209 ED0C D23B}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 ECFD DC35}} || {{nowrap|8209 ED00 DAE7}} || {{nowrap|8209 ED03 D998}} || {{nowrap|8209 ED06 D844}} || {{nowrap|8209 ED09 D6E6}} || {{nowrap|8209 ED0C D583}}
|- style=&quot;font-size:small:smallbackground-color: #ffff00;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 ECFD DF78}} || {{nowrap|8209 ED00 DE27}} || {{nowrap|8209 ED03 DCDA}} || {{nowrap|8209 ED06 DB89}} || {{nowrap|8209 ED09 DA2F}} || {{nowrap|8209 ED0C D8CE}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 ECFD E2BE}} || {{nowrap|8209 ED00 E169}} || {{nowrap|8209 ED03 E01A}} || {{nowrap|8209 ED06 DECC}} || {{nowrap|8209 ED09 DD77}} || {{nowrap|8209 ED0C DC19}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 ECFD E605}} || {{nowrap|8209 ED00 E4AC}} || {{nowrap|8209 ED03 E35B}} || {{nowrap|8209 ED06 E20D}} || {{nowrap|8209 ED09 E0BC}} || {{nowrap|8209 ED0C DF63}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 ECFD E94E}} || {{nowrap|8209 ED00 E7EF}} || {{nowrap|8209 ED03 E69B}} || {{nowrap|8209 ED06 E54D}} || {{nowrap|8209 ED09 E3FE}} || {{nowrap|8209 ED0C E2AA}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 ECFD EC96}} || {{nowrap|8209 ED00 EB35}} || {{nowrap|8209 ED03 E9DC}} || {{nowrap|8209 ED06 E88B}} || {{nowrap|8209 ED09 E73E}} || {{nowrap|8209 ED0C E5ED}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 19}} || {{nowrap|8209 ECFD EFDE}} || {{nowrap|8209 ED00 EE7B}} || {{nowrap|8209 ED03 ED1E}} || {{nowrap|8209 ED06 EBCA}} || {{nowrap|8209 ED09 EA7B}} || {{nowrap|8209 ED0C E92D}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 ECFD F323}} || {{nowrap|8209 ED00 F1C2}} || {{nowrap|8209 ED03 F061}} || {{nowrap|8209 ED06 EF08}} || {{nowrap|8209 ED09 EDB8}} || {{nowrap|8209 ED0C EC6A}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 ECFD F665}} || {{nowrap|8209 ED00 F508}} || {{nowrap|8209 ED03 F3A5}} || {{nowrap|8209 ED06 F248}} || {{nowrap|8209 ED09 F0F4}} || {{nowrap|8209 ED0C EFA6}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 ECFD F9A5}} || {{nowrap|8209 ED00 F84C}} || {{nowrap|8209 ED03 F6EB}} || {{nowrap|8209 ED06 F58B}} || {{nowrap|8209 ED09 F432}} || {{nowrap|8209 ED0C F2E2}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 ECFD FCE4}} || {{nowrap|8209 ED00 FB90}} || {{nowrap|8209 ED03 FA32}} || {{nowrap|8209 ED06 F8D0}} || {{nowrap|8209 ED09 F774}} || {{nowrap|8209 ED0C F620}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 ECFE 0023}} || {{nowrap|8209 ED00 FED3}} || {{nowrap|8209 ED03 FD7A}} || {{nowrap|8209 ED06 FC19}} || {{nowrap|8209 ED09 FAB8}} || {{nowrap|8209 ED0C F961}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 ECFE 0363}} || {{nowrap|8209 ED01 0214}} || {{nowrap|8209 ED04 00C0}} || {{nowrap|8209 ED06 FF63}} || {{nowrap|8209 ED09 FE00}} || {{nowrap|8209 ED0C FCA4}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 ECFE 06A3}} || {{nowrap|8209 ED01 0556}} || {{nowrap|8209 ED04 0405}} || {{nowrap|8209 ED07 02AC}} || {{nowrap|8209 ED0A 014B}} || {{nowrap|8209 ED0C FFEA}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 ECFE 09E5}} || {{nowrap|8209 ED01 0896}} || {{nowrap|8209 ED04 0748}} || {{nowrap|8209 ED07 05F3}} || {{nowrap|8209 ED0A 0496}} || {{nowrap|8209 ED0D 0334}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 ECFE 0D28}} || {{nowrap|8209 ED01 0BD7}} || {{nowrap|8209 ED04 0A89}} || {{nowrap|8209 ED07 0938}} || {{nowrap|8209 ED0A 07E0}} || {{nowrap|8209 ED0D 067E}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 ECFE 106D}} || {{nowrap|8209 ED01 0F17}} || {{nowrap|8209 ED04 0DC9}} || {{nowrap|8209 ED07 0C7B}} || {{nowrap|8209 ED0A 0B27}} || {{nowrap|8209 ED0D 09C9}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 ECFE 13B3}} || {{nowrap|8209 ED01 1259}} || {{nowrap|8209 ED04 1108}} || {{nowrap|8209 ED07 0FBB}} || {{nowrap|8209 ED0A 0E6A}} || {{nowrap|8209 ED0D 0D11}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 8}} || {{nowrap|8209 ECFE 16FA}} || {{nowrap|8209 ED01 159C}} || {{nowrap|8209 ED04 1447}} || {{nowrap|8209 ED07 12F9}} || {{nowrap|8209 ED0A 11AA}} || {{nowrap|8209 ED0D 1056}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 ECFE 1A41}} || {{nowrap|8209 ED01 18DF}} || {{nowrap|8209 ED04 1786}} || {{nowrap|8209 ED07 1635}} || {{nowrap|8209 ED0A 14E8}} || {{nowrap|8209 ED0D 1397}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 ECFE 1D86}} || {{nowrap|8209 ED01 1C24}} || {{nowrap|8209 ED04 1AC6}} || {{nowrap|8209 ED07 1972}} || {{nowrap|8209 ED0A 1824}} || {{nowrap|8209 ED0D 16D5}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 ECFE 20CB}} || {{nowrap|8209 ED01 1F6A}} || {{nowrap|8209 ED04 1E09}} || {{nowrap|8209 ED07 1CB0}} || {{nowrap|8209 ED0A 1B60}} || {{nowrap|8209 ED0D 1A12}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 ECFE 240E}} || {{nowrap|8209 ED01 22B1}} || {{nowrap|8209 ED04 214E}} || {{nowrap|8209 ED07 1FF1}} || {{nowrap|8209 ED0A 1E9D}} || {{nowrap|8209 ED0D 1D4F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 ECFE 2750}} || {{nowrap|8209 ED01 25F7}} || {{nowrap|8209 ED04 2496}} || {{nowrap|8209 ED07 2336}} || {{nowrap|8209 ED0A 21DE}} || {{nowrap|8209 ED0D 208D}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 ECFE 2A91}} || {{nowrap|8209 ED01 293D}} || {{nowrap|8209 ED04 27E0}} || {{nowrap|8209 ED07 267E}} || {{nowrap|8209 ED0A 2521}} || {{nowrap|8209 ED0D 23CD}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 ECFE 2DD2}} || {{nowrap|8209 ED01 2C81}} || {{nowrap|8209 ED04 2B29}} || {{nowrap|8209 ED07 29C8}} || {{nowrap|8209 ED0A 2867}} || {{nowrap|8209 ED0D 270F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 ECFE 3112}} || {{nowrap|8209 ED01 2FC4}} || {{nowrap|8209 ED04 2E70}} || {{nowrap|8209 ED07 2D13}} || {{nowrap|8209 ED0A 2BB0}} || {{nowrap|8209 ED0D 2A53}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 ECFE 3453}} || {{nowrap|8209 ED01 3305}} || {{nowrap|8209 ED04 31B5}} || {{nowrap|8209 ED07 305C}} || {{nowrap|8209 ED0A 2EFB}} || {{nowrap|8209 ED0D 2D9B}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 ECFE 3794}} || {{nowrap|8209 ED01 3645}} || {{nowrap|8209 ED04 34F7}} || {{nowrap|8209 ED07 33A3}} || {{nowrap|8209 ED0A 3246}} || {{nowrap|8209 ED0D 30E4}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 ECFE 3AD6}} || {{nowrap|8209 ED01 3985}} || {{nowrap|8209 ED04 3837}} || {{nowrap|8209 ED07 36E7}} || {{nowrap|8209 ED0A 358F}} || {{nowrap|8209 ED0D 342E}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 ECFE 3E19}} || {{nowrap|8209 ED01 3CC4}} || {{nowrap|8209 ED04 3B76}} || {{nowrap|8209 ED07 3A27}} || {{nowrap|8209 ED0A 38D3}} || {{nowrap|8209 ED0D 3776}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 27}} || {{nowrap|8209 ECFE 415E}} || {{nowrap|8209 ED01 4004}} || {{nowrap|8209 ED04 3EB3}} || {{nowrap|8209 ED07 3D65}} || {{nowrap|8209 ED0A 3C14}} || {{nowrap|8209 ED0D 3ABC}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 ECFE 44A3}} || {{nowrap|8209 ED01 4345}} || {{nowrap|8209 ED04 41F0}} || {{nowrap|8209 ED07 40A1}} || {{nowrap|8209 ED0A 3F53}} || {{nowrap|8209 ED0D 3DFE}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 ECFE 47E9}} || {{nowrap|8209 ED01 4687}} || {{nowrap|8209 ED04 452E}} || {{nowrap|8209 ED07 43DD}} || {{nowrap|8209 ED0A 4290}} || {{nowrap|8209 ED0D 413F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 ECFE 4B2F}} || {{nowrap|8209 ED01 49CD}} || {{nowrap|8209 ED04 486F}} || {{nowrap|8209 ED07 471B}} || {{nowrap|8209 ED0A 45CD}} || {{nowrap|8209 ED0D 447E}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 ECFE 4E75}} || {{nowrap|8209 ED01 4D14}} || {{nowrap|8209 ED04 4BB3}} || {{nowrap|8209 ED07 4A5B}} || {{nowrap|8209 ED0A 490A}} || {{nowrap|8209 ED0D 47BD}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 ECFE 51BA}} || {{nowrap|8209 ED01 505D}} || {{nowrap|8209 ED04 4EFB}} || {{nowrap|8209 ED07 4D9E}} || {{nowrap|8209 ED0A 4C4A}} || {{nowrap|8209 ED0D 4AFB}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 ECFE 54FE}} || {{nowrap|8209 ED01 53A5}} || {{nowrap|8209 ED04 5245}} || {{nowrap|8209 ED07 50E4}} || {{nowrap|8209 ED0A 4F8B}} || {{nowrap|8209 ED0D 4E3B}}
|- style=&quot;font-size:small:smallbackground-color: #ffff00;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 ECFE 5840}} || {{nowrap|8209 ED01 56EC}} || {{nowrap|8209 ED04 558F}} || {{nowrap|8209 ED07 542D}} || {{nowrap|8209 ED0A 52D0}} || {{nowrap|8209 ED0D 517C}}

|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
|| {{nowrap|}} || {{nowrap|1988}} || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 ECFE 5B81}} || {{nowrap|8209 ED01 5A31}} || {{nowrap|8209 ED04 58D9}} || {{nowrap|8209 ED07 5778}} || {{nowrap|8209 ED0A 5617}} || {{nowrap|8209 ED0D 54BF}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 ECFE 5EC1}} || {{nowrap|8209 ED01 5D73}} || {{nowrap|8209 ED04 5C20}} || {{nowrap|8209 ED07 5AC3}} || {{nowrap|8209 ED0A 5961}} || {{nowrap|8209 ED0D 5804}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 ECFE 6201}} || {{nowrap|8209 ED01 60B4}} || {{nowrap|8209 ED04 5F64}} || {{nowrap|8209 ED07 5E0C}} || {{nowrap|8209 ED0A 5CAB}} || {{nowrap|8209 ED0D 5B4A}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 ECFE 6541}} || {{nowrap|8209 ED01 63F3}} || {{nowrap|8209 ED04 62A5}} || {{nowrap|8209 ED07 6151}} || {{nowrap|8209 ED0A 5FF4}} || {{nowrap|8209 ED0D 5E92}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 15}} || {{nowrap|8209 ECFE 6882}} || {{nowrap|8209 ED01 6730}} || {{nowrap|8209 ED04 65E2}} || {{nowrap|8209 ED07 6492}} || {{nowrap|8209 ED0A 633A}} || {{nowrap|8209 ED0D 61D9}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 ECFE 6BC3}} || {{nowrap|8209 ED01 6A6D}} || {{nowrap|8209 ED04 691F}} || {{nowrap|8209 ED07 67D0}} || {{nowrap|8209 ED0A 667C}} || {{nowrap|8209 ED0D 651F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 13}} || {{nowrap|8209 ECFE 6F06}} || {{nowrap|8209 ED01 6DAC}} || {{nowrap|8209 ED04 6C5B}} || {{nowrap|8209 ED07 6B0D}} || {{nowrap|8209 ED0A 69BD}} || {{nowrap|8209 ED0D 6864}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 ECFE 724B}} || {{nowrap|8209 ED01 70ED}} || {{nowrap|8209 ED04 6F98}} || {{nowrap|8209 ED07 6E4A}} || {{nowrap|8209 ED0A 6CFC}} || {{nowrap|8209 ED0D 6BA7}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 ECFE 7593}} || {{nowrap|8209 ED01 7431}} || {{nowrap|8209 ED04 72D8}} || {{nowrap|8209 ED07 7187}} || {{nowrap|8209 ED0A 703A}} || {{nowrap|8209 ED0D 6EE9}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 ECFE 78DB}} || {{nowrap|8209 ED01 7779}} || {{nowrap|8209 ED04 761B}} || {{nowrap|8209 ED07 74C6}} || {{nowrap|8209 ED0A 7378}} || {{nowrap|8209 ED0D 7229}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 ECFE 7C22}} || {{nowrap|8209 ED01 7AC2}} || {{nowrap|8209 ED04 7961}} || {{nowrap|8209 ED07 7808}} || {{nowrap|8209 ED0A 76B7}} || {{nowrap|8209 ED0D 7569}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 ECFE 7F69}} || {{nowrap|8209 ED01 7E0C}} || {{nowrap|8209 ED04 7CAA}} || {{nowrap|8209 ED07 7B4C}} || {{nowrap|8209 ED0A 79F8}} || {{nowrap|8209 ED0D 78A9}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1989}} || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 ECFE 82AD}} || {{nowrap|8209 ED01 8155}} || {{nowrap|8209 ED04 7FF5}} || {{nowrap|8209 ED07 7E94}} || {{nowrap|8209 ED0A 7D3B}} || {{nowrap|8209 ED0D 7BEA}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 ECFE 85F0}} || {{nowrap|8209 ED01 849D}} || {{nowrap|8209 ED04 8340}} || {{nowrap|8209 ED07 81DE}} || {{nowrap|8209 ED0A 8080}} || {{nowrap|8209 ED0D 7F2C}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 ECFE 8930}} || {{nowrap|8209 ED01 87E1}} || {{nowrap|8209 ED04 8689}} || {{nowrap|8209 ED07 8529}} || {{nowrap|8209 ED0A 83C8}} || {{nowrap|8209 ED0D 826F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 ECFE 8C6F}} || {{nowrap|8209 ED01 8B21}} || {{nowrap|8209 ED04 89CE}} || {{nowrap|8209 ED07 8872}} || {{nowrap|8209 ED0A 8710}} || {{nowrap|8209 ED0D 85B2}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 4}} || {{nowrap|8209 ECFE 8FAD}} || {{nowrap|8209 ED01 8E5F}} || {{nowrap|8209 ED04 8D10}} || {{nowrap|8209 ED07 8BB8}} || {{nowrap|8209 ED0A 8A57}} || {{nowrap|8209 ED0D 88F6}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 ECFE 92EB}} || {{nowrap|8209 ED01 919C}} || {{nowrap|8209 ED04 904E}} || {{nowrap|8209 ED07 8EFB}} || {{nowrap|8209 ED0A 8D9E}} || {{nowrap|8209 ED0D 8C3C}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 ECFE 962A}} || {{nowrap|8209 ED01 94D8}} || {{nowrap|8209 ED04 938B}} || {{nowrap|8209 ED07 923B}} || {{nowrap|8209 ED0A 90E3}} || {{nowrap|8209 ED0D 8F82}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 ECFE 996B}} || {{nowrap|8209 ED01 9816}} || {{nowrap|8209 ED04 96C7}} || {{nowrap|8209 ED07 9579}} || {{nowrap|8209 ED0A 9425}} || {{nowrap|8209 ED0D 92C8}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 ECFE 9CAF}} || {{nowrap|8209 ED01 9B55}} || {{nowrap|8209 ED04 9A04}} || {{nowrap|8209 ED07 98B7}} || {{nowrap|8209 ED0A 9766}} || {{nowrap|8209 ED0D 960E}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 ECFE 9FF6}} || {{nowrap|8209 ED01 9E98}} || {{nowrap|8209 ED04 9D43}} || {{nowrap|8209 ED07 9BF5}} || {{nowrap|8209 ED0A 9AA6}} || {{nowrap|8209 ED0D 9952}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 ECFE A33F}} || {{nowrap|8209 ED01 A1DE}} || {{nowrap|8209 ED04 A084}} || {{nowrap|8209 ED07 9F33}} || {{nowrap|8209 ED0A 9DE5}} || {{nowrap|8209 ED0D 9C95}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 ECFE A689}} || {{nowrap|8209 ED01 A527}} || {{nowrap|8209 ED04 A3C9}} || {{nowrap|8209 ED07 A274}} || {{nowrap|8209 ED0A A125}} || {{nowrap|8209 ED0D 9FD7}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 ECFE A9D2}} || {{nowrap|8209 ED01 A872}} || {{nowrap|8209 ED04 A711}} || {{nowrap|8209 ED07 A5B7}} || {{nowrap|8209 ED0A A466}} || {{nowrap|8209 ED0D A318}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1990}} || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 ECFE AD19}} || {{nowrap|8209 ED01 ABBD}} || {{nowrap|8209 ED04 AA5B}} || {{nowrap|8209 ED07 A8FD}} || {{nowrap|8209 ED0A A7A8}} || {{nowrap|8209 ED0D A65A}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 ECFE B05D}} || {{nowrap|8209 ED01 AF06}} || {{nowrap|8209 ED04 ADA6}} || {{nowrap|8209 ED07 AC45}} || {{nowrap|8209 ED0A AAEB}} || {{nowrap|8209 ED0D A99A}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 ECFE B39E}} || {{nowrap|8209 ED01 B24B}} || {{nowrap|8209 ED04 B0EF}} || {{nowrap|8209 ED07 AF8D}} || {{nowrap|8209 ED0A AE2F}} || {{nowrap|8209 ED0D ACDA}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 ECFE B6DD}} || {{nowrap|8209 ED01 B58D}} || {{nowrap|8209 ED04 B436}} || {{nowrap|8209 ED07 B2D5}} || {{nowrap|8209 ED0A B174}} || {{nowrap|8209 ED0D B01A}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 23}} || {{nowrap|8209 ECFE BA19}} || {{nowrap|8209 ED01 B8CB}} || {{nowrap|8209 ED04 B778}} || {{nowrap|8209 ED07 B61C}} || {{nowrap|8209 ED0A B4BA}} || {{nowrap|8209 ED0D B35C}}
|- style=&quot;font-size:small:smallbackground-color: #ffff00;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 ECFE BD56}} || {{nowrap|8209 ED01 BC08}} || {{nowrap|8209 ED04 BAB9}} || {{nowrap|8209 ED07 B961}} || {{nowrap|8209 ED0A B801}} || {{nowrap|8209 ED0D B69F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 ECFE C093}} || {{nowrap|8209 ED01 BF45}} || {{nowrap|8209 ED04 BDF7}} || {{nowrap|8209 ED07 BCA4}} || {{nowrap|8209 ED0A BB47}} || {{nowrap|8209 ED0D B9E5}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 ECFE C3D3}} || {{nowrap|8209 ED01 C282}} || {{nowrap|8209 ED04 C134}} || {{nowrap|8209 ED07 BFE4}} || {{nowrap|8209 ED0A BE8C}} || {{nowrap|8209 ED0D BD2B}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 ECFE C716}} || {{nowrap|8209 ED01 C5C0}} || {{nowrap|8209 ED04 C471}} || {{nowrap|8209 ED07 C323}} || {{nowrap|8209 ED0A C1CF}} || {{nowrap|8209 ED0D C072}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 ECFE CA5B}} || {{nowrap|8209 ED01 C901}} || {{nowrap|8209 ED04 C7B0}} || {{nowrap|8209 ED07 C662}} || {{nowrap|8209 ED0A C511}} || {{nowrap|8209 ED0D C3B9}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 ECFE CDA4}} || {{nowrap|8209 ED01 CC45}} || {{nowrap|8209 ED04 CAF0}} || {{nowrap|8209 ED07 C9A1}} || {{nowrap|8209 ED0A C853}} || {{nowrap|8209 ED0D C6FF}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 ECFE D0EF}} || {{nowrap|8209 ED01 CF8D}} || {{nowrap|8209 ED04 CE33}} || {{nowrap|8209 ED07 CCE2}} || {{nowrap|8209 ED0A CB94}} || {{nowrap|8209 ED0D CA44}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1991}} || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 ECFE D43A}} || {{nowrap|8209 ED01 D2D8}} || {{nowrap|8209 ED04 D179}} || {{nowrap|8209 ED07 D024}} || {{nowrap|8209 ED0A CED5}} || {{nowrap|8209 ED0D CD87}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 ECFE D783}} || {{nowrap|8209 ED01 D623}} || {{nowrap|8209 ED04 D4C2}} || {{nowrap|8209 ED07 D368}} || {{nowrap|8209 ED0A D216}} || {{nowrap|8209 ED0D D0C8}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 ECFE DAC8}} || {{nowrap|8209 ED01 D96D}} || {{nowrap|8209 ED04 D80B}} || {{nowrap|8209 ED07 D6AC}} || {{nowrap|8209 ED0A D557}} || {{nowrap|8209 ED0D D408}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 ECFE DE0A}} || {{nowrap|8209 ED01 DCB3}} || {{nowrap|8209 ED04 DB53}} || {{nowrap|8209 ED07 D9F2}} || {{nowrap|8209 ED0A D898}} || {{nowrap|8209 ED0D D747}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 12}} || {{nowrap|8209 ECFE E149}} || {{nowrap|8209 ED01 DFF6}} || {{nowrap|8209 ED04 DE9B}} || {{nowrap|8209 ED07 DD38}} || {{nowrap|8209 ED0A DBDA}} || {{nowrap|8209 ED0D DA85}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 ECFE E486}} || {{nowrap|8209 ED01 E336}} || {{nowrap|8209 ED04 E1DF}} || {{nowrap|8209 ED07 E07F}} || {{nowrap|8209 ED0A DF1E}} || {{nowrap|8209 ED0D DDC4}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 ECFE E7C2}} || {{nowrap|8209 ED01 E675}} || {{nowrap|8209 ED04 E522}} || {{nowrap|8209 ED07 E3C5}} || {{nowrap|8209 ED0A E263}} || {{nowrap|8209 ED0D E105}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 ECFE EAFF}} || {{nowrap|8209 ED01 E9B1}} || {{nowrap|8209 ED04 E862}} || {{nowrap|8209 ED07 E70A}} || {{nowrap|8209 ED0A E5AA}} || {{nowrap|8209 ED0D E448}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 ECFE EE3D}} || {{nowrap|8209 ED01 ECEE}} || {{nowrap|8209 ED04 EBA0}} || {{nowrap|8209 ED07 EA4D}} || {{nowrap|8209 ED0A E8F0}} || {{nowrap|8209 ED0D E78E}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 ECFE F17E}} || {{nowrap|8209 ED01 F02C}} || {{nowrap|8209 ED04 EEDE}} || {{nowrap|8209 ED07 ED8E}} || {{nowrap|8209 ED0A EC36}} || {{nowrap|8209 ED0D EAD6}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 ECFE F4C2}} || {{nowrap|8209 ED01 F36C}} || {{nowrap|8209 ED04 F21D}} || {{nowrap|8209 ED07 F0CF}} || {{nowrap|8209 ED0A EF7C}} || {{nowrap|8209 ED0D EE1F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 ECFE F80A}} || {{nowrap|8209 ED01 F6AF}} || {{nowrap|8209 ED04 F55E}} || {{nowrap|8209 ED07 F410}} || {{nowrap|8209 ED0A F2C0}} || {{nowrap|8209 ED0D F168}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1992}} || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 ECFE FB55}} || {{nowrap|8209 ED01 F9F6}} || {{nowrap|8209 ED04 F8A0}} || {{nowrap|8209 ED07 F751}} || {{nowrap|8209 ED0A F603}} || {{nowrap|8209 ED0D F4B0}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 ECFE FEA0}} || {{nowrap|8209 ED01 FD3F}} || {{nowrap|8209 ED04 FBE4}} || {{nowrap|8209 ED07 FA92}} || {{nowrap|8209 ED0A F944}} || {{nowrap|8209 ED0D F7F4}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 ECFF 01EA}} || {{nowrap|8209 ED02 0088}} || {{nowrap|8209 ED04 FF29}} || {{nowrap|8209 ED07 FDD3}} || {{nowrap|8209 ED0A FC84}} || {{nowrap|8209 ED0D FB36}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 ECFF 0531}} || {{nowrap|8209 ED02 03D1}} || {{nowrap|8209 ED05 0270}} || {{nowrap|8209 ED08 0115}} || {{nowrap|8209 ED0A FFC3}} || {{nowrap|8209 ED0D FE76}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 1}} || {{nowrap|8209 ECFF 0874}} || {{nowrap|8209 ED02 0719}} || {{nowrap|8209 ED05 05B7}} || {{nowrap|8209 ED08 0458}} || {{nowrap|8209 ED0B 0302}} || {{nowrap|8209 ED0E 01B4}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 ECFF 0BB4}} || {{nowrap|8209 ED02 0A5E}} || {{nowrap|8209 ED05 08FE}} || {{nowrap|8209 ED08 079C}} || {{nowrap|8209 ED0B 0642}} || {{nowrap|8209 ED0E 04F1}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 ECFF 0EF2}} || {{nowrap|8209 ED02 0DA0}} || {{nowrap|8209 ED05 0C44}} || {{nowrap|8209 ED08 0AE2}} || {{nowrap|8209 ED0B 0984}} || {{nowrap|8209 ED0E 082F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 ECFF 122F}} || {{nowrap|8209 ED02 10DF}} || {{nowrap|8209 ED05 0F88}} || {{nowrap|8209 ED08 0E28}} || {{nowrap|8209 ED0B 0CC7}} || {{nowrap|8209 ED0E 0B6D}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 ECFF 156B}} || {{nowrap|8209 ED02 141D}} || {{nowrap|8209 ED05 12CA}} || {{nowrap|8209 ED08 116E}} || {{nowrap|8209 ED0B 100C}} || {{nowrap|8209 ED0E 0EAE}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 ECFF 18A9}} || {{nowrap|8209 ED02 175B}} || {{nowrap|8209 ED05 160B}} || {{nowrap|8209 ED08 14B4}} || {{nowrap|8209 ED0B 1353}} || {{nowrap|8209 ED0E 11F2}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 25}} || {{nowrap|8209 ECFF 1BE9}} || {{nowrap|8209 ED02 1A9A}} || {{nowrap|8209 ED05 194C}} || {{nowrap|8209 ED08 17F9}} || {{nowrap|8209 ED0B 169C}} || {{nowrap|8209 ED0E 153A}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 ECFF 1F2C}} || {{nowrap|8209 ED02 1DDA}} || {{nowrap|8209 ED05 1C8C}} || {{nowrap|8209 ED08 1B3D}} || {{nowrap|8209 ED0B 19E5}} || {{nowrap|8209 ED0E 1885}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 ECFF 2272}} || {{nowrap|8209 ED02 211C}} || {{nowrap|8209 ED05 1FCD}} || {{nowrap|8209 ED08 1E7F}} || {{nowrap|8209 ED0B 1D2C}} || {{nowrap|8209 ED0E 1BCF}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1993}} || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 22}} || {{nowrap|8209 ECFF 2905}} || {{nowrap|8209 ED02 2460}} || {{nowrap|8209 ED05 230E}} || {{nowrap|8209 ED08 21C0}} || {{nowrap|8209 ED0B 2070}} || {{nowrap|8209 ED0E 1F19}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 ECFF 2C4F}} || {{nowrap|8209 ED02 27A6}} || {{nowrap|8209 ED05 2650}} || {{nowrap|8209 ED08 2500}} || {{nowrap|8209 ED0B 23B2}} || {{nowrap|8209 ED0E 225F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 ECFF 2F97}} || {{nowrap|8209 ED02 2AED}} || {{nowrap|8209 ED05 2992}} || {{nowrap|8209 ED08 2840}} || {{nowrap|8209 ED0B 26F2}} || {{nowrap|8209 ED0E 25A2}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 ECFF 32DC}} || {{nowrap|8209 ED02 2E35}} || {{nowrap|8209 ED05 2CD6}} || {{nowrap|8209 ED08 2B80}} || {{nowrap|8209 ED0B 2A31}} || {{nowrap|8209 ED0E 28E3}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 20}} || {{nowrap|8209 ECFF 361E}} || {{nowrap|8209 ED02 317D}} || {{nowrap|8209 ED05 301B}} || {{nowrap|8209 ED08 2EC0}} || {{nowrap|8209 ED0B 2D6E}} || {{nowrap|8209 ED0E 2C21}}
|- style=&quot;font-size:small:smallbackground-color: #ffff00;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 ECFF 395D}} || {{nowrap|8209 ED02 34C3}} || {{nowrap|8209 ED05 3361}} || {{nowrap|8209 ED08 3202}} || {{nowrap|8209 ED0B 30AC}} || {{nowrap|8209 ED0E 2F5E}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 ECFF 3C9B}} || {{nowrap|8209 ED02 3807}} || {{nowrap|8209 ED05 36A7}} || {{nowrap|8209 ED08 3545}} || {{nowrap|8209 ED0B 33EB}} || {{nowrap|8209 ED0E 329A}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 ECFF 3FD8}} || {{nowrap|8209 ED02 3B48}} || {{nowrap|8209 ED05 39ED}} || {{nowrap|8209 ED08 388A}} || {{nowrap|8209 ED0B 372C}} || {{nowrap|8209 ED0E 35D7}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 ECFF 4316}} || {{nowrap|8209 ED02 3E89}} || {{nowrap|8209 ED05 3D31}} || {{nowrap|8209 ED08 3BD1}} || {{nowrap|8209 ED0B 3A70}} || {{nowrap|8209 ED0E 3916}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 ECFF 4656}} || {{nowrap|8209 ED02 41C8}} || {{nowrap|8209 ED05 4076}} || {{nowrap|8209 ED08 3F1A}} || {{nowrap|8209 ED0B 3DB8}} || {{nowrap|8209 ED0E 3C59}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 ECFF 4998}} || {{nowrap|8209 ED02 4508}} || {{nowrap|8209 ED05 43B9}} || {{nowrap|8209 ED08 4262}} || {{nowrap|8209 ED0B 4102}} || {{nowrap|8209 ED0E 3FA0}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 ECFF 4998}} || {{nowrap|8209 ED02 4849}} || {{nowrap|8209 ED05 46FB}} || {{nowrap|8209 ED08 45A8}} || {{nowrap|8209 ED0B 444C}} || {{nowrap|8209 ED0E 42EA}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1994}} || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 ECFF 4CDD}} || {{nowrap|8209 ED02 4B8A}} || {{nowrap|8209 ED05 4A3C}} || {{nowrap|8209 ED08 48ED}} || {{nowrap|8209 ED0B 4795}} || {{nowrap|8209 ED0E 4635}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 ECFF 5023}} || {{nowrap|8209 ED02 4ECC}} || {{nowrap|8209 ED05 4D7D}} || {{nowrap|8209 ED08 4C2F}} || {{nowrap|8209 ED0B 4ADC}} || {{nowrap|8209 ED0E 4980}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 ECFF 536B}} || {{nowrap|8209 ED02 520F}} || {{nowrap|8209 ED05 50BD}} || {{nowrap|8209 ED08 4F6F}} || {{nowrap|8209 ED0B 4E1F}} || {{nowrap|8209 ED0E 4CC8}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 ECFF 56B3}} || {{nowrap|8209 ED02 5553}} || {{nowrap|8209 ED05 53FD}} || {{nowrap|8209 ED08 52AE}} || {{nowrap|8209 ED0B 5160}} || {{nowrap|8209 ED0E 500D}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 9}} || {{nowrap|8209 ECFF 59FB}} || {{nowrap|8209 ED02 5899}} || {{nowrap|8209 ED05 573E}} || {{nowrap|8209 ED08 55EC}} || {{nowrap|8209 ED0B 549E}} || {{nowrap|8209 ED0E 534F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 ECFF 5D41}} || {{nowrap|8209 ED02 5BDF}} || {{nowrap|8209 ED05 5A80}} || {{nowrap|8209 ED08 592A}} || {{nowrap|8209 ED0B 57DB}} || {{nowrap|8209 ED0E 568D}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 ECFF 6085}} || {{nowrap|8209 ED02 5F26}} || {{nowrap|8209 ED05 5DC4}} || {{nowrap|8209 ED08 5C69}} || {{nowrap|8209 ED0B 5B17}} || {{nowrap|8209 ED0E 59C9}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 ECFF 63C6}} || {{nowrap|8209 ED02 626B}} || {{nowrap|8209 ED05 6109}} || {{nowrap|8209 ED08 5FAA}} || {{nowrap|8209 ED0B 5E54}} || {{nowrap|8209 ED0E 5D06}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 ECFF 6706}} || {{nowrap|8209 ED02 65AF}} || {{nowrap|8209 ED05 6450}} || {{nowrap|8209 ED08 62EE}} || {{nowrap|8209 ED0B 6194}} || {{nowrap|8209 ED0E 6043}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 ECFF 6A45}} || {{nowrap|8209 ED02 68F3}} || {{nowrap|8209 ED05 6797}} || {{nowrap|8209 ED08 6635}} || {{nowrap|8209 ED0B 64D7}} || {{nowrap|8209 ED0E 6382}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 ECFF 6D85}} || {{nowrap|8209 ED02 6C35}} || {{nowrap|8209 ED05 6ADF}} || {{nowrap|8209 ED08 697F}} || {{nowrap|8209 ED0B 681D}} || {{nowrap|8209 ED0E 66C4}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 ECFF 70C5}} || {{nowrap|8209 ED02 6F77}} || {{nowrap|8209 ED05 6E25}} || {{nowrap|8209 ED08 6CC9}} || {{nowrap|8209 ED0B 6B67}} || {{nowrap|8209 ED0E 6A08}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1995}} || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 ECFF 7748}} || {{nowrap|8209 ED02 72B8}} || {{nowrap|8209 ED05 7169}} || {{nowrap|8209 ED08 7012}} || {{nowrap|8209 ED0B 6EB2}} || {{nowrap|8209 ED0E 6D50}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 ECFF 7A8C}} || {{nowrap|8209 ED02 75F9}} || {{nowrap|8209 ED05 74AB}} || {{nowrap|8209 ED08 7358}} || {{nowrap|8209 ED0B 71FD}} || {{nowrap|8209 ED0E 709B}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 ECFF 7DD1}} || {{nowrap|8209 ED02 7939}} || {{nowrap|8209 ED05 77EB}} || {{nowrap|8209 ED08 769C}} || {{nowrap|8209 ED0B 7545}} || {{nowrap|8209 ED0E 73E5}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 ECFF 8117}} || {{nowrap|8209 ED02 7C7A}} || {{nowrap|8209 ED05 7B2A}} || {{nowrap|8209 ED08 79DD}} || {{nowrap|8209 ED0B 788A}} || {{nowrap|8209 ED0E 772F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 ECFF 845E}} || {{nowrap|8209 ED02 7FBB}} || {{nowrap|8209 ED05 7E69}} || {{nowrap|8209 ED08 7D1B}} || {{nowrap|8209 ED0B 7BCC}} || {{nowrap|8209 ED0E 7A75}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 28}} || {{nowrap|8209 ECFF 87A4}} || {{nowrap|8209 ED02 82FE}} || {{nowrap|8209 ED05 81A8}} || {{nowrap|8209 ED08 8058}} || {{nowrap|8209 ED0B 7F0A}} || {{nowrap|8209 ED0E 7DB8}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 ECFF 8AE9}} || {{nowrap|8209 ED02 8642}} || {{nowrap|8209 ED05 84E7}} || {{nowrap|8209 ED08 8395}} || {{nowrap|8209 ED0B 8247}} || {{nowrap|8209 ED0E 80F7}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 ECFF 8E2D}} || {{nowrap|8209 ED02 8988}} || {{nowrap|8209 ED05 8828}} || {{nowrap|8209 ED08 86D2}} || {{nowrap|8209 ED0B 8583}} || {{nowrap|8209 ED0E 8435}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 ECFF 9170}} || {{nowrap|8209 ED02 8CCE}} || {{nowrap|8209 ED05 8B6C}} || {{nowrap|8209 ED08 8A11}} || {{nowrap|8209 ED0B 88C0}} || {{nowrap|8209 ED0E 8772}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 ECFF 94B2}} || {{nowrap|8209 ED02 9015}} || {{nowrap|8209 ED05 8EB3}} || {{nowrap|8209 ED08 8D54}} || {{nowrap|8209 ED0B 8BFF}} || {{nowrap|8209 ED0E 8AB0}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 ECFF 97F3}} || {{nowrap|8209 ED02 935C}} || {{nowrap|8209 ED05 91FC}} || {{nowrap|8209 ED08 909B}} || {{nowrap|8209 ED0B 8F40}} || {{nowrap|8209 ED0E 8DEF}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 ECFF 9B34}} || {{nowrap|8209 ED02 96A1}} || {{nowrap|8209 ED05 9546}} || {{nowrap|8209 ED08 93E4}} || {{nowrap|8209 ED0B 9285}} || {{nowrap|8209 ED0E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 ECFF 9B34}} || {{nowrap|8209 ED02 99E5}} || {{nowrap|8209 ED05 988E}} || {{nowrap|8209 ED08 972F}} || {{nowrap|8209 ED0B 95CD}} || {{nowrap|8209 ED0E 9473}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 19}} || {{nowrap|8209 ECFF 9E74}} || {{nowrap|8209 ED02 9D27}} || {{nowrap|8209 ED05 9BD4}} || {{nowrap|8209 ED08 9A79}} || {{nowrap|8209 ED0B 9917}} || {{nowrap|8209 ED0E 97B8}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 ECFF A1B5}} || {{nowrap|8209 ED02 A067}} || {{nowrap|8209 ED05 9F18}} || {{nowrap|8209 ED08 9DC2}} || {{nowrap|8209 ED0B 9C62}} || {{nowrap|8209 ED0E 9B01}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 ECFF A4F7}} || {{nowrap|8209 ED02 A3A7}} || {{nowrap|8209 ED05 A259}} || {{nowrap|8209 ED08 A107}} || {{nowrap|8209 ED0B 9FAC}} || {{nowrap|8209 ED0E 9E4A}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 ECFF A839}} || {{nowrap|8209 ED02 A6E6}} || {{nowrap|8209 ED05 A598}} || {{nowrap|8209 ED08 A449}} || {{nowrap|8209 ED0B A2F3}} || {{nowrap|8209 ED0E A193}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 17}} || {{nowrap|8209 ECFF AB7C}} || {{nowrap|8209 ED02 AA25}} || {{nowrap|8209 ED05 A8D6}} || {{nowrap|8209 ED08 A788}} || {{nowrap|8209 ED0B A635}} || {{nowrap|8209 ED0E A4DA}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 ECFF AEC1}} || {{nowrap|8209 ED02 AD65}} || {{nowrap|8209 ED05 AC12}} || {{nowrap|8209 ED08 AAC4}} || {{nowrap|8209 ED0B A975}} || {{nowrap|8209 ED0E A81E}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 ECFF B206}} || {{nowrap|8209 ED02 B0A6}} || {{nowrap|8209 ED05 AF50}} || {{nowrap|8209 ED08 AE00}} || {{nowrap|8209 ED0B ACB3}} || {{nowrap|8209 ED0E AB60}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 ECFF B54C}} || {{nowrap|8209 ED02 B3EA}} || {{nowrap|8209 ED05 B28F}} || {{nowrap|8209 ED08 B13D}} || {{nowrap|8209 ED0B AFEF}} || {{nowrap|8209 ED0E AEA0}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 ECFF B893}} || {{nowrap|8209 ED02 B731}} || {{nowrap|8209 ED05 B5D2}} || {{nowrap|8209 ED08 B47C}} || {{nowrap|8209 ED0B B32D}} || {{nowrap|8209 ED0E B1DF}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 ECFF BBD9}} || {{nowrap|8209 ED02 BA7A}} || {{nowrap|8209 ED05 B918}} || {{nowrap|8209 ED08 B7BD}} || {{nowrap|8209 ED0B B66B}} || {{nowrap|8209 ED0E B51E}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 ECFF BF1E}} || {{nowrap|8209 ED02 BDC3}} || {{nowrap|8209 ED05 BC61}} || {{nowrap|8209 ED08 BB02}} || {{nowrap|8209 ED0B B9AC}} || {{nowrap|8209 ED0E B85D}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 ECFF C261}} || {{nowrap|8209 ED02 C10B}} || {{nowrap|8209 ED05 BFAC}} || {{nowrap|8209 ED08 BE4A}} || {{nowrap|8209 ED0B BCEF}} || {{nowrap|8209 ED0E BB9D}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 ECFF C5A2}} || {{nowrap|8209 ED02 C451}} || {{nowrap|8209 ED05 C2F6}} || {{nowrap|8209 ED08 C194}} || {{nowrap|8209 ED0B C035}} || {{nowrap|8209 ED0E BEDF}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 ECFF C8E3}} || {{nowrap|8209 ED02 C794}} || {{nowrap|8209 ED05 C63F}} || {{nowrap|8209 ED08 C4E0}} || {{nowrap|8209 ED0B C37E}} || {{nowrap|8209 ED0E C223}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 ECFF CC23}} || {{nowrap|8209 ED02 CAD6}} || {{nowrap|8209 ED05 C984}} || {{nowrap|8209 ED08 C82A}} || {{nowrap|8209 ED0B C6C8}} || {{nowrap|8209 ED0E C569}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 ECFF CF63}} || {{nowrap|8209 ED02 CE15}} || {{nowrap|8209 ED05 CCC6}} || {{nowrap|8209 ED08 CB70}} || {{nowrap|8209 ED0B CA11}} || {{nowrap|8209 ED0E C8AF}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 6}} || {{nowrap|8209 ECFF D2A3}} || {{nowrap|8209 ED02 D153}} || {{nowrap|8209 ED05 D005}} || {{nowrap|8209 ED08 CEB3}} || {{nowrap|8209 ED0B CD58}} || {{nowrap|8209 ED0E CBF6}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 ECFF D5E3}} || {{nowrap|8209 ED02 D490}} || {{nowrap|8209 ED05 D342}} || {{nowrap|8209 ED08 D1F3}} || {{nowrap|8209 ED0B D09C}} || {{nowrap|8209 ED0E CF3D}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 ECFF D925}} || {{nowrap|8209 ED02 D7CD}} || {{nowrap|8209 ED05 D67E}} || {{nowrap|8209 ED08 D530}} || {{nowrap|8209 ED0B D3DE}} || {{nowrap|8209 ED0E D283}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 ECFF DC69}} || {{nowrap|8209 ED02 DB0D}} || {{nowrap|8209 ED05 D9BB}} || {{nowrap|8209 ED08 D86D}} || {{nowrap|8209 ED0B D71E}} || {{nowrap|8209 ED0E D5C7}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 ECFF DFB0}} || {{nowrap|8209 ED02 DE50}} || {{nowrap|8209 ED05 DCF9}} || {{nowrap|8209 ED08 DBAA}} || {{nowrap|8209 ED0B DA5C}} || {{nowrap|8209 ED0E D90A}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 ECFF E2F8}} || {{nowrap|8209 ED02 E196}} || {{nowrap|8209 ED05 E03A}} || {{nowrap|8209 ED08 DEE8}} || {{nowrap|8209 ED0B DD9A}} || {{nowrap|8209 ED0E DC4B}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 ECFF E640}} || {{nowrap|8209 ED02 E4DE}} || {{nowrap|8209 ED05 E37F}} || {{nowrap|8209 ED08 E228}} || {{nowrap|8209 ED0B E0D9}} || {{nowrap|8209 ED0E DF8B}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 ECFF E987}} || {{nowrap|8209 ED02 E829}} || {{nowrap|8209 ED05 E6C7}} || {{nowrap|8209 ED08 E56B}} || {{nowrap|8209 ED0B E419}} || {{nowrap|8209 ED0E E2CB}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 ECFF ECCD}} || {{nowrap|8209 ED02 EB73}} || {{nowrap|8209 ED05 EA11}} || {{nowrap|8209 ED08 E8B1}} || {{nowrap|8209 ED0B E75B}} || {{nowrap|8209 ED0E E60C}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 ECFF F010}} || {{nowrap|8209 ED02 EEBB}} || {{nowrap|8209 ED05 ED5C}} || {{nowrap|8209 ED08 EBFB}} || {{nowrap|8209 ED0B EA9F}} || {{nowrap|8209 ED0E E94D}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 ECFF F352}} || {{nowrap|8209 ED02 F201}} || {{nowrap|8209 ED05 F0A7}} || {{nowrap|8209 ED08 EF45}} || {{nowrap|8209 ED0B EDE5}} || {{nowrap|8209 ED0E EC8F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 ECFF F692}} || {{nowrap|8209 ED02 F543}} || {{nowrap|8209 ED05 F3EE}} || {{nowrap|8209 ED08 F28F}} || {{nowrap|8209 ED0B F12D}} || {{nowrap|8209 ED0E EFD2}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 ECFF F9D0}} || {{nowrap|8209 ED02 F882}} || {{nowrap|8209 ED05 F731}} || {{nowrap|8209 ED08 F5D6}} || {{nowrap|8209 ED0B F474}} || {{nowrap|8209 ED0E F315}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 25}} || {{nowrap|8209 ECFF FD0D}} || {{nowrap|8209 ED02 FBBF}} || {{nowrap|8209 ED05 FA70}} || {{nowrap|8209 ED08 F91A}} || {{nowrap|8209 ED0B F7BB}} || {{nowrap|8209 ED0E F659}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 ED00 004B}} || {{nowrap|8209 ED02 FEFB}} || {{nowrap|8209 ED05 FDAE}} || {{nowrap|8209 ED08 FC5C}} || {{nowrap|8209 ED0B FB01}} || {{nowrap|8209 ED0E F99F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 ED00 038B}} || {{nowrap|8209 ED03 0238}} || {{nowrap|8209 ED06 00EA}} || {{nowrap|8209 ED08 FF9B}} || {{nowrap|8209 ED0B FE45}} || {{nowrap|8209 ED0E FCE6}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 ED00 06CE}} || {{nowrap|8209 ED03 0576}} || {{nowrap|8209 ED06 0427}} || {{nowrap|8209 ED09 02D9}} || {{nowrap|8209 ED0C 0187}} || {{nowrap|8209 ED0F 002C}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 ED00 0A14}} || {{nowrap|8209 ED03 08B8}} || {{nowrap|8209 ED06 0765}} || {{nowrap|8209 ED09 0617}} || {{nowrap|8209 ED0C 04C8}} || {{nowrap|8209 ED0F 0371}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 ED00 0D5C}} || {{nowrap|8209 ED03 0BFC}} || {{nowrap|8209 ED06 0AA5}} || {{nowrap|8209 ED09 0955}} || {{nowrap|8209 ED0C 0807}} || {{nowrap|8209 ED0F 06B5}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 ED00 10A6}} || {{nowrap|8209 ED03 0F44}} || {{nowrap|8209 ED06 0DE8}} || {{nowrap|8209 ED09 0C95}} || {{nowrap|8209 ED0C 0B47}} || {{nowrap|8209 ED0F 09F8}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 ED00 13EF}} || {{nowrap|8209 ED03 128E}} || {{nowrap|8209 ED06 112E}} || {{nowrap|8209 ED09 0FD7}} || {{nowrap|8209 ED0C 0E87}} || {{nowrap|8209 ED0F 0D3A}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 ED00 1738}} || {{nowrap|8209 ED03 15D9}} || {{nowrap|8209 ED06 1477}} || {{nowrap|8209 ED09 131B}} || {{nowrap|8209 ED0C 11C9}} || {{nowrap|8209 ED0F 107B}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 ED00 1A7D}} || {{nowrap|8209 ED03 1924}} || {{nowrap|8209 ED06 17C2}} || {{nowrap|8209 ED09 1662}} || {{nowrap|8209 ED0C 150B}} || {{nowrap|8209 ED0F 13BC}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 ED00 1DC0}} || {{nowrap|8209 ED03 1C6B}} || {{nowrap|8209 ED06 1B0C}} || {{nowrap|8209 ED09 19AA}} || {{nowrap|8209 ED0C 184F}} || {{nowrap|8209 ED0F 16FC}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 ED00 20FF}} || {{nowrap|8209 ED03 1FAE}} || {{nowrap|8209 ED06 1E54}} || {{nowrap|8209 ED09 1CF3}} || {{nowrap|8209 ED0C 1B93}} || {{nowrap|8209 ED0F 1A3C}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 14}} || {{nowrap|8209 ED00 243C}} || {{nowrap|8209 ED03 22EE}} || {{nowrap|8209 ED06 2198}} || {{nowrap|8209 ED09 203A}} || {{nowrap|8209 ED0C 1ED8}} || {{nowrap|8209 ED0F 1D7C}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 ED00 2779}} || {{nowrap|8209 ED03 262B}} || {{nowrap|8209 ED06 24DA}} || {{nowrap|8209 ED09 2380}} || {{nowrap|8209 ED0C 221E}} || {{nowrap|8209 ED0F 20BE}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 ED00 2AB6}} || {{nowrap|8209 ED03 2968}} || {{nowrap|8209 ED06 2819}} || {{nowrap|8209 ED09 26C3}} || {{nowrap|8209 ED0C 2564}} || {{nowrap|8209 ED0F 2403}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 ED00 2DF4}} || {{nowrap|8209 ED03 2CA4}} || {{nowrap|8209 ED06 2B57}} || {{nowrap|8209 ED09 2A05}} || {{nowrap|8209 ED0C 28AA}} || {{nowrap|8209 ED0F 2748}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 ED00 3135}} || {{nowrap|8209 ED03 2FE2}} || {{nowrap|8209 ED06 2E94}} || {{nowrap|8209 ED09 2D45}} || {{nowrap|8209 ED0C 2BEF}} || {{nowrap|8209 ED0F 2A8F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 ED00 3479}} || {{nowrap|8209 ED03 3322}} || {{nowrap|8209 ED06 31D2}} || {{nowrap|8209 ED09 3084}} || {{nowrap|8209 ED0C 2F32}} || {{nowrap|8209 ED0F 2DD7}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 ED00 37C1}} || {{nowrap|8209 ED03 3664}} || {{nowrap|8209 ED06 3511}} || {{nowrap|8209 ED09 33C3}} || {{nowrap|8209 ED0C 3274}} || {{nowrap|8209 ED0F 311E}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 ED00 3B0B}} || {{nowrap|8209 ED03 39AA}} || {{nowrap|8209 ED06 3853}} || {{nowrap|8209 ED09 3703}} || {{nowrap|8209 ED0C 35B6}} || {{nowrap|8209 ED0F 3464}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 ED00 3E56}} || {{nowrap|8209 ED03 3CF4}} || {{nowrap|8209 ED06 3B98}} || {{nowrap|8209 ED09 3A45}} || {{nowrap|8209 ED0C 38F7}} || {{nowrap|8209 ED0F 37A8}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 ED00 41A0}} || {{nowrap|8209 ED03 403F}} || {{nowrap|8209 ED06 3EDF}} || {{nowrap|8209 ED09 3D88}} || {{nowrap|8209 ED0C 3C38}} || {{nowrap|8209 ED0F 3AEA}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 ED00 44E8}} || {{nowrap|8209 ED03 438A}} || {{nowrap|8209 ED06 4228}} || {{nowrap|8209 ED09 40CB}} || {{nowrap|8209 ED0C 3F78}} || {{nowrap|8209 ED0F 3E2A}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 ED00 482B}} || {{nowrap|8209 ED03 46D2}} || {{nowrap|8209 ED06 4570}} || {{nowrap|8209 ED09 4410}} || {{nowrap|8209 ED0C 42B9}} || {{nowrap|8209 ED0F 4169}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 3}} || {{nowrap|8209 ED00 4B6B}} || {{nowrap|8209 ED03 4A16}} || {{nowrap|8209 ED06 48B8}} || {{nowrap|8209 ED09 4756}} || {{nowrap|8209 ED0C 45FA}} || {{nowrap|8209 ED0F 44A7}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 ED00 4EA9}} || {{nowrap|8209 ED03 4D58}} || {{nowrap|8209 ED06 4BFE}} || {{nowrap|8209 ED09 4A9D}} || {{nowrap|8209 ED0C 493D}} || {{nowrap|8209 ED0F 47E6}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 ED00 51E5}} || {{nowrap|8209 ED03 5097}} || {{nowrap|8209 ED06 4F42}} || {{nowrap|8209 ED09 4DE3}} || {{nowrap|8209 ED0C 4C81}} || {{nowrap|8209 ED0F 4B26}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 ED00 5522}} || {{nowrap|8209 ED03 53D4}} || {{nowrap|8209 ED06 5283}} || {{nowrap|8209 ED09 5129}} || {{nowrap|8209 ED0C 4FC7}} || {{nowrap|8209 ED0F 4E67}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 ED00 585F}} || {{nowrap|8209 ED03 5711}} || {{nowrap|8209 ED06 55C2}} || {{nowrap|8209 ED09 546D}} || {{nowrap|8209 ED0C 530E}} || {{nowrap|8209 ED0F 51AC}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 ED00 5B9F}} || {{nowrap|8209 ED03 5A4F}} || {{nowrap|8209 ED06 5901}} || {{nowrap|8209 ED09 57AF}} || {{nowrap|8209 ED0C 5654}} || {{nowrap|8209 ED0F 54F2}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 ED00 5EE1}} || {{nowrap|8209 ED03 5D8E}} || {{nowrap|8209 ED06 5C40}} || {{nowrap|8209 ED09 5AF1}} || {{nowrap|8209 ED0C 599B}} || {{nowrap|8209 ED0F 583B}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 ED00 6227}} || {{nowrap|8209 ED03 60CF}} || {{nowrap|8209 ED06 5F7F}} || {{nowrap|8209 ED09 5E32}} || {{nowrap|8209 ED0C 5CE0}} || {{nowrap|8209 ED0F 5B85}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 ED00 6571}} || {{nowrap|8209 ED03 6414}} || {{nowrap|8209 ED06 62C1}} || {{nowrap|8209 ED09 6173}} || {{nowrap|8209 ED0C 6024}} || {{nowrap|8209 ED0F 5ECE}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 ED00 68BC}} || {{nowrap|8209 ED03 675C}} || {{nowrap|8209 ED06 6604}} || {{nowrap|8209 ED09 64B4}} || {{nowrap|8209 ED0C 6366}} || {{nowrap|8209 ED0F 6214}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 ED00 6C07}} || {{nowrap|8209 ED03 6AA5}} || {{nowrap|8209 ED06 6948}} || {{nowrap|8209 ED09 67F5}} || {{nowrap|8209 ED0C 66A6}} || {{nowrap|8209 ED0F 6557}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 ED00 6F4F}} || {{nowrap|8209 ED03 6DEE}} || {{nowrap|8209 ED06 6C8E}} || {{nowrap|8209 ED09 6B36}} || {{nowrap|8209 ED0C 69E6}} || {{nowrap|8209 ED0F 6898}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 ED00 7294}} || {{nowrap|8209 ED03 7136}} || {{nowrap|8209 ED06 6FD4}} || {{nowrap|8209 ED09 6E77}} || {{nowrap|8209 ED0C 6D24}} || {{nowrap|8209 ED0F 6BD6}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|May 22}} || {{nowrap|8209 ED00 75D5}} || {{nowrap|8209 ED03 747C}} || {{nowrap|8209 ED06 731B}} || {{nowrap|8209 ED09 71BB}} || {{nowrap|8209 ED0C 7063}} || {{nowrap|8209 ED0F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 ED00 7915}} || {{nowrap|8209 ED03 77C0}} || {{nowrap|8209 ED06 7662}} || {{nowrap|8209 ED09 7500}} || {{nowrap|8209 ED0C 73A4}} || {{nowrap|8209 ED0F 7251}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 ED00 7C52}} || {{nowrap|8209 ED03 7B01}} || {{nowrap|8209 ED06 79A7}} || {{nowrap|8209 ED09 7846}} || {{nowrap|8209 ED0C 76E6}} || {{nowrap|8209 ED0F 758F}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 ED00 7F8E}} || {{nowrap|8209 ED03 7E40}} || {{nowrap|8209 ED06 7CEB}} || {{nowrap|8209 ED09 7B8C}} || {{nowrap|8209 ED0C 7A2A}} || {{nowrap|8209 ED0F 78CE}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 ED00 82CB}} || {{nowrap|8209 ED03 817E}} || {{nowrap|8209 ED06 802C}} || {{nowrap|8209 ED09 7ED2}} || {{nowrap|8209 ED0C 7D70}} || {{nowrap|8209 ED0F 7C11}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 ED00 860A}} || {{nowrap|8209 ED03 84BC}} || {{nowrap|8209 ED06 836D}} || {{nowrap|8209 ED09 8218}} || {{nowrap|8209 ED0C 80B9}} || {{nowrap|8209 ED0F 7F57}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 ED00 894C}} || {{nowrap|8209 ED03 87FB}} || {{nowrap|8209 ED06 86AE}} || {{nowrap|8209 ED09 855C}} || {{nowrap|8209 ED0C 8402}} || {{nowrap|8209 ED0F 82A0}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 ED00 8C90}} || {{nowrap|8209 ED03 8B3D}} || {{nowrap|8209 ED06 89EF}} || {{nowrap|8209 ED09 88A0}} || {{nowrap|8209 ED0C 874A}} || {{nowrap|8209 ED0F 85EC}}
|- style=&quot;background-color: #eaecf0;{{text default color}}; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;{{text default color}};&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 ED00 8FD8}} || {{nowrap|8209 ED03 8E80}} || {{nowrap|8209 ED06 8D30}} || {{nowrap|8209 ED09 8BE2}} || {{nowrap|8209 ED0C 8A90}} || {{nowrap|8209 ED0F 8936}}
|- style=&quot;font-size:small:small;background-color: #ffffff;{{text default color}};&quot;
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|}</text>
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  </page>
  <page>
    <title>Athena problem</title>
    <ns>0</ns>
    <id>329548</id>
    <revision>
      <id>2831828</id>
      <parentid>2829786</parentid>
      <timestamp>2026-09-06T18:16:25Z</timestamp>
      <contributor>
        <username>Athene241</username>
        <id>3100061</id>
      </contributor>
      <comment>/* Solve the problem */</comment>
      <origin>2831828</origin>
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      <text bytes="157410" sha1="11rva51285ey6rt9xv0ttvy2y0smhry" xml:space="preserve">{{mathematics}}
'''Athena problem''' is an [[:w:List of unsolved problems in mathematics|unsolved problem]] in [[:w:Number theory|number theory]] and [[:w:Formal language theory|formal language theory]] and [[:w:Order theory|order theory]], this problem is named after the ancient Greek goddess [[:w:Athena|Athena]] (which is associated with [[:w:Wisdom|wisdom]]). Athena problem is: Give a [[:w:Natural number|natural number]] ''b'' &gt; 1, find the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the set of the &quot;[[:w:Prime number|prime number]] [[:w:Greater than|&gt;]] ''b''&quot; [[:w:Numerical digit|digit]] [[:w:String (computer science)|string]]s in the [[:w:Positional numeral system|positional numeral system]] with [[:w:Radix|base]] ''b'' for the [[:w:Subsequence|subsequence]] [[:w:Partially ordered set|ordering]]. (A string ''x'' is a subsequence of another string ''y'', if ''x'' can be obtained from ''y'' by deleting zero or more of the [[:w:Character (computing)|character]]s in ''y''. For example, 514 is a subsequence of 352148, &quot;string&quot; is a subsequence of &quot;meistersinger&quot;. In contrast, 758 is not a subsequence of 378259, &quot;abc&quot; is not a subsequence of &quot;cbacacba&quot;, since the characters must be in the same order) (Unlike [[:w:Substring|substring]], subsequence is not required to occupy consecutive positions within the original sequences, e.g. the [[:w:Longest common subsequence|longest common subsequence problem]] is different from the [[:w:Longest common substring|longest common substring problem]])

Using [[:w:Formal language theory|formal language theory]] terminology, Athena problem is finding the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the [[:w:Formal language|language]] of base-''b'' [[:w:Representation (mathematics)|representation]]s of the [[:w:Prime number|prime number]]s [[:w:Greater than|&gt;]] ''b'' (which is a set of [[:w:String (computer science)|string]]s of [[:w:Symbol|symbol]]s over the [[:w:Alphabet (formal languages)|alphabet]] ''Σ''&lt;sub&gt;''b''&lt;/sub&gt; := {0, 1, ..., ''b''−1}), under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] &quot;is a subsequence of&quot;, which is a [[:w:Partially ordered set|partial ordering]]), for a given natural number ''b'' &gt; 1 (You can draw this partial ordering as a [[:w:Hasse diagram|Hasse diagram]] to find all [[:w:Minimal element|minimal element]]s), this set is called '''Athena set''', and the prime numbers in this set are called '''Athena primes'''.

By [[:w:Higman's lemma|Higman's lemma]], there are no [[:w:Infinite set|infinite]] [[:w:Antichain|antichain]]s for the subsequence ordering (i.e. the subsequence ordering is always a [[:w:Well-quasi-ordering|well quasi order]]) (i.e. under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] &quot;is a subsequence of&quot;, which is a [[:w:Partially ordered set|partial ordering]]), every set of pairwise incomparable (i.e. not [[:w:Comparability|comparable]]) strings is finite), thus there must be only finitely many such minimal elements. In other words, the Athena set in every base ''b'' must be a [[:w:Finite set|finite set]], and every base ''b'' ≥ 2 has only finitely many Athena primes, e.g. in [[:w:Decimal|decimal]] (base ''b'' = 10), the Athena set has exactly 77 [[:w:Element of a set|element]]s (they are exactly the Athena primes in decimal (base ''b'' = 10)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}.

Determining the set of the minimal elements of a arbitrary set of strings under the subsequence ordering is in general [[:w:List of unsolved problems in mathematics|unsolvable]], and can be difficult even when this set is relatively simple (such as the base ''b'' representations of the prime numbers &gt; ''b'', whose set is exactly the Athena set in base ''b'').

Although the set ''M''(''S'') of minimal strings is necessarily [[:w:Finite set|finite]], determining it explicitly for a given ''S'' can be a difficult computational problem. We use some [[:w:Number theory|numbertheoretic]] [[:w:Heuristic argument|heuristic]]s to [[:w:Computing|compute]] ''M''(''L''&lt;sub&gt;''b''&lt;/sub&gt;) (i.e. to compute the Athena set in base ''b''), where ''L''&lt;sub&gt;''b''&lt;/sub&gt; is the [[:w:Formal language|language]] of [[:w:Radix|base]]-''b'' representations of the [[:w:Prime number|prime number]]s which are [[:w:Greater than|&gt;]] ''b'', for 2 ≤ ''b'' ≤ 36.

For bases 2 ≤ ''b'' ≤ 36, Athena problem is fully solved in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24, and also solved in bases ''b'' = 11, 13, 16, 22, 30 if [[:w:Probable prime|probable prime]]s are allowed. For the unsolved bases ''b'' = 17, 19, 21, 23, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, Athena problem is solved (if probable primes are allowed) except 771 [[:w:Indexed family|families]] of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be [[:w:Empty string|empty]]) of digits in base ''b'', ''y'' is a digit in base ''b'') = sequence {''xz'', ''xyz'', ''xyyz'', ''xyyyz'', ''xyyyyz'', ''xyyyyyz'', ...} (i.e. &quot;''xy''&lt;sup&gt;+&lt;/sup&gt;''z''&quot; in [[:w:Regular expression|regular expression]]), all of these 771 families contain no primes &gt; ''b'' or probable primes &gt; ''b'' with length ≤ 100000. (The chance that an unproven probable prime in these sets is in fact composite is less than 10&lt;sup&gt;−2000&lt;/sup&gt;, see https://t5k.org/notes/prp_prob.html)

== Solve the problem ==

To solve the Athena problem for a given base ''b'', we must [[:w:Computing|compute]] the elements up to families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), and find the smallest prime &gt; ''b'' in all such families.

We call families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') &quot;linear&quot; families, and we reduce these families by removing all trailing digits ''y'' from ''x'', and removing all leading digits ''y'' from ''z'', to make the families be easier, e.g. family 12333{3}33345 in base ''b'' is reduced to family 12{3}45 in base ''b'', since they are in fact the same family. Our [[:w:Algorithm|algorithm]] then proceeds as follows:

* 1. ''M'' := {minimal primes in base ''b'' of length 2 or 3}, ''L'' := union of all ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'') such that ''x'' ≠ 0 and ''gcd''(''z'', ''b'') = 1 and ''Y'' is the set of digits ''y'' in base ''b'' such that ''xyz'' has no subsequence in ''M''.
* 2. While ''L'' contains nonlinear families (families which are not linear families): Explore each family of ''L'', and update ''L''. Examine each family of ''L'' by:
* 2.1. Let ''w'' be the shortest string in the family. If ''w'' has a subsequence in ''M'', then remove the family from ''L''. If ''w'' represents a prime, then add ''w'' to ''M'' and remove the family from ''L''.
* 2.2. If possible, simplify the family.
* 2.3. Using the techniques below (covering congruence, algebraic factorization, or combine of them), check if the family can be proven to only contain composites (only count the numbers &gt; ''b''), and if so then remove the family from ''L''.
* 3. Update ''L'', after each split examine the new families as in step 2.

e.g. in decimal (base ''b'' = 10):

''M'' := {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991}

''L'' := {2{0,2}1, 2{0,8}7, 3{0,3,6,9}3, 3{0,3,6,9}9, 4{6}9, 5{0,5,8}1, 5{0,2}7, 6{0,3,6,9}3, 6{0,3,4,6,9}9, 7{0,7}7, 8{0,5}1, 8{0}7, 9{0,2,5,8}1, 9{0,3,6,9}3, 9{0,3,4,6,9}9}

and since 2221 is prime, it follows that the family 2{0,2}1 splits into the families 2{0}1 and 2{0}2{0}1

and since the family 2{0}1 can be proven to contain no primes &gt; base (since all numbers in this family are divisible by 3), it can be removed

and since 20201 is prime, it follows that the family 2{0}2{0}1 splits into the families 2{0}21 and 22{0}1

221 and 2021 are composites, but 20021 is prime, thus add 20021 to ''L''

none of 221, 2201, 22001, 220001, 2200001 are primes, but 22000001 is prime, thus add 22000001 to ''L''

and since the family 3{0,3,6,9}3 can be proven to contain no primes &gt; base (since all numbers in this family are divisible by 3), it can be removed

etc.

Since the number of possible (first digit,last digit) (also called (initial digit,final digit)) combos ([[:w:Ordered pair|ordered pair]]s) of a prime &gt; ''b'' in base ''b'' is (''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(''b'') (all digits except 0 can be the first digit of a prime &gt; ''b'' in base ''b'' (thus ''b''−1 possible digits), but only the digits coprime to ''b'' can be the last digit of a prime &gt; ''b'' in base ''b'' (thus ''eulerphi''(''b'') possible digits), and by the [[:w:Rule of product|rule of product]], there are (''b''−1)×''eulerphi''(''b'') choices of the (first digit,last digit) combo, also, both &quot;numbers of Athena primes in base ''b''&quot; and &quot;length of the largest Athena prime in base ''b''&quot; are [[:w:Asymptotic analysis|roughly]] ''[[:w:E (mathematical_constant)|e]]''&lt;sup&gt;''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)&lt;/sup&gt;.

Shrinking the family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'')

* If ''y'' ∈ ''Y'' and the string ''xyyz'' represents a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''}''z'' ∪ ''x''{''Y'' \ ''y''}''y''{''Y'' \ ''y''}''z''.
* If ''y''&lt;sub&gt;1&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;2&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;1&lt;/sub&gt; ≠ ''y''&lt;sub&gt;2&lt;/sub&gt; and the string ''xy''&lt;sub&gt;1&lt;/sub&gt;''y''&lt;sub&gt;2&lt;/sub&gt;''z'' represents a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''&lt;sub&gt;1&lt;/sub&gt;}{''Y'' \ ''y''&lt;sub&gt;2&lt;/sub&gt;}''z''.
* If ''y''&lt;sub&gt;1&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;2&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;1&lt;/sub&gt; ≠ ''y''&lt;sub&gt;2&lt;/sub&gt; and both the strings ''xy''&lt;sub&gt;1&lt;/sub&gt;''y''&lt;sub&gt;2&lt;/sub&gt;''z'' and ''xy''&lt;sub&gt;2&lt;/sub&gt;''y''&lt;sub&gt;1&lt;/sub&gt;''z'' represent a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or have a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''&lt;sub&gt;1&lt;/sub&gt;}''z'' ∪ ''x''{''Y'' \ ''y''&lt;sub&gt;2&lt;/sub&gt;}''z''.

e.g. in decimal (base ''b'' = 10):

* 2221 is a prime &gt; 10, thus the family 2{0,2}1 splits into the two families 2{0}1 and 2{0}2{0}1.
* 227 is a prime &gt; 10, and it is a subsequence of 5227, thus the family 5{0,2}7 splits into the two families 5{0}7 and 5{0}2{0}7.
* 449 is a prime &gt; 10, and it is a subsequence of 6449, thus the family 6{0,3,4,6,9}9 splits into the two families 6{0,3,6,9}9 and 6{0,3,6,9}4{0,3,6,9}9.
* Both 5051 and 5501 are primes &gt; 10, thus the family 5{0,5}1 splits into the two families 5{0}1 and 5{5}1 = {5}1.
* 8501 is a prime &gt; 10, thus the family 8{0,5}1 splits into the family 8{0}{5}1.
* 887 is a prime &gt; 10, and it is a subsequence of 2887, also 2087 is a prime &gt; 10, thus the family 2{0,8}7 splits into the two families 2{0}7 and 28{0}7.
* 349 and 449 are primes &gt; 10, and they are subsequences of 9349 and 9449, respectively, also 9049, 9649, 9949 are primes &gt; 10, thus the family 9{0,3,4,6,9}9 splits into the two families 9{0,3,6,9}9 and 94{0,3,6,9}9.
* 251, 281, 521, 821, 881 are primes &gt; 10, and they are subsequences of 9251, 9281, 9521, 9821, 9881, respectively, also 9001, 9221, 9551, 9851 are primes &gt; 10, thus the family 9{0,2,5,8}1 splits into the numbers {91, 901, 921, 951, 981, 9021, 9051, 9081, 9201, 9501, 9581, 9801, 90581, 95081, 95801}.

If the methods we have discussed cannot be used to rule out or shrink ''x''{''Y''}''z'' where ''Y'' = {''y''&lt;sub&gt;1&lt;/sub&gt;, ''y''&lt;sub&gt;2&lt;/sub&gt;, ..., ''y''&lt;sub&gt;''n''&lt;/sub&gt;}, then we can replace ''x''{''Y''}''z'' by ''xy''&lt;sub&gt;1&lt;/sub&gt;{''Y''}''z'' ∪ ''xy''&lt;sub&gt;2&lt;/sub&gt;{''Y''}''z'' ∪ ... ∪ ''xy''&lt;sub&gt;''n''&lt;/sub&gt;{''Y''}''z'' and re-run the methods on this new [[:w:Formal language|language]].

If all remain families are linear families (i.e. of the form ''x''{''y''}''z'', where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), then we search the smallest (probable) primes in these families and add these primes to the list.

e.g. in decimal (base ''b'' = 10):

* The smallest prime in the family 5{0}27 is 5000000000000000000000000000027.
* The smallest prime in the family {5}1 is 555555555551.
* The smallest prime in the family 8{5}1 is 8555555555555555555551, but 8555555555555555555551 is not a minimal element since 555555555551 is a subsequence of 8555555555555555555551.

There is no guarantee that the techniques discussed will ever terminate, but in practice they often do. They are able to determine the Athena set in base ''b'' for 2 ≤ ''b'' ≤ 16 and ''b'' = 18, 20, 22, 24, 30. The bases ''b'' = 17, 19, 21, 23, 25 ≤ ''b'' ≤ 29, 31 ≤ ''b'' ≤ 36 are solved with the exception of 771 families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'').

The following is a &quot;[[:w:Semi-algorithm|semi-algorithm]]&quot; that is guaranteed to solve the Athena problem for a given base ''b'', but it is not so easy to implement:

# ''M'' = ''[[:w:Empty string|∅]]''
# while (''L'' ≠ ''∅'') do
# choose ''x'', a shortest string in ''L''
# ''M'' := ''M'' ∪ {''x''}
# ''L'' := ''L'' − ''sup''({''x''})

In practice, for arbitrary ''L'', we cannot feasibly carry out step 5. Instead, we work with ''L''&amp;#39;, some regular overapproximation to ''L'', until we can show ''L''&amp;#39; = ''∅'' (which implies ''L'' = ''∅''). In practice, ''L''&amp;#39; is usually chosen to be a finite [[:w:Union (set theory)|union]] of sets of the form ''L''&lt;sub&gt;1&lt;/sub&gt;{''L''&lt;sub&gt;2&lt;/sub&gt;}''L''&lt;sub&gt;3&lt;/sub&gt;, where each of ''L''&lt;sub&gt;1&lt;/sub&gt;, ''L''&lt;sub&gt;2&lt;/sub&gt;, ''L''&lt;sub&gt;3&lt;/sub&gt; is finite. In the case we consider in this project, we then have to determine whether such a family contains a prime or not.

Thus, the [[:w:Time complexity|time complexity]] of the Athena problem in base ''b'' may be ''[[:w:Big O notation|O]]''(''[[:w:E (mathematical_constant)|e]]''&lt;sup&gt;''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)&lt;/sup&gt;), and the [[:w:CPU time|CPU time]] of the Athena problem in base ''b'' may be longer than [[:w:Age of the universe|the age of the universe]] for bases ''b'' = 19, 23, 25, 27, 29, 31, 32, 33, 34, 35, also, Athena problem in bases ''b'' around 500 may be [[:w:NP-complete|NP-complete]] or [[:w:NP-hard|NP-hard]], or an [[:w:Undecidable problem|undecidable problem]], or an example of [[:w:Gödel's incompleteness theorems|Gödel's incompleteness theorems]] (like the [[:w:Continuum hypothesis|continuum hypothesis]] and the [[:w:Halting problem|halting problem]]).

To solve the Athena problem (i.e. to compute the Athena set), we need to determine whether a given family contains a prime. In practice, if family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'') could not be ruled out as only containing composites and ''Y'' contains two or more digits, then a relatively small prime &gt; ''b'' could always be found in this family. Intuitively, this is because there are a large number of small strings in such a family, and at least one is likely to be prime (e.g. there are 2&lt;sup&gt;''n''−2&lt;/sup&gt; strings of length ''n'' in the family 1{3,7}9, and there are over a thousand strings of length 12 in the family 1{3,7}9, thus it is very impossible that these numbers are all composite). In the case ''Y'' contains only one digit, this family is of the form ''x''{''y''}''z'', and there is only a single string of each length &gt; (the length of ''x'' + the length of ''z''), and it is not known if the following [[:w:Decision problem|decision problem]] is recursively solvable (just like [[:w:Sierpiński number|Sierpiński problem]] and [[:w:Riesel number|Riesel problem]], Sierpiński problem and Riesel problem can be generalized to other bases ''b'' (references: http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm), in fact, Athena problem base ''b'' covers the Sierpiński problem base ''b'' and the Riesel problem base ''b'' with ''k'' &lt; ''b'', i.e. finding the smallest prime of the form ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 and ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (or prove such prime does not exist) with ''k'' &lt; ''b'' (specially, for bases ''b'' such that the conjectured smallest Sierpiński number or the conjectured smallest Riesel number is &lt; ''b'', Athena problem base ''b'' covers the Sierpiński problem base ''b'' or the Riesel problem base ''b'', respectively), since the smallest prime of the form ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 and ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (if exists) must be a minimal element in base ''b'', also, Athena problem base ''b'' covers finding the smallest prime of these forms in base ''b'' (or proving that such prime does not exist) (in fact, it is known that exactly what bases 2 ≤ ''b'' ≤ 1024 have the families listed in the table below as unsolved families, all of these families in all bases 2 ≤ ''b'' ≤ 1024 have been searched to length ≥ 10000 (for the family (''sqrt''(''b'')×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''sqrt''(''b'')+1), bases 2 ≤ ''b'' ≤ 1048576, searched to length ≥ 5000)): (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1) (for this form, ''n'' must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepu.txt, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379, https://pzktupel.de/Primetables/TableRepunitGen.php, https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A128164, https://oeis.org/A285642; or for prime bases ''b'': https://oeis.org/A065854, https://oeis.org/A279068), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 1) (references of this form: http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A228101), (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/2 (for odd ''b'') (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 2) (reference of this form: http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt), (''sqrt''(''b'')×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''sqrt''(''b'')+1) (for square ''b'') (for this form, 2×''n''+1 must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepuP.txt, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/488, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://oeis.org/A084742, https://oeis.org/A084741; or for bases ''b'' with ''sqrt''(''b'') prime: https://oeis.org/A065507), ((''b''−2)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''−1) (''n'' ≥ 2) (reference of this form: https://oeis.org/A243404), 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://oeis.org/A119624), 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&amp;d=1567314217, https://oeis.org/A119591), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+2 (''n'' ≥ 1) (references of this form: https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067), ''b''&lt;sup&gt;''n''&lt;/sup&gt;−2 (''n'' ≥ 2) (references of this form: https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A250200, https://oeis.org/A255707, https://oeis.org/A084714; or for prime bases ''b'': https://oeis.org/A292201), (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (''n'' ≥ 1) (references of this form: http://www.noprimeleftbehind.net/Williams-primes-MP.htm, http://www.bitman.name/math/table/477, https://pzktupel.de/Primetables/TableWilliams2.php, https://oeis.org/A305531; or for prime bases ''b'': https://oeis.org/A087139), (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (''n'' ≥ 1) (references of this form: https://harvey563.tripod.com/wills.txt, http://www.noprimeleftbehind.net/Williams-primes-MM.htm, http://www.bitman.name/math/table/484, https://pzktupel.de/Primetables/TableWilliams1.php; or for prime bases ''b'': https://oeis.org/A122396), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''−1) (''n'' ≥ 1) (references of this form: http://www.bitman.name/math/table/795, https://pzktupel.de/Primetables/TableWilliams6.php, https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179), ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''−1) (''n'' ≥ 2) (references of this form: http://www.bitman.name/math/table/792, https://pzktupel.de/Primetables/TableWilliams5.php, https://oeis.org/A113516, https://oeis.org/A343589; or for prime bases ''b'': https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/435)):

'''Problem: Given strings ''x'', ''z'' (may be empty), a digit ''y'', and a base ''b'' (''x'' does not [[:w:Leading zero|start with the digit 0]], ''z'' ends with a digit which [[:w:Coprime integers|coprime]] to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty), does there exist a prime number whose base-''b'' expansion is of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' for some ''n'' ≥ 0?'''

An [[:w:Algorithm|algorithm]] to solve this problem, for example, would allow us to decide if there are any additional [[:w:Fermat prime|Fermat prime]]s other than the known ones (corresponding to ''n'' = 0, 1, 2, 3, 4). To see this, take ''b'' = 2, ''x'' = 1, ''y'' = 0, and ''z'' = 0&lt;sub&gt;16&lt;/sub&gt;1. Since if 2&lt;sup&gt;''n''&lt;/sup&gt;+1 is prime then ''n'' must be a [[:w:Power of 2|power of two]], a prime of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' must be a new Fermat prime. Besides, it would allow us to decide if there are infinitely many [[:w:Mersenne prime|Mersenne prime]]s (of the form 2&lt;sup&gt;''p''&lt;/sup&gt;−1 with prime ''p''). To see this, take ''b'' = 2, ''x'' = ''𝜆'' (the [[:w:Empty string|empty string]]), ''y'' = 1, and ''z'' = 1&lt;sub&gt;''n''+1&lt;/sub&gt;, where ''n'' is the exponent of the Mersenne prime which we want to know whether it is the largest Mersenne prime or not. Since if 2&lt;sup&gt;''n''&lt;/sup&gt;−1 is prime then ''n'' must be a [[:w:Prime number|prime]], a prime of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' must be a new Mersenne prime. Also, it would allow us to decide whether 78557 is the smallest [[:w:Sierpinski number|Sierpinski number]] (i.e. odd numbers ''k'' such that ''k''×2&lt;sup&gt;''n''&lt;/sup&gt;+1 is composite for all ''n'' ≥ 1) and whether 509203 is the smallest [[:w:Riesel number|Riesel number]] (i.e. odd numbers ''k'' such that ''k''×2&lt;sup&gt;*n*&lt;/sup&gt;−1 is composite for all ''n'' ≥ 1), etc.

'''Conjecture (this conjecture is very important for the Athena problem): If family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' (with fixed strings ''x'', ''z'' (may be empty), fixed digit ''y'', and variable ''n'') in base ''b'' (with fixed ''b'' ≥ 2) (''x'' does not start with the digit 0, ''z'' ends with a digit which coprime to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty) cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' contains infinitely many primes (this is equivalent to: If form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) (with fixed integers ''a'' ≥ 1, ''b'' ≥ 2, ''c'' ≠ 0 (with ''gcd''(''a'',''c'') = 1 and ''gcd''(''b'',''c'') = 1), and variable ''n'') cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) contains infinitely many primes).'''

(in fact, this conjecture is equivalent to the conjecture (to prove this, by change the base (''b'') to a power of ''b'' which is larger than the largest prime in a given family (in base ''b'') which only contains finitely many primes): If family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' (with fixed strings ''x'', ''z'' (may be empty), fixed digit ''y'', and variable ''n'') in base ''b'' (with fixed ''b'' ≥ 2) (''x'' does not start with the digit 0, ''z'' ends with a digit which coprime to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty) cannot be proven to only contain composites (by covering congruence, algebraic factorization, or combine of them), then family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' contains at least one prime (this is equivalent to: If form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) (with fixed integers ''a'' ≥ 1, ''b'' ≥ 2, ''c'' ≠ 0 (with ''gcd''(''a'',''c'') = 1 and ''gcd''(''b'',''c'') = 1), and variable ''n'') cannot be proven to only contain composites (by covering congruence, algebraic factorization, or combine of them), then form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) contains at least one prime), like the [[:w:Bunyakovsky conjecture|Bunyakovsky conjecture]] and the [[:w:Dickson's conjecture|Dickson's conjecture]] and the [[:w:Schinzel's hypothesis H|Schinzel's hypothesis ''H'']], if such ''n'' always exists, then there must be always infinitely many such ''n'', to prove this, add another polynomial for the cases of the Dickson's conjecture and the Schinzel's hypothesis ''H'', also, change the polynomial (e.g. change ''n'' to ''r''×''n'' or ''n''&lt;sup&gt;''r''&lt;/sup&gt; for all integers ''r'' &gt; 1) for the cases of the Bunyakovsky conjecture and the Schinzel's hypothesis ''H'')

Some families can be ruled out to contain no prime &gt; ''b'' by [[:w:Covering set|covering congruence]], [[:w:Factorization of polynomials|algebraic factorization]] (e.g. [[:w:Difference of two squares|difference of two squares]], [[:w:Sum of two cubes|sum of two cubes]], [[:w:Sophie Germain's identity|Sophie Germain's identity of ''x''&lt;sup&gt;4&lt;/sup&gt;+4×''y''&lt;sup&gt;4&lt;/sup&gt;]]), or combine of them, e.g.

* The base 9 family 2{7}: Always divisible by 2 or 5
* The base 11 family 2{5}: Always divisible by 2 or 3
* The base 14 family B{0}1: Always divisible by 3 or 5
* The base 13 family 95{0}3: Always divisible by 5, 7, or 17
* The base 16 family {4}D: Always divisible by 3, 7, or 13
* The base 16 family {8}F: Always divisible by 3, 7, or 13
* The base 21 family {7}D: Always divisible by 2, 13, or 17
* The base 23 family {D}GA: Always divisible by 2, 5, 7, 37, or 79
* The base 9 family {1}: Can be written as (9&lt;sup&gt;''n''&lt;/sup&gt;−1)/8 and can be factored as (3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (3&lt;sup&gt;''n''&lt;/sup&gt;+1) / 8
* The base 8 family 1{0}1: Can be written as 8&lt;sup&gt;''n''&lt;/sup&gt;+1 and can be factored as (2&lt;sup&gt;''n''&lt;/sup&gt;+1) × (4&lt;sup&gt;''n''&lt;/sup&gt;−2&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 9 family 3{8}: Can be written as 4×9&lt;sup&gt;''n''&lt;/sup&gt;−1 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 16 family 1{5}: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;−1)/3 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+1) / 3
* The base 16 family {4}1: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;−49)/15 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−7) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+7) / 15
* The base 27 family 7{Q}: Can be written as 8×27&lt;sup&gt;''n''&lt;/sup&gt;−1 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (4×9&lt;sup&gt;''n''&lt;/sup&gt;+2×3&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 27 family 9{G}: Can be written as (125×27&lt;sup&gt;''n''&lt;/sup&gt;−8)/13 and can be factored as (5×3&lt;sup&gt;''n''&lt;/sup&gt;−2) × (25×9&lt;sup&gt;''n''&lt;/sup&gt;+10×3&lt;sup&gt;''n''&lt;/sup&gt;+4)
* The base 16 family {C}D: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;+1)/5 and can be factored as (2×4&lt;sup&gt;''n''&lt;/sup&gt;−2×2&lt;sup&gt;''n''&lt;/sup&gt;+1) × (2×4&lt;sup&gt;''n''&lt;/sup&gt;+2×2&lt;sup&gt;''n''&lt;/sup&gt;+1) / 5
* The base 14 family 8{D}: Can be written as 9×14&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is odd and can be factored as (3×14&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (3×14&lt;sup&gt;''n''/2&lt;/sup&gt;+1) if ''n'' is even
* The base 12 family {B}9B: Can be written as 12&lt;sup&gt;''n''&lt;/sup&gt;−25, it is divisible by 13 if ''n'' is odd and can be factored as (12&lt;sup&gt;''n''/2&lt;/sup&gt;−5) × (12&lt;sup&gt;''n''/2&lt;/sup&gt;+5) if ''n'' is even
* The base 14 family {D}5: Can be written as 14&lt;sup&gt;''n''&lt;/sup&gt;−9, it is divisible by 5 if ''n'' is odd and can be factored as (14&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (14&lt;sup&gt;''n''/2&lt;/sup&gt;+3) if ''n'' is even
* The base 17 family 1{9}: Can be written as (25×17&lt;sup&gt;''n''&lt;/sup&gt;−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (5×17&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (5×17&lt;sup&gt;''n''/2&lt;/sup&gt;+3) / 16 if ''n'' is even
* The base 17 family 7{9}: Can be written as (121×17&lt;sup&gt;''n''&lt;/sup&gt;−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (11×17&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (11×17&lt;sup&gt;''n''/2&lt;/sup&gt;+3) / 16 if ''n'' is even
* The base 19 family 1{6}: Can be written as (4×19&lt;sup&gt;''n''&lt;/sup&gt;−1)/3, it is divisible by 5 if ''n'' is odd and can be factored as (2×19&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (2×19&lt;sup&gt;''n''/2&lt;/sup&gt;+1) / 3 if ''n'' is even
* The base 24 family 3{N}: Can be written as 4×24&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is odd and can be factored as (2×24&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (2×24&lt;sup&gt;''n''/2&lt;/sup&gt;+1) if ''n'' is even
* The base 24 family 5{N}: Can be written as 6×24&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is even and can be factored as (12×24&lt;sup&gt;(''n''−1)/2&lt;/sup&gt;−1) × (12×24&lt;sup&gt;(''n''−1)/2&lt;/sup&gt;+1) if ''n'' is odd

If the conjecture above is true, then the [[:w:Sierpiński number|Sierpiński conjecture]] and [[:w:Riesel number|Riesel conjecture]] are also true, and the [http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm Sierpiński conjectures] and the [http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm Riesel conjectures] in all bases ''b'' are also true, and the [http://www.noprimeleftbehind.net/crus/SNOB-Sierp-conjectures.htm real Sierpiński conjectures] and the [http://www.noprimeleftbehind.net/crus/Real-Riesel-conjectures.htm real Riesel conjectures] are also true, also, if the Athena conjecture is true, then there are infinitely many primes of these forms for fixed bases ''b'' ≥ 2 and variable exponents ''n'':

* (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1) for all bases ''b'' which are not [[:w:Perfect power|perfect power]]s (for this form, ''n'' must be prime) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepu.txt, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379, https://pzktupel.de/Primetables/TableRepunitGen.php, https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A128164, https://oeis.org/A285642; or for prime bases ''b'': https://oeis.org/A065854, https://oeis.org/A279068)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' which are not of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 (for this form, ''n'' must be power of 2) (references of this form: http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A228101)
* (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/2 for all odd bases ''b'' which are not of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 (for this form, ''n'' must be power of 2) (reference of this form: http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt)
* (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''+1) for all bases ''b'' which are neither of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 nor of the form 4×''m''&lt;sup&gt;4&lt;/sup&gt; (for this form, ''n'' must be prime) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepuP.txt, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/488, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://oeis.org/A084742, https://oeis.org/A084741; or for prime bases ''b'': https://oeis.org/A065507)
* ((''b''−2)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''−1) for all bases ''b'' &gt; 2 (reference of this form: https://oeis.org/A243404)
* 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' &lt; 201446503145165177, not == 1 mod 3 (references of this form: https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://oeis.org/A119624)
* 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&amp;d=1567314217, https://oeis.org/A119591)
* 3×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b''
* 3×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b''
* 4×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 5, not == 14 mod 15, not [[:w:Fourth power|fourth power]]s
* 4×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 3, not == 4 mod 5, not [[:w:Square number|square]]s
* 5×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' &lt; 140324348, not == 1 mod 3
* 5×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b''
* 6×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 7, not == 34 mod 35
* 6×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 5, not == 34 mod 35, not of the form 6×''m''&lt;sup&gt;2&lt;/sup&gt; with ''m'' == 2, 3 mod 5
* 7×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b''
* 7×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' &lt; 9162668342, not == 1 mod 3
* 8×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 3, not == 20 mod 21, not == 47, 83 mod 195, not == 467, 4343, 9887, 25448, 35978, 41522, 42647, 57083 mod 73815, not == 722, 83813, 206672, 239432, 322523, 1283843, 1519577, 1522553 mod 1551615, ..., not [[:w:Cube (algebra)|cube]]s
* 8×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 7, not == 20 mod 21, not == 83, 307 mod 455, not == 1266, 13593, 27292, 46353 mod 63973, ..., not [[:w:Cube (algebra)|cube]]s
* 9×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' &lt; 177744, not == 1 mod 5
* 9×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' not == 4 mod 5, not [[:w:Square number|square]]s
* 10×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 11, not == 32 mod 33 (references of this form: https://oeis.org/A088782)
* 10×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 3, not == 32 mod 33
* 11×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' not == 1 mod 3, not == 14 mod 15
* 11×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' not == 1 mod 5, not == 14 mod 15, not of the form 11×''m''&lt;sup&gt;2&lt;/sup&gt; with ''m'' == 2, 3 mod 5
* 12×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 13, not == 142 mod 143, not == 562, 828, 900, 1166 mod 1729, not == 597, 1143 mod 1885, not == 296, 901, 1759, 3090, 4553, 5521, 5807, 6016, 6984, 7094, 7270, 7380, 7479, 8447, 8557, 8733, 8843, 9910, 10020, 10196, 10306, 11483, 11769, 12737, 14200, 15531, 16994, 18457 mod 19019, not == 563, 1433, 13212, 15097, 19848, 20718, 32497, 34382, 39133, 51782, 53667, 58418, 58452, 60337, 60883, 71067, 72952, 77737, 79622, 80168, 94267, 97022, 98583, 98907, 113552, 116307, 117868, 118192, 131967, 132513, 132837, 134398, 151252, 151798, 152122, 153683, 170537, 171083, 172968, 177753, 179638, 189822, 190368, 192253, 192287, 197038, 198923, 211572, 213568, 216323, 218208, 229987, 232853, 235608, 237493, 249272 mod 250705, ...
* 12×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 11, not == 142 mod 143, not == 307, 1143 mod 1595, not == 901, 6016, 7479, 18457 mod 19019, ...
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+2 for all odd bases ''b'' &lt; 201446503145165177, not == 1 mod 3 (references of this form: https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−2 for all odd bases ''b'' (references of this form: https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A250200, https://oeis.org/A255707, https://oeis.org/A084714; or for prime bases ''b'': https://oeis.org/A292201)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+3 for all even bases ''b'' not divisible by 3
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−3 for all even bases ''b'' not divisible by 3
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+4 for all odd bases ''b'' not == 1 mod 5, not == 14 mod 15, not [[:w:Fourth power|fourth power]]s
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−4 for all odd bases ''b'' not == 1 mod 3, not == 4 mod 5, not [[:w:Square number|square]]s
* (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' (references of this form: http://www.noprimeleftbehind.net/Williams-primes-MP.htm, http://www.bitman.name/math/table/477, https://pzktupel.de/Primetables/TableWilliams2.php, https://oeis.org/A305531; or for prime bases ''b'': https://oeis.org/A087139)
* (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: https://harvey563.tripod.com/wills.txt, http://www.noprimeleftbehind.net/Williams-primes-MM.htm, http://www.bitman.name/math/table/484, https://pzktupel.de/Primetables/TableWilliams1.php; or for prime bases ''b'': https://oeis.org/A122396)
* (''b''+1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 3 (references of this form: http://www.noprimeleftbehind.net/Williams-primes-PP.htm, http://www.bitman.name/math/table/474, https://pzktupel.de/Primetables/TableWilliams4.php)
* (''b''+1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: http://www.noprimeleftbehind.net/Williams-primes-PM.htm, http://www.bitman.name/math/table/471, https://pzktupel.de/Primetables/TableWilliams3.php)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''−1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/795, https://pzktupel.de/Primetables/TableWilliams6.php, https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''−1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/792, https://pzktupel.de/Primetables/TableWilliams5.php, https://oeis.org/A113516, https://oeis.org/A343589; or for prime bases ''b'': https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/435)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''+1) for all bases ''b'' not == 1 mod 3 (references of this form: http://www.bitman.name/math/table/801, https://pzktupel.de/Primetables/TableWilliams8.php, https://oeis.org/A346149, https://oeis.org/A346154)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''+1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/798, https://pzktupel.de/Primetables/TableWilliams7.php, https://oeis.org/A178250)

By the [[:w:Prime number theorem|prime number theorem]], the [[:w:Probability|chance]] that a [[:w:Random number|random]] ''n''-digit base ''b'' number is prime is [[:w:Asymptotic analysis|approximately]] 1/''n'' (more accurately, the chance is approximately 1/(''n''×''ln''(''b'')), where ''ln'' is the [[:w:Natural logarithm|natural logarithm]]). If one conjectures the numbers ''x''{''y''}''z'' behave similarly (i.e. the numbers ''x''{''y''}''z'' is a [[:w:Pseudorandomness|pseudorandom sequence]]) you would expect [[:w:Harmonic_series (mathematics)|1/1 + 1/2 + 1/3 + 1/4 + ... = ∞]] primes of the form ''x''{''y''}''z'' (of course, this does not always happen, since some ''x''{''y''}''z'' families can be ruled out to contain no prime &gt; ''b'' (by covering congruence, algebraic factorization, or combine of them), but it is at least a reasonable conjecture in the absence of evidence to the contrary. Hence, the [[:w:Heuristic argument|heuristic argument]] suggests there are always infinitely many primes in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') if it cannot be ruled out to contain no prime or only contain finitely many primes, by covering congruence, algebraic factorization, or combine of them. However, some families ''x''{''y''}''z'' could not be proven to contain no primes &gt; ''b'' (by covering congruence, algebraic factorization, or combine of them) but no primes &gt; ''b'' could be found in the family, even after searching through numbers with over 100000 digits. In such a case, the only way to proceed is to [[:w:Primality test|test the primality]] of larger and larger numbers of such form and hope a prime is eventually discovered. e.g. the smallest (probable) prime in the family A{3}A in base ''b'' = 13 is A3&lt;sub&gt;592197&lt;/sub&gt;A, its algebraic form is (41×13&lt;sup&gt;592198&lt;/sup&gt;+27)/4, when written in decimal contains 659677 digits (it is only probable prime, i.e. not definitely prime, since technically, probable primality tests were used to show this (which have a ''very'' small chance of making an error, see https://t5k.org/notes/prp_prob.html) because all known primality tests run far too slowly to run on numbers of this size unless either [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] (or both) can be ≥ 1/3 factored).

The numbers in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') are of the form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) for some fixed ''a'', ''b'', ''c'' such that ''a'' ≥ 1, ''b'' ≥ 2 (''b'' is the base), ''c'' ≠ 0, ''gcd''(''a'',''c'') = 1, ''gcd''(''b'',''c'') = 1. Except in the [[:w:Special case|special case]] ''c'' = ±1 and ''gcd''(''a''+''c'',''b''−1) = 1 (the only case which [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] is [[:w:Triviality (mathematics)|trivially]] fully factored), when ''n'' is large the known [[:w:Primality test|primality test]]s for such a number are too inefficient to run (since they are [https://t5k.org/glossary/xpage/OrdinaryPrime.html ordinary primes]). In this case one must resort to a [[:w:Probabilistic algorithm|probable]] primality test such as a [[:w:Miller–Rabin primality test|Miller–Rabin primality test]] or a [[:w:Baillie–PSW primality test|Baillie–PSW primality test]], unless a divisor of the number can be found. Since we are testing many numbers in an [[:w:Exponential growth|exponential sequence]], it is possible to use a sieving process to find divisors rather than using [[:w:Trial division|trial division]].

To do this, we made use of Geoffrey Reynolds' ''srsieve'' software (download: https://pzktupel.de/Software/srsieve_1.1.4.7z). This program uses the [[:w:Baby-step giant-step|baby-step giant-step]] [[:w:Algorithm|algorithm]] to find all primes ''p'' which divide ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'' where ''p'' and ''n'' lie in a [[:w:Interval_(mathematics)|specified range]]. Since this program cannot handle the general case (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) &gt; 1 we only used it to sieve the sequence ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'' for primes ''p'' not dividing ''gcd''(''a''+''c'',''b''−1), and initialized the list of candidates to not include ''n'' for which there is some prime ''p'' dividing ''gcd''(''a''+''c'',''b''−1) for which ''p'' dividing (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1). The program had to be modified slightly to remove a check which would prevent it from running in the case when ''a'', ''b'', and ''c'' were all odd (since then 2 divides ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'', but 2 may not divide (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1)).

Once the numbers with small divisors had been removed, it remained to test the remaining numbers using a probable primality test. For this we used the software ''LLR'' by Jean Penné. (download: http://jpenne.free.fr/index2.html). Although undocumented, it is possible to run this program on numbers of the form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) &gt; 1, so this program required no modifications. A script was also written which allowed one to run ''srsieve'' while ''LLR'' was testing the remaining candidates, so that when a divisor was found by srsieve on a number which had not yet been tested by ''LLR'' it would be removed from the list of candidates.

For the primes &lt; 10&lt;sup&gt;25000&lt;/sup&gt; for the &quot;easy&quot; bases (bases ''b'' with ≤ 150 primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; (base ''b'' = 26 has 83 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 3 unsolved families, base ''b'' = 36 has 75 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 4 unsolved families, base ''b'' = 17 has 99 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 18 unsolved families, base ''b'' = 21 has 80 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 12 unsolved families, base ''b'' = 19 has 201 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 23 unsolved families), i.e. bases *b* = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36), we employed ''CM'' by Andreas Enge (download: https://www.multiprecision.org/cm/download.html), an elliptic curve primality proving implementation.

Currently, the final goal of the Athena problem project is finding the Athena set (i.e. finding all Athena primes) and proving that this set is exactly the Athena set (i.e. proving that these are all Athena primes (including the primality proving for the probable primes)) in all bases 2 ≤ ''b'' ≤ 36, i.e. solving all families in all bases 2 ≤ ''b'' ≤ 36. Solving all (unsolved) families in all bases 2 ≤ ''b'' ≤ 36 (and proving the primality of all probable primes in the sets of all bases 2 ≤ ''b'' ≤ 36) is not possible but we aim to solve many of them (and proving the primality of many of them), at least find a ''probable'' prime for many of them (since the smallest prime in a family may be too large (&gt; 10&lt;sup&gt;25000&lt;/sup&gt;) to be proved primality, unless its *N*−1 or/and *N*+1 can be ≥ 25% factored).

== Data ==

These are the results of the Athena problem in bases 2 ≤ ''b'' ≤ 36 (we stop at base 36 since this base is the maximum base for which it is possible to write the numbers with the [[:w:Symbol|symbol]]s 0, 1, 2, ..., 9 and A, B, C, ..., Z (i.e. the 10 [[:w:Arabic numerals|Arabic numerals]] and the 26 [[:w:Latin script|Latin letters]]): (some large Athena primes are only probable primes, i.e. not definitely primes, since they are too large to be [[:w:Elliptic curve primality|ECPP proved]] and [[:w:Pocklington primality test#Extensions and variants|neither ''N''−1 nor ''N''+1 can be ≥ 1/3 factored]], all of them pass the [[:w:Baillie–PSW primality test|Baillie–PSW primality test]] and the [[:w:Strong pseudoprime|strong primality test]] (i.e. the [[:w:Miller–Rabin primality test|Miller–Rabin primality test]]) with all prime bases ''p'' ≤ 61, however, all Athena primes &lt; 10&lt;sup&gt;25000&lt;/sup&gt; for bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 36 are definitely primes, most of them &gt; 10&lt;sup&gt;299&lt;/sup&gt; are proven primes with [[:w:Elliptic curve primality|ECPP proving]], others &gt; 10&lt;sup&gt;299&lt;/sup&gt; are proven primes with [[:w:Pocklington primality test#Extensions and variants|''N''−1 or ''N''+1 proving]])

The Athena primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 which are proven primes with ''N''−1 or ''N''+1 proving includes the Athena primes whose ''N''−1 or ''N''+1 is trivially fully factored:

* the 3176th Athena prime in base 13, 81010&lt;sub&gt;415&lt;/sub&gt;1, which equals 17746×13&lt;sup&gt;416&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003590431555, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003590431556&amp;open=ecm
* the 3177th Athena prime in base 13, 8110&lt;sub&gt;435&lt;/sub&gt;1, which equals 1366×13&lt;sup&gt;436&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000002373259109, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000002373259124&amp;open=ecm
* the 3188th Athena prime in base 13, 930&lt;sub&gt;1551&lt;/sub&gt;1, which equals 120×13&lt;sup&gt;1552&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961452, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961453&amp;open=ecm
* the 3191st Athena prime in base 13, 390&lt;sub&gt;6266&lt;/sub&gt;1, which equals 48×13&lt;sup&gt;6267&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961441, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961451&amp;open=ecm
* the 649th Athena prime in base 14, 34D&lt;sub&gt;708&lt;/sub&gt;, which equals 47×14&lt;sup&gt;708&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001540144903, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001540144907&amp;open=ecm
* the 650th Athena prime in base 14, 4D&lt;sub&gt;19698&lt;/sub&gt;, which equals 5×14&lt;sup&gt;19698&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000884560233, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000884560625&amp;open=ecm
* the 2335th Athena prime in base 16, 88F&lt;sub&gt;545&lt;/sub&gt;, which equals 137×16&lt;sup&gt;545&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000413679658, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000413877337&amp;open=ecm
* the 10317th Athena prime in base 17, 5A70&lt;sub&gt;274&lt;/sub&gt;1, which equals 1622×17&lt;sup&gt;275&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003782940709, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003782941930&amp;open=ecm
* the 10359th Athena prime in base 17, 9D0&lt;sub&gt;1067&lt;/sub&gt;1, which equals 166×17&lt;sup&gt;1068&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961369, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961370&amp;open=ecm
* the 10370th Athena prime in base 17, A0&lt;sub&gt;1355&lt;/sub&gt;1, which equals 10×17&lt;sup&gt;1356&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000034167087, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000271866825&amp;open=ecm
* the 10386th Athena prime in base 17, 530&lt;sub&gt;4867&lt;/sub&gt;1, which equals 88×17&lt;sup&gt;4868&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000762660735, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000762660737&amp;open=ecm
* the 10408th Athena prime in base 17, 570&lt;sub&gt;51310&lt;/sub&gt;1, which equals 92×17&lt;sup&gt;51311&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961389, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469616&amp;open=ecm
* the 10412th Athena prime in base 17, 970&lt;sub&gt;166047&lt;/sub&gt;1, which equals 160×17&lt;sup&gt;166048&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (&gt;10&lt;sup&gt;199999&lt;/sup&gt;) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817312&amp;open=ecm
* the 10413th Athena prime in base 17, F70&lt;sub&gt;186767&lt;/sub&gt;1, which equals 262×17&lt;sup&gt;186768&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (&gt;10&lt;sup&gt;199999&lt;/sup&gt;) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817317&amp;open=ecm
* the 3310th Athena prime in base 20, JCJ&lt;sub&gt;629&lt;/sub&gt;, which equals 393×20&lt;sup&gt;629&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001559454258, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001559454271&amp;open=ecm
* the 13373rd Athena prime in base 21, 5D0&lt;sub&gt;19848&lt;/sub&gt;1, which equals 118×21&lt;sup&gt;19849&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000777265872, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469310&amp;open=ecm
* the 3408th Athena prime in base 24, 88N&lt;sub&gt;5951&lt;/sub&gt;, which equals 201×24&lt;sup&gt;5951&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003593275880, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000003593373246&amp;open=ecm
* the 25509th Athena prime in base 28, EB0&lt;sub&gt;405&lt;/sub&gt;1, which equals 403×28&lt;sup&gt;406&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001534442374, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000001534442380&amp;open=ecm
* the 2616th Athena prime in base 30, C0&lt;sub&gt;1022&lt;/sub&gt;1, which equals 12×30&lt;sup&gt;1023&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000785448736, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785448737&amp;open=ecm
* the 2619th Athena prime in base 30, OT&lt;sub&gt;34205&lt;/sub&gt;, which equals 25×30&lt;sup&gt;34205&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000800812865, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000819405041&amp;open=ecm
* the 35237th Athena prime in base 36, P8Z&lt;sub&gt;390&lt;/sub&gt;, which equals 909×36&lt;sup&gt;390&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000764100228, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000764100231&amp;open=ecm

and the Athena primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 whose ''N''−1 or ''N''+1 is ≥ 1/3 factored: (''R''&lt;sub&gt;''n''&lt;/sub&gt;(''b'') means the [[:w:Repunit|repunit]] in base ''b'' with length ''n''), i.e. ''R''&lt;sub&gt;''n''&lt;/sub&gt;(''b'') = (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1), &quot;''S''&lt;sub&gt;''n''&lt;/sub&gt;(''b'')&quot; means ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)

* the 3168th Athena prime in base 13, 9&lt;sub&gt;308&lt;/sub&gt;1, ''N''−1 is 117×''R''&lt;sub&gt;308&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;308&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;308&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=308&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;308&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=308&amp;c0=-&amp;EN=&amp;LM=
* the 3179th Athena prime in base 13, B&lt;sub&gt;563&lt;/sub&gt;C, ''N''−1 is 11×''R''&lt;sub&gt;564&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;564&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;564&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=564&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;564&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=564&amp;c0=-&amp;EN=&amp;LM=
* the 3180th Athena prime in base 13, 1B&lt;sub&gt;576&lt;/sub&gt;, ''N''−1 is 23×''R''&lt;sub&gt;576&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;576&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;576&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=576&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;576&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=576&amp;c0=-&amp;EN=&amp;LM=
* the 10320th Athena prime in base 17, 9&lt;sub&gt;292&lt;/sub&gt;1, ''N''−1 is 153×''R''&lt;sub&gt;292&lt;/sub&gt;(17), thus factor ''N''−1 is equivalent to factor the Cunningham number 17&lt;sup&gt;292&lt;/sup&gt;−1, and for the algebraic factors of 17&lt;sup&gt;292&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=17&amp;Exp=292&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 17&lt;sup&gt;292&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=17&amp;Exp=292&amp;c0=-&amp;EN=&amp;LM=
* the 13304th Athena prime in base 21, 7&lt;sub&gt;230&lt;/sub&gt;1, ''N''−1 is 147×''R''&lt;sub&gt;230&lt;/sub&gt;(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21&lt;sup&gt;230&lt;/sup&gt;−1, and for the algebraic factors of 21&lt;sup&gt;230&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&amp;Exp=230&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 21&lt;sup&gt;230&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&amp;Exp=230&amp;c0=-&amp;EN=&amp;LM=
* the 13355th Athena prime in base 21, 3&lt;sub&gt;1063&lt;/sub&gt;2, ''N''+1 is 3×''R''&lt;sub&gt;1064&lt;/sub&gt;(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21&lt;sup&gt;1064&lt;/sup&gt;−1, and for the algebraic factors of 21&lt;sup&gt;1064&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&amp;Exp=1064&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 21&lt;sup&gt;1064&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&amp;Exp=1064&amp;c0=-&amp;EN=&amp;LM=
* the 25199th Athena prime in base 26, 9K&lt;sub&gt;343&lt;/sub&gt;AP, ''N''+1 is 6370×''R''&lt;sub&gt;344&lt;/sub&gt;(26), thus factor ''N''+1 is equivalent to factor the Cunningham number 26&lt;sup&gt;344&lt;/sup&gt;−1, and for the algebraic factors of 26&lt;sup&gt;344&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&amp;Exp=344&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 26&lt;sup&gt;344&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&amp;Exp=344&amp;c0=-&amp;EN=&amp;LM=
* the 25200th Athena prime in base 26, 8&lt;sub&gt;354&lt;/sub&gt;1, ''N''−1 is 208×''R''&lt;sub&gt;354&lt;/sub&gt;(26), thus factor ''N''−1 is equivalent to factor the Cunningham number 26&lt;sup&gt;354&lt;/sup&gt;−1, and for the algebraic factors of 26&lt;sup&gt;354&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&amp;Exp=354&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 26&lt;sup&gt;354&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&amp;Exp=354&amp;c0=-&amp;EN=&amp;LM=

All numbers are written in base ''b'', [[:w:Senary#Base 36 as senary compression|using A to Z to represent digit values 10 to 35]], &quot;{}&quot; means repeating, e.g. family 12{3}45 means the sequence {1245, 12345, 123345, 1233345, 12333345, 123333345, ...} (where the members are expressed as base ''b'' strings), subscripts are used to indicate repetitions of digits, e.g. 123&lt;sub&gt;4&lt;/sub&gt;567 means 123333567 (all subscripts are written in decimal).

Base 2: 1 Athena prime (the largest of which has 2 digits (it is 11, and its value is 3 in decimal)): {11}

Base 3: 3 Athena primes (the largest of which has 3 digits (it is 111, and its value is 13 in decimal)): {12, 21, 111}

Base 4: 5 Athena primes (the largest of which has 3 digits (it is 221, and its value is 41 in decimal)): {11, 13, 23, 31, 221}

Base 5: 22 Athena primes (the largest of which has 96 digits (it is 10&lt;sub&gt;93&lt;/sub&gt;13, and its algebraic form is 5&lt;sup&gt;95&lt;/sup&gt;+8)): {12, 21, 23, 32, 34, 43, 104, 111, 131, 133, 313, 401, 414, 3101, 10103, 14444, 30301, 33001, 33331, 44441, 300031, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013}

Base 6: 11 Athena primes (the largest of which has 5 digits (it is 40041, and its value is 5209 in decimal)): {11, 15, 21, 25, 31, 35, 45, 51, 4401, 4441, 40041}

Base 7: 71 Athena primes (the largest of which has 17 digits (it is 3&lt;sub&gt;16&lt;/sub&gt;1, and its algebraic form is (7&lt;sup&gt;17&lt;/sup&gt;−5)/2)): {14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 113, 115, 131, 133, 155, 212, 221, 304, 313, 335, 344, 346, 364, 445, 515, 533, 535, 544, 551, 553, 1022, 1051, 1112, 1202, 1211, 1222, 2111, 3031, 3055, 3334, 3503, 3505, 3545, 4504, 4555, 5011, 5455, 5545, 5554, 6034, 6634, 11111, 11201, 30011, 30101, 31001, 31111, 33001, 33311, 35555, 40054, 100121, 150001, 300053, 351101, 531101, 1100021, 33333301, 5100000001, 33333333333333331}

Base 8: 75 Athena primes (the largest of which has 221 digits (it is 4&lt;sub&gt;220&lt;/sub&gt;7, and its algebraic form is (4×8&lt;sup&gt;221&lt;/sup&gt;+17)/7)): {13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 107, 111, 117, 141, 147, 161, 177, 225, 255, 301, 343, 361, 401, 407, 417, 431, 433, 463, 467, 471, 631, 643, 661, 667, 701, 711, 717, 747, 767, 3331, 3411, 4043, 4443, 4611, 5205, 6007, 6101, 6441, 6477, 6707, 6777, 7461, 7641, 47777, 60171, 60411, 60741, 444641, 500025, 505525, 3344441, 4444477, 5500525, 5550525, 55555025, 444444441, 744444441, 77774444441, 7777777777771, 555555555555525, 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447}

Base 9: 151 Athena primes (the largest of which has 1161 digits (it is 30&lt;sub&gt;1158&lt;/sub&gt;11, and its algebraic form is 3×9&lt;sup&gt;1160&lt;/sup&gt;+10)): {12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 117, 131, 135, 151, 155, 175, 177, 238, 272, 308, 315, 331, 337, 355, 371, 375, 377, 438, 504, 515, 517, 531, 537, 557, 564, 601, 638, 661, 702, 711, 722, 735, 737, 751, 755, 757, 771, 805, 838, 1011, 1015, 1101, 1701, 2027, 2207, 3017, 3057, 3101, 3501, 3561, 3611, 3688, 3868, 5035, 5051, 5071, 5101, 5501, 5554, 5705, 5707, 7017, 7075, 7105, 7301, 8535, 8544, 8555, 8854, 20777, 22227, 22777, 30161, 33388, 50161, 50611, 53335, 55111, 55535, 55551, 57061, 57775, 70631, 71007, 77207, 100037, 100071, 100761, 105007, 270707, 301111, 305111, 333035, 333385, 333835, 338885, 350007, 500075, 530005, 555611, 631111, 720707, 2770007, 3030335, 7776662, 30300005, 30333335, 38333335, 51116111, 70000361, 300030005, 300033305, 351111111, 1300000007, 5161111111, 8333333335, 300000000035, 311111111161, 544444444444, 2000000000007, 5700000000001, 7270000000007, 88888888833335, 100000000000507, 5111111111111161, 7277777777777777707, 8888888888888888888335, 30000000000000000000051, 1000000000000000000000000057, 56111111111111111111111111111111111111, 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666662, 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777707, 300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011}

Base 10: 77 Athena primes (the largest of which has 31 digits (it is 50&lt;sub&gt;28&lt;/sub&gt;27, and its algebraic form is 5×10&lt;sup&gt;30&lt;/sup&gt;+27)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}

Base 11: 1068 Athena (probable) primes (including 1 unproven probable prime: 57&lt;sub&gt;62668&lt;/sub&gt;), the largest of which has 62669 digits (it is 57&lt;sub&gt;62668&lt;/sub&gt;, and its algebraic form is (57×11&lt;sup&gt;62668&lt;/sup&gt;−7)/10), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel11 Data of Athena (probable) primes base 11]

Base 12: 106 Athena primes (the largest of which has 42 digits (it is 40&lt;sub&gt;39&lt;/sub&gt;77, and its algebraic form is 4×12&lt;sup&gt;41&lt;/sup&gt;+91)): {11, 15, 17, 1B, 25, 27, 31, 35, 37, 3B, 45, 4B, 51, 57, 5B, 61, 67, 6B, 75, 81, 85, 87, 8B, 91, 95, A7, AB, B5, B7, 221, 241, 2A1, 2B1, 2BB, 401, 421, 447, 471, 497, 565, 655, 665, 701, 70B, 721, 747, 771, 77B, 797, 7A1, 7BB, 907, 90B, 9BB, A41, B21, B2B, 2001, 200B, 202B, 222B, 229B, 292B, 299B, 4441, 4707, 4777, 6A05, 6AA5, 729B, 7441, 7B41, 929B, 9777, 992B, 9947, 997B, 9997, A0A1, A201, A605, A6A5, AA65, B001, B0B1, BB01, BB41, 600A5, 7999B, 9999B, AAAA1, B04A1, B0B9B, BAA01, BAAA1, BB09B, BBBB1, 44AAA1, A00065, BBBAA1, AAA0001, B00099B, AA000001, BBBBBB99B, B0000000000000000000000000009B, 400000000000000000000000000000000000000077}

Base 13: 3197 Athena (probable) primes (including 4 unproven probable primes: C5&lt;sub&gt;23755&lt;/sub&gt;C, 80&lt;sub&gt;32017&lt;/sub&gt;111, 95&lt;sub&gt;197420&lt;/sub&gt;, A3&lt;sub&gt;592197&lt;/sub&gt;A), the largest of which has 592199 digits (it is A3&lt;sub&gt;592197&lt;/sub&gt;A, and its algebraic form is (41×13&lt;sup&gt;592198&lt;/sup&gt;+27)/4), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel13 Data of Athena (probable) primes base 13]

Base 14: 650 Athena primes, the largest of which has 19699 digits (it is 4D&lt;sub&gt;19698&lt;/sub&gt;, and its algebraic form is 5×14&lt;sup&gt;19698&lt;/sup&gt;−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel14 Data of Athena primes base 14]

Base 15: 1284 Athena primes, the largest of which has 157 digits (it is 7&lt;sub&gt;155&lt;/sub&gt;97, and its algebraic form is (15&lt;sup&gt;157&lt;/sup&gt;+59)/2), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel15 Data of Athena primes base 15]

Base 16: 2347 Athena (probable) primes (including 3 unproven probable primes: DB&lt;sub&gt;32234&lt;/sub&gt;, 4&lt;sub&gt;72785&lt;/sub&gt;DD, 3&lt;sub&gt;116137&lt;/sub&gt;AF), the largest of which has 116139 digits (it is 3&lt;sub&gt;116137&lt;/sub&gt;AF, and its algebraic form is (16&lt;sup&gt;116139&lt;/sup&gt;+619)/5), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel16 Data of Athena (probable) primes base 16]

Base 17: 10415 known Athena (probable) primes (including many unproven probable primes) and 12 unsolved families (1{7}, 1F{0}7, 4{7}A, 70F{0}D, 8{B}9, 9{5}9, A{D}F, B{0}B3, {B}E9, {B}EE, F1{9}, FD0{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel17 Data of known Athena (probable) primes base 17]

Base 18: 549 Athena primes, the largest of which has 6271 digits (it is C0&lt;sub&gt;6268&lt;/sub&gt;C5, and its algebraic form is 12×18&lt;sup&gt;6270&lt;/sup&gt;+221), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel18 Data of Athena primes base 18]

Base 19: 31417 known Athena (probable) primes (including many unproven probable primes) and 17 unsolved families (4B5{0}H, {5}3, 5{H}05, 5{H}0H, 5{H}5, 66{B}, 71{0}177, 7AF{0}H, 97{0}3, C{H}C, EE1{6}, F{7}5, F{B}G, F{D}F, H0F{0}7A, HB{0}5B5, II{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel19 Data of known Athena (probable) primes base 19]

Base 20: 3314 Athena primes, the largest of which has 6271 digits (it is G0&lt;sub&gt;6269&lt;/sub&gt;D, and its algebraic form is 16×20&lt;sup&gt;6270&lt;/sup&gt;+13), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel20 Data of Athena primes base 20]

Base 21: 13386 known Athena (probable) primes (including many unproven probable primes) and 8 unsolved families (5{0}DJ, {9}D, B3{0}EB, B{H}6H, C{F}0K, {F}35, G{0}FK, H{0}7771, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel21 Data of known Athena (probable) primes base 21]

Base 22: 8003 Athena (probable) primes (including 1 unproven probable prime: BK&lt;sub&gt;22001&lt;/sub&gt;5), the largest of which has 22003 digits (it is BK&lt;sub&gt;22001&lt;/sub&gt;5, and its algebraic form is (251×22&lt;sup&gt;22002&lt;/sup&gt;−335)/21), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel22 Data of Athena (probable) primes base 22]

Base 23: 65178 known Athena (probable) primes (including many unproven probable primes) and 87 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel23 Data of known Athena (probable) primes base 23] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left23 Data of unsolved families for Athena problem base 23]

Base 24: 3409 Athena primes, the largest of which has 8134 digits (it is N00N&lt;sub&gt;8129&lt;/sub&gt;LN, and its algebraic form is 13249×24&lt;sup&gt;8131&lt;/sup&gt;−49), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel24 Data of Athena primes base 24]

Base 25: 133639 known Athena (probable) primes (including many unproven probable primes) and 85 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel25 Data of known Athena (probable) primes base 25] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left25 Data of unsolved families for Athena problem base 25]

Base 26: 25256 known Athena (probable) primes (including 7 unproven probable primes: 5&lt;sub&gt;19391&lt;/sub&gt;6F, 7&lt;sub&gt;20279&lt;/sub&gt;OL, LD0&lt;sub&gt;20975&lt;/sub&gt;7, 6K&lt;sub&gt;23300&lt;/sub&gt;5, J0&lt;sub&gt;44303&lt;/sub&gt;KCB, M0&lt;sub&gt;61186&lt;/sub&gt;2BB, 85M&lt;sub&gt;197060&lt;/sub&gt;B) and 3 unsolved families ({A}6F, {H}MH, {I}GL, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel26 Data of known Athena (probable) primes base 26]

Base 27: 102852 known Athena (probable) primes (including many unproven probable primes) and 44 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel27 Data of known Athena (probable) primes base 27] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left27 Data of unsolved families for Athena problem base 27]

Base 28: 25528 known Athena (probable) primes (including 3 unproven probable primes: N6&lt;sub&gt;24051&lt;/sub&gt;LR, 5OA&lt;sub&gt;31238&lt;/sub&gt;F, O4O&lt;sub&gt;94535&lt;/sub&gt;9) and 1 unsolved family (O{A}F, no primes or probable primes with length ≤ 900000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel28 Data of known Athena (probable) primes base 28]

Base 29: 355242 known Athena (probable) primes (including many unproven probable primes) and 125 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel29 Data of known Athena (probable) primes base 29] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left29 Data of unsolved families for Athena problem base 29]

Base 30: 2619 Athena (probable) primes (including 1 unproven probable prime: I0&lt;sub&gt;24608&lt;/sub&gt;D), the largest of which has 34206 digits (it is OT&lt;sub&gt;34205&lt;/sub&gt;, and its algebraic form is 25×30&lt;sup&gt;34205&lt;/sup&gt;−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel30 Data of Athena (probable) primes base 30]

Base 31: 569323 known Athena (probable) primes (including many unproven probable primes) and 77 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel31 Data of known Athena (probable) primes base 31] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left31 Data of unsolved families for Athena problem base 31]

Base 32: 168882 known Athena (probable) primes (including many unproven probable primes) and 120 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel32 Data of known Athena (probable) primes base 32] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left32 Data of unsolved families for Athena problem base 32]

Base 33: 280012 known Athena (probable) primes (including many unproven probable primes) and 81 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel33 Data of known Athena (probable) primes base 33] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left33 Data of unsolved families for Athena problem base 33]

Base 34: 184785 known Athena (probable) primes (including many unproven probable primes) and 47 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel34 Data of known Athena (probable) primes base 34] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left34 Data of unsolved families for Athena problem base 34]

Base 35: 720002 known Athena (probable) primes (including many unproven probable primes) and 60 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel35 Data of known Athena (probable) primes base 35] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left35 Data of unsolved families for Athena problem base 35]

Base 36: 35286 known Athena (probable) primes (including 3 unproven probable primes: 7K&lt;sub&gt;26567&lt;/sub&gt;Z, S0&lt;sub&gt;75007&lt;/sub&gt;8H, P&lt;sub&gt;81993&lt;/sub&gt;SZ) and 4 unsolved families (B{0}EUV, HM{0}N, N{0}YYN, O{L}Z, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel36 Data of known Athena (probable) primes base 36]

== Condensed table for bases 2 ≤ ''b'' ≤ 36 ==

{|class=&quot;wikitable&quot;
||''b''||number of Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||base-''b'' form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' (write &quot;''d''&lt;sub&gt;''n''&lt;/sub&gt;&quot; if there are 5 or more (''n'') consecutive same digits ''d'')||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' in decimal||algebraic ((''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1)) form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||''factordb'' entry of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' written in base ''b'' (use lower case letters instead of upper case letters)||number of unsolved families in the Athena problem in base ''b'' (all of these left families are linear families)||searching limit of length for the unsolved families in the Athena problem in base ''b'' (if there are different searching limits for the unsolved families in the Athena problem in base ''b'', choose the lowest searching limit)||
|-
||2||1||11||2||1||3||http://factordb.com/index.php?id=3&amp;open=ecm||http://factordb.com/index.php?showid=3&amp;base=2||0||–||
|-
||3||3||111&lt;br&gt;21&lt;br&gt;12||3&lt;br&gt;2&lt;br&gt;2||2&lt;br&gt;1&lt;br&gt;1||13&lt;br&gt;7&lt;br&gt;5||http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=7&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=5&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=13&amp;base=3&lt;br&gt;http://factordb.com/index.php?showid=7&amp;base=3&lt;br&gt;http://factordb.com/index.php?showid=5&amp;base=3&lt;nowiki/&gt;||0||–||
|-
||4||5||221&lt;br&gt;31&lt;br&gt;23&lt;br&gt;13&lt;br&gt;11||3&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;1&lt;br&gt;1||41&lt;br&gt;13&lt;br&gt;11&lt;br&gt;7&lt;br&gt;5||http://factordb.com/index.php?id=41&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=11&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=7&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=5&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=41&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=13&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=11&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=7&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=5&amp;base=4&lt;nowiki/&gt;||0||–||
|-
||5||22||10&lt;sub&gt;93&lt;/sub&gt;13&lt;br&gt;300031&lt;br&gt;44441&lt;br&gt;33331&lt;br&gt;33001&lt;br&gt;30301&lt;br&gt;14444&lt;br&gt;10103&lt;br&gt;3101&lt;br&gt;414||96&lt;br&gt;6&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;4&lt;br&gt;3||67&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;3&lt;br&gt;3&lt;br&gt;3||5&lt;sup&gt;95&lt;/sup&gt;+8&lt;br&gt;9391&lt;br&gt;3121&lt;br&gt;2341&lt;br&gt;2251&lt;br&gt;1951&lt;br&gt;1249&lt;br&gt;653&lt;br&gt;401&lt;br&gt;109||http://factordb.com/index.php?id=1100000000034686071&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=9391&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=3121&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2341&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2251&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1951&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1249&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=653&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=401&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=109&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000000034686071&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=9391&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=3121&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=2341&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=2251&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=1951&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=1249&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=653&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=401&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=109&amp;base=5&lt;nowiki/&gt;||0||–||
|-
||6||11||40041&lt;br&gt;4441&lt;br&gt;4401&lt;br&gt;51&lt;br&gt;45&lt;br&gt;35&lt;br&gt;31&lt;br&gt;25&lt;br&gt;21&lt;br&gt;15||5&lt;br&gt;4&lt;br&gt;4&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||5209&lt;br&gt;1033&lt;br&gt;1009&lt;br&gt;31&lt;br&gt;29&lt;br&gt;23&lt;br&gt;19&lt;br&gt;17&lt;br&gt;13&lt;br&gt;11||http://factordb.com/index.php?id=5209&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1033&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1009&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=31&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=29&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=23&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=19&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=17&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=11&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=5209&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=1033&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=1009&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=31&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=29&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=23&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=19&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=17&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=13&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=11&amp;base=6&lt;nowiki/&gt;||0||–||
|-
||7||71||3&lt;sub&gt;16&lt;/sub&gt;1&lt;br&gt;510&lt;sub&gt;7&lt;/sub&gt;1&lt;br&gt;3&lt;sub&gt;6&lt;/sub&gt;01&lt;br&gt;1100021&lt;br&gt;531101&lt;br&gt;351101&lt;br&gt;300053&lt;br&gt;150001&lt;br&gt;100121&lt;br&gt;40054||17&lt;br&gt;10&lt;br&gt;8&lt;br&gt;7&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;5||15&lt;br&gt;9&lt;br&gt;7&lt;br&gt;6&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;4||(7&lt;sup&gt;17&lt;/sup&gt;−5)/2&lt;br&gt;36×7&lt;sup&gt;8&lt;/sup&gt;+1&lt;br&gt;(7&lt;sup&gt;8&lt;/sup&gt;−47)/2&lt;br&gt;134471&lt;br&gt;91631&lt;br&gt;62819&lt;br&gt;50459&lt;br&gt;28813&lt;br&gt;16871&lt;br&gt;9643||http://factordb.com/index.php?id=116315256993601&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=207532837&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2882377&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=134471&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=91631&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=62819&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=50459&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=28813&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=16871&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=9643&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=116315256993601&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=207532837&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=2882377&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=134471&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=91631&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=62819&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=50459&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=28813&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=16871&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=9643&amp;base=7&lt;nowiki/&gt;||0||–||
|-
||8||75||4&lt;sub&gt;220&lt;/sub&gt;7&lt;br&gt;5&lt;sub&gt;13&lt;/sub&gt;25&lt;br&gt;7&lt;sub&gt;12&lt;/sub&gt;1&lt;br&gt;77774&lt;sub&gt;6&lt;/sub&gt;1&lt;br&gt;74&lt;sub&gt;7&lt;/sub&gt;1&lt;br&gt;4&lt;sub&gt;8&lt;/sub&gt;1&lt;br&gt;5&lt;sub&gt;5&lt;/sub&gt;025&lt;br&gt;5550525&lt;br&gt;5500525&lt;br&gt;4&lt;sub&gt;5&lt;/sub&gt;77||221&lt;br&gt;15&lt;br&gt;13&lt;br&gt;11&lt;br&gt;9&lt;br&gt;9&lt;br&gt;8&lt;br&gt;7&lt;br&gt;7&lt;br&gt;7||200&lt;br&gt;14&lt;br&gt;12&lt;br&gt;10&lt;br&gt;9&lt;br&gt;8&lt;br&gt;8&lt;br&gt;7&lt;br&gt;7&lt;br&gt;7||(4×8&lt;sup&gt;221&lt;/sup&gt;+17)/7&lt;br&gt;(5×8&lt;sup&gt;15&lt;/sup&gt;−173)/7&lt;br&gt;8&lt;sup&gt;13&lt;/sup&gt;−7&lt;br&gt;(28669×8&lt;sup&gt;7&lt;/sup&gt;−25)/7&lt;br&gt;(53×8&lt;sup&gt;8&lt;/sup&gt;−25)/7&lt;br&gt;(4×8&lt;sup&gt;9&lt;/sup&gt;−25)/7&lt;br&gt;(5×8&lt;sup&gt;8&lt;/sup&gt;−2413)/7&lt;br&gt;1495381&lt;br&gt;1474901&lt;br&gt;(4×8&lt;sup&gt;7&lt;/sup&gt;+185)/7||http://factordb.com/index.php?id=1100000000416605822&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=25131694349141&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=549755813881&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=8589035809&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=127027489&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=76695841&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=11983381&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1495381&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1474901&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1198399&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000000416605822&amp;base=8&lt;br&gt;http://factordb.com/index.php?showid=25131694349141&amp;base=8&lt;br&gt;http://factordb.com/index.php?showid=549755813881&amp;base=8&lt;br&gt;http://factordb.com/index.php?showid=8589035809&amp;base=8&lt;br&gt;http://factordb.com/index.php?showid=127027489&amp;base=8&lt;br&gt;http://factordb.com/index.php?showid=76695841&amp;base=8&lt;br&gt;http://factordb.com/index.php?showid=11983381&amp;base=8&lt;br&gt;http://factordb.com/index.php?showid=1495381&amp;base=8&lt;br&gt;http://factordb.com/index.php?showid=1474901&amp;base=8&lt;br&gt;http://factordb.com/index.php?showid=1198399&amp;base=8&lt;nowiki/&gt;||0||–||
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||33||280012~280093||DP&lt;sub&gt;95093&lt;/sub&gt;M5&lt;br&gt;HJ0&lt;sub&gt;94295&lt;/sub&gt;J&lt;br&gt;90&lt;sub&gt;93597&lt;/sub&gt;Q&lt;br&gt;9F0&lt;sub&gt;93157&lt;/sub&gt;N&lt;br&gt;7&lt;sub&gt;89449&lt;/sub&gt;333H&lt;br&gt;K3&lt;sub&gt;80751&lt;/sub&gt;6K&lt;br&gt;D&lt;sub&gt;80107&lt;/sub&gt;9UD&lt;br&gt;VFU&lt;sub&gt;72204&lt;/sub&gt;FK&lt;br&gt;J&lt;sub&gt;68715&lt;/sub&gt;2BJ&lt;br&gt;DF0&lt;sub&gt;68367&lt;/sub&gt;J||95096&lt;br&gt;94298&lt;br&gt;93599&lt;br&gt;93160&lt;br&gt;89453&lt;br&gt;80754&lt;br&gt;80110&lt;br&gt;72208&lt;br&gt;68718&lt;br&gt;68370||144405&lt;br&gt;143193&lt;br&gt;142131&lt;br&gt;141465&lt;br&gt;135835&lt;br&gt;122626&lt;br&gt;121648&lt;br&gt;109649&lt;br&gt;104350&lt;br&gt;103821||(441×33&lt;sup&gt;95095&lt;/sup&gt;−3833)/32&lt;br&gt;580×33&lt;sup&gt;94296&lt;/sup&gt;+19&lt;br&gt;9×33&lt;sup&gt;93598&lt;/sup&gt;+26&lt;br&gt;312×33&lt;sup&gt;93158&lt;/sup&gt;+23&lt;br&gt;(7×33&lt;sup&gt;89453&lt;/sup&gt;−4743239)/32&lt;br&gt;(643×33&lt;sup&gt;80753&lt;/sup&gt;+3709)/32&lt;br&gt;(13×33&lt;sup&gt;80110&lt;/sup&gt;−121453)/32&lt;br&gt;(16623×33&lt;sup&gt;72206&lt;/sup&gt;−8095)/16&lt;br&gt;(19×33&lt;sup&gt;68718&lt;/sup&gt;−600883)/32&lt;br&gt;444×33&lt;sup&gt;68368&lt;/sup&gt;+19||http://factordb.com/index.php?id=1100000005652348775&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652362811&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652375073&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652389776&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652430746&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652446200&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652461592&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614764298&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614770536&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614784274&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000005652348775&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652362811&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652375073&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652389776&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652430746&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652446200&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652461592&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614764298&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614770536&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614784274&amp;base=33&lt;nowiki/&gt;||81||100000||
|-
||34||184785~184832||GFGC&lt;sub&gt;99996&lt;/sub&gt;5&lt;br&gt;90&lt;sub&gt;97950&lt;/sub&gt;FJ&lt;br&gt;NM0&lt;sub&gt;85218&lt;/sub&gt;KX&lt;br&gt;F&lt;sub&gt;83189&lt;/sub&gt;H2HP&lt;br&gt;P&lt;sub&gt;79441&lt;/sub&gt;444P&lt;br&gt;6&lt;sub&gt;77027&lt;/sub&gt;8X&lt;br&gt;XQIQ&lt;sub&gt;72241&lt;/sub&gt;D&lt;br&gt;T&lt;sub&gt;66530&lt;/sub&gt;IF&lt;br&gt;4&lt;sub&gt;66152&lt;/sub&gt;B&lt;br&gt;2EEC&lt;sub&gt;66039&lt;/sub&gt;7||100000&lt;br&gt;97953&lt;br&gt;85222&lt;br&gt;83193&lt;br&gt;79445&lt;br&gt;77029&lt;br&gt;72245&lt;br&gt;66532&lt;br&gt;66153&lt;br&gt;66043||153148&lt;br&gt;150013&lt;br&gt;130516&lt;br&gt;127408&lt;br&gt;121669&lt;br&gt;117968&lt;br&gt;110642&lt;br&gt;101893&lt;br&gt;101312&lt;br&gt;101143||(209246×34&lt;sup&gt;99997&lt;/sup&gt;−81)/11&lt;br&gt;9×34&lt;sup&gt;97952&lt;/sup&gt;+529&lt;br&gt;804×34&lt;sup&gt;85220&lt;/sup&gt;+713&lt;br&gt;(5×34&lt;sup&gt;83193&lt;/sup&gt;+700233)/11&lt;br&gt;(25×34&lt;sup&gt;79445&lt;/sup&gt;−28062367)/33&lt;br&gt;(2×34&lt;sup&gt;77029&lt;/sup&gt;+1043)/11&lt;br&gt;(1288676×34&lt;sup&gt;72242&lt;/sup&gt;−455)/33&lt;br&gt;(29×34&lt;sup&gt;66532&lt;/sup&gt;−12833)/33&lt;br&gt;(4×34&lt;sup&gt;66153&lt;/sup&gt;+227)/33&lt;br&gt;(30826×34&lt;sup&gt;66040&lt;/sup&gt;−59)/11||http://factordb.com/index.php?id=1100000004702891268&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702894713&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702900996&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702910376&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702913746&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702918600&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399656529&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399657696&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399658651&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399659716&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000004702891268&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702894713&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702900996&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702910376&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702913746&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702918600&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399656529&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399657696&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399658651&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399659716&amp;base=34&lt;nowiki/&gt;||47||100000||
|-
||35||720002~720062||N0N&lt;sub&gt;99971&lt;/sub&gt;9&lt;br&gt;V0&lt;sub&gt;83669&lt;/sub&gt;E73&lt;br&gt;N&lt;sub&gt;81563&lt;/sub&gt;K7N&lt;br&gt;BJ0&lt;sub&gt;81279&lt;/sub&gt;N&lt;br&gt;J0&lt;sub&gt;80062&lt;/sub&gt;FUH&lt;br&gt;43V&lt;sub&gt;79754&lt;/sub&gt;&lt;br&gt;9&lt;sub&gt;76600&lt;/sub&gt;K3&lt;br&gt;LB&lt;sub&gt;71366&lt;/sub&gt;PB&lt;br&gt;Q&lt;sub&gt;64150&lt;/sub&gt;H&lt;br&gt;50&lt;sub&gt;63397&lt;/sub&gt;5R||99974&lt;br&gt;83673&lt;br&gt;81566&lt;br&gt;81282&lt;br&gt;80066&lt;br&gt;79756&lt;br&gt;76602&lt;br&gt;71369&lt;br&gt;64151&lt;br&gt;63400||154367&lt;br&gt;129197&lt;br&gt;125944&lt;br&gt;125505&lt;br&gt;123628&lt;br&gt;123148&lt;br&gt;118279&lt;br&gt;110199&lt;br&gt;99054&lt;br&gt;97894||(27393×35&lt;sup&gt;99972&lt;/sup&gt;−499)/34&lt;br&gt;31×35&lt;sup&gt;83672&lt;/sup&gt;+17398&lt;br&gt;(23×35&lt;sup&gt;81566&lt;/sup&gt;−144013)/34&lt;br&gt;404×35&lt;sup&gt;81280&lt;/sup&gt;+23&lt;br&gt;19×35&lt;sup&gt;80065&lt;/sup&gt;+19442&lt;br&gt;(4893×35&lt;sup&gt;79754&lt;/sup&gt;−31)/34&lt;br&gt;(9×35&lt;sup&gt;76602&lt;/sup&gt;+12877)/34&lt;br&gt;(725×35&lt;sup&gt;71368&lt;/sup&gt;+16649)/34&lt;br&gt;(13×35&lt;sup&gt;64151&lt;/sup&gt;−166)/17&lt;br&gt;5×35&lt;sup&gt;63399&lt;/sup&gt;+202||http://factordb.com/index.php?id=1100000008248342445&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248353306&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248375642&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248397018&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248412468&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248418540&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248423670&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192119974&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192126630&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192129294&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000008248342445&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248353306&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248375642&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248397018&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248412468&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248418540&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248423670&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192119974&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192126630&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192129294&amp;base=35&lt;nowiki/&gt;||60||100000||
|-
||36||35286~35290||P&lt;sub&gt;81993&lt;/sub&gt;SZ&lt;br&gt;S0&lt;sub&gt;75007&lt;/sub&gt;8H&lt;br&gt;7K&lt;sub&gt;26567&lt;/sub&gt;Z&lt;br&gt;J&lt;sub&gt;10117&lt;/sub&gt;LJ&lt;br&gt;VL0&lt;sub&gt;7258&lt;/sub&gt;J&lt;br&gt;EO0&lt;sub&gt;6177&lt;/sub&gt;V&lt;br&gt;FZ&lt;sub&gt;5777&lt;/sub&gt;3P&lt;br&gt;T09&lt;sub&gt;4618&lt;/sub&gt;1&lt;br&gt;RY&lt;sub&gt;4562&lt;/sub&gt;H&lt;br&gt;OZ&lt;sub&gt;3932&lt;/sub&gt;AZ||81995&lt;br&gt;75010&lt;br&gt;26569&lt;br&gt;10119&lt;br&gt;7261&lt;br&gt;6180&lt;br&gt;5780&lt;br&gt;4621&lt;br&gt;4564&lt;br&gt;3935||127609&lt;br&gt;116739&lt;br&gt;41349&lt;br&gt;15748&lt;br&gt;11301&lt;br&gt;9618&lt;br&gt;8996&lt;br&gt;7192&lt;br&gt;7103&lt;br&gt;6124||(5×36&lt;sup&gt;81995&lt;/sup&gt;+821)/7&lt;br&gt;28×36&lt;sup&gt;75009&lt;/sup&gt;+305&lt;br&gt;(53×36&lt;sup&gt;26568&lt;/sup&gt;+101)/7&lt;br&gt;(19×36&lt;sup&gt;10119&lt;/sup&gt;+2501)/35&lt;br&gt;1137×36&lt;sup&gt;7259&lt;/sup&gt;+19&lt;br&gt;528×36&lt;sup&gt;6178&lt;/sup&gt;+31&lt;br&gt;16×36&lt;sup&gt;5779&lt;/sup&gt;−1163&lt;br&gt;(36549×36&lt;sup&gt;4619&lt;/sup&gt;−289)/35&lt;br&gt;(979×36&lt;sup&gt;4563&lt;/sup&gt;−629)/35&lt;br&gt;25×36&lt;sup&gt;3934&lt;/sup&gt;−901||http://factordb.com/index.php?id=1100000002394962083&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004020085177&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003896952461&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362491&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362489&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362488&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362487&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362486&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362485&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000000840634476&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000002394962083&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000004020085177&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003896952461&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362491&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362489&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362488&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362487&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362486&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362485&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000000840634476&amp;base=36&lt;nowiki/&gt;||4||200000||
|}

== The fully proof of Athena problem in decimal (base ''b'' = 10) ==

'''Bold''' for the Athena primes, ''x'' ◁ ''y'' means ''x'' is a subsequence of ''y''.

Assume ''p'' is a prime &gt; 10, and the last digit of ''p'' must lie in {1,3,7,9}.

Case 1: ''p'' ends with 1.

In this case we can write ''p'' = ''x''1. If ''x'' contains 1, 3, 4, 6, or 7, then (respectively) '''11''' ◁ ''p'', '''31''' ◁ ''p'', '''41''' ◁ ''p'', '''61''' ◁ ''p'', or '''71''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 8, or 9.

Case 1.1: ''p'' begins with 2.

In this case we can write ''p'' = 2''y''1. If 5 ◁ ''y'', then '''251''' ◁ ''p''. If 8 ◁ ''y'', then '''281''' ◁ ''p''. If 9 ◁ ''y'', then 29 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2.

If 22 ◁ ''y'', then '''2221''' ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's.

If ''y'' contains no 2's, then ''p'' ∈ 2{0}1. But then, since the sum of the digits of ''p'' is 3, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' contains exactly one 2, then we can write ''p'' = 2''z''2''w''1, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''20201''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty.

If ''z'' is empty, then ''p'' ∈ 22{0}1, and the smallest prime ''p'' ∈ 22{0}1 is '''22000001'''.

If ''w'' is empty, then ''p'' ∈ 2{0}21, and the smallest prime ''p'' ∈ 2{0}21 is '''20021'''.

Case 1.2: ''p'' begins with 5.

In this case we can write ''p'' = 5''y''1. If 2 ◁ ''y'', then '''521''' ◁ ''p''. If 9 ◁ ''y'', then 59 ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 5, or 8.

If 05 ◁ ''y'', then '''5051''' ◁ ''p''. If 08 ◁ ''y'', then '''5081''' ◁ ''p''. If 50 ◁ ''y'', then '''5501''' ◁ ''p''. If 58 ◁ ''y'', then '''5581''' ◁ ''p''. If 80 ◁ ''y'', then '''5801''' ◁ ''p''. If 85 ◁ ''y'', then '''5851''' ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ {5} ∪ {8}.

If ''y'' ∈ {0}, then ''p'' ∈ 5{0}1. But then, since the sum of the digits of ''p'' is 6, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' ∈ {5}, then ''p'' ∈ 5{5}1, and the smallest prime ''p'' ∈ 5{5}1 is '''555555555551'''.

If ''y'' ∈ {8}, since if 88 ◁ ''y'', then 881 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'',8}, and thus ''p'' ∈ {51,581}, but 51 and 581 are both composite.

Case 1.3: ''p'' begins with 8.

In this case we can write p = 8''y''1. If 2 ◁ ''y'', then '''821''' ◁ ''p''. If 8 ◁ ''y'', then '''881''' ◁ ''p''. If 9 ◁ ''y'', then 89 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 5.

If 50 ◁ ''y'', then '''8501''' ◁ ''p''. Hence we may assume y ∈ {0}{5}.

If 005 ◁ ''y'', then '''80051''' ◁ p. Hence we may assume y ∈ {0} ∪ {5} ∪ 0{5}.

If y ∈ {0}, then ''p'' ∈ 8{0}1. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime.

If y ∈ {5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'', 5, 55, 555, 5555, 55555, 555555, 5555555, 55555555, 555555555, 5555555555}, and thus ''p'' ∈ {81, 851, 8551, 85551, 855551, 8555551, 85555551, 855555551, 8555555551, 85555555551, 855555555551}, but all of these numbers are composite.

If y ∈ 0{5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {0, 05, 055, 0555, 05555, 055555, 0555555, 05555555, 055555555, 0555555555, 05555555555}, and thus ''p'' ∈ {801, 8051, 80551, 805551, 8055551, 80555551, 805555551, 8055555551, 80555555551, 805555555551, 8055555555551}, and of these numbers only 80555551 and 8055555551 are primes, but 80555551 ◁ 8055555551, thus only '''80555551''' is a minimal element.

Case 1.4: ''p'' begins with 9.

In this case we can write p = 9''y''1. If 9 ◁ ''y'', then '''991''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 2, 5, or 8.

If 00 ◁ ''y'', then '''9001''' ◁ ''p''. If 22 ◁ ''y'', then '''9221''' ◁ ''p''. If 55 ◁ ''y'', then '''9551''' ◁ ''p''. If 88 ◁ ''y'', then 881 ◁ ''p''. Hence we may assume ''y'' contains at most one 0, at most one 2, at most one 5, and at most one 8.

If ''y'' only contains at most one 0 and does not contain any of {2,5,8}, then ''y'' ∈ {''𝜆'',0}, and thus ''p'' ∈ {91,901}, but 91 and 901 are both composite. If ''y'' only contains at most one 0 and only one of {2,5,8}, then the sum of the digits of ''p'' is divisible by 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume ''y'' contains at least two of {2,5,8}.

If 25 ◁ ''y'', then 251 ◁ ''p''. If 28 ◁ ''y'', then 281 ◁ ''p''. If 52 ◁ ''y'', then 521 ◁ ''p''. If 82 ◁ ''y'', then 821 ◁ ''p''. Hence we may assume ''y'' contains no 2's (since if ''y'' contains 2, then ''y'' cannot contain either 5's or 8's, which is a contradiction).

If 85 ◁ ''y'', then '''9851''' ◁ ''p''. Hence we may assume ''y'' ∈ {58,580,508,058}, and thus ''p'' ∈ {9581,95801,95081,90581}, and of these numbers only 95801 is prime, but 95801 is not a minimal element since 5801 ◁ 95801.

Case 2: ''p'' ends with 3.

In this case we can write p = ''x''3. If ''x'' contains 1, 2, 4, 5, 7, or 8, then (respectively) '''13''' ◁ ''p'', '''23''' ◁ ''p'', '''43''' ◁ ''p'', '''53''' ◁ ''p'', '''73''' ◁ ''p'', or '''83''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime.

Case 3: ''p'' ends with 7.

In this case we can write ''p'' = ''x''7. If ''x'' contains 1, 3, 4, 6, or 9, then (respectively) '''17''' ◁ ''p'', '''37''' ◁ ''p'', '''47''' ◁ ''p'', '''67''' ◁ ''p'', or '''97''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 7, or 8.

Case 3.1: ''p'' begins with 2.

In this case we can write ''p'' = 2''y''7. If 2 ◁ ''y'', then '''227''' ◁ ''p''. If 5 ◁ ''y'', then '''257''' ◁ ''p''. If 7 ◁ ''y'', then '''277''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 8.

If 08 ◁ ''y'', then '''2087''' ◁ ''p''. If 88 ◁ ''y'', then 887 ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ 8{0}.

If ''y'' ∈ {0}, then ''p'' ∈ 2{0}7. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime.

If y ∈ 8{0}, then ''p'' ∈ 28{0}7. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 40&lt;sub&gt;''n''&lt;/sub&gt;1 = 280&lt;sub&gt;''n''&lt;/sub&gt;7.

Case 3.2: ''p'' begins with 5.

In this case we can write ''p'' = 5''y''7. If 5 ◁ ''y'', then '''557''' ◁ ''p''. If 7 ◁ ''y'', then '''577''' ◁ ''p''. If 8 ◁ ''y'', then '''587''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2.

If 22 ◁ ''y'', then 227 ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's.

If ''y'' contains no 2's, then ''p'' ∈ 5{0}7. But then, since the sum of the digits of ''p'' is 12, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' contains exactly one 2, then we can write ''p'' = 5''z''2''w''7, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''50207''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty.

If ''z'' is empty, then ''p'' ∈ 52{0}7, and the smallest prime ''p'' ∈ 52{0}7 is '''5200007'''.

If ''w'' is empty, then ''p'' ∈ 5{0}27, and the smallest prime ''p'' ∈ 5{0}27 is '''5000000000000000000000000000027'''.

Case 3.3: ''p'' begins with 7.

In this case we can write ''p'' = 7''y''7. If 2 ◁ ''y'', then '''727''' ◁ ''p''. If 5 ◁ ''y'', then '''757''' ◁ ''p''. If 8 ◁ ''y'', then '''787''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 7, and thus all digits of ''p'' are 0 or 7. But then, since the digits of ''p'' all have a common factor 7, ''p'' is divisible by 7, so ''p'' cannot be prime.

Case 3.4: ''p'' begins with 8.

In this case we can write ''p'' = 8''y''7. If 2 ◁ ''y'', then '''827''' ◁ ''p''. If 5 ◁ ''y'', then '''857''' ◁ ''p''. If 7 ◁ ''y'', then '''877''' ◁ ''p''. If 8 ◁ ''y'', then '''887''' ◁ ''p''. Hence we may assume ''y'' ∈ {0}, and thus ''p'' ∈ 8{0}7. But then, since the sum of the digits of ''p'' is 15, ''p'' is divisible by 3, so ''p'' cannot be prime.

Case 4: ''p'' ends with 9.

In this case we can write ''p'' = ''x''9. If ''x'' contains 1, 2, 5, 7, or 8, then (respectively) '''19''' ◁ ''p'', '''29''' ◁ ''p'', '''59''' ◁ ''p'', '''79''' ◁ ''p'', or '''89''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 4, 6, or 9.

If 44 ◁ ''x'', then '''449''' ◁ ''p''. Hence we may assume ''x'' contains zero or one 4's.

If x contains no 4's, then all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume that ''x'' contains exactly one 4.

Case 4.1: ''p'' begins with 3.

In this case we can write ''p'' = 3''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. We must have '''349''' ◁ ''p''.

Case 4.2: ''p'' begins with 4.

In this case we can write ''p'' = 4''y''9, where all digits of ''y'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''409''' ◁ ''p''. If 3 ◁ ''y'', then 43 ◁ ''p''. If 9 ◁ ''y'', then '''499''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}, and thus ''p'' ∈ 4{6}9. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 6&lt;sub&gt;''n''&lt;/sub&gt;7 = 46&lt;sub&gt;''n''&lt;/sub&gt;9.

Case 4.3: ''p'' begins with 6.

In this case we can write p = 6''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 6 ◁ ''z'', then '''6469''' ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' is empty.

If 3 ◁ ''y'', then 349 ◁ ''p''. If 9 ◁ ''y'', then '''6949''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 6.

If 06 ◁ ''y'', then '''60649''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}{0}.

If 666 ◁ ''y'', then '''666649''' ◁ ''p''. If 00000 ◁ ''y'', then '''60000049''' ◁ ''p''. Hence we may assume ''y'' ∈ {''𝜆'', 0, 00, 000, 0000, 6, 60, 600, 6000, 60000, 66, 660, 6600, 66000, 660000}, and thus ''p'' ∈ {649, 6049, 60049, 600049, 6000049, 6649, 66049, 660049, 6600049, 66000049, 66649, 666049, 6660049, 66600049, 666000049}, and of these numbers only '''66000049''' and '''66600049''' are primes.

Case 4.4: ''p'' begins with 9.

In this case we can write p = 9''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''9049''' ◁ ''p''. If 3 ◁ ''y'', then 349 ◁ ''p''. If 6 ◁ ''y'', then '''9649''' ◁ ''p''. If 9 ◁ ''y'', then '''9949''' ◁ ''p''. Hence we may assume ''y'' is empty.

If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' ∈ {6}, and thus ''p'' ∈ 94{6}9, and the smallest prime ''p'' ∈ 94{6}9 is 946669.

[[Category:Number theory]]</text>
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    <revision>
      <id>2831829</id>
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      <text bytes="157601" sha1="7s2olwc1l7oj50gxa0qyr3pgklrzi90" xml:space="preserve">{{mathematics}}
'''Athena problem''' is an [[:w:List of unsolved problems in mathematics|unsolved problem]] in [[:w:Number theory|number theory]] and [[:w:Formal language theory|formal language theory]] and [[:w:Order theory|order theory]], this problem is named after the ancient Greek goddess [[:w:Athena|Athena]] (which is associated with [[:w:Wisdom|wisdom]]). Athena problem is: Give a [[:w:Natural number|natural number]] ''b'' &gt; 1, find the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the set of the &quot;[[:w:Prime number|prime number]] [[:w:Greater than|&gt;]] ''b''&quot; [[:w:Numerical digit|digit]] [[:w:String (computer science)|string]]s in the [[:w:Positional numeral system|positional numeral system]] with [[:w:Radix|base]] ''b'' for the [[:w:Subsequence|subsequence]] [[:w:Partially ordered set|ordering]]. (A string ''x'' is a subsequence of another string ''y'', if ''x'' can be obtained from ''y'' by deleting zero or more of the [[:w:Character (computing)|character]]s in ''y''. For example, 514 is a subsequence of 352148, &quot;string&quot; is a subsequence of &quot;meistersinger&quot;. In contrast, 758 is not a subsequence of 378259, &quot;abc&quot; is not a subsequence of &quot;cbacacba&quot;, since the characters must be in the same order) (Unlike [[:w:Substring|substring]], subsequence is not required to occupy consecutive positions within the original sequences, e.g. the [[:w:Longest common subsequence|longest common subsequence problem]] is different from the [[:w:Longest common substring|longest common substring problem]])

Using [[:w:Formal language theory|formal language theory]] terminology, Athena problem is finding the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the [[:w:Formal language|language]] of base-''b'' [[:w:Representation (mathematics)|representation]]s of the [[:w:Prime number|prime number]]s [[:w:Greater than|&gt;]] ''b'' (which is a set of [[:w:String (computer science)|string]]s of [[:w:Symbol|symbol]]s over the [[:w:Alphabet (formal languages)|alphabet]] ''Σ''&lt;sub&gt;''b''&lt;/sub&gt; := {0, 1, ..., ''b''−1}), under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] &quot;is a subsequence of&quot;, which is a [[:w:Partially ordered set|partial ordering]]), for a given natural number ''b'' &gt; 1 (You can draw this partial ordering as a [[:w:Hasse diagram|Hasse diagram]] to find all [[:w:Minimal element|minimal element]]s), this set is called '''Athena set''', and the prime numbers in this set are called '''Athena primes'''.

By [[:w:Higman's lemma|Higman's lemma]], there are no [[:w:Infinite set|infinite]] [[:w:Antichain|antichain]]s for the subsequence ordering (i.e. the subsequence ordering is always a [[:w:Well-quasi-ordering|well quasi order]]) (i.e. under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] &quot;is a subsequence of&quot;, which is a [[:w:Partially ordered set|partial ordering]]), every set of pairwise incomparable (i.e. not [[:w:Comparability|comparable]]) strings is finite), thus there must be only finitely many such minimal elements. In other words, the Athena set in every base ''b'' must be a [[:w:Finite set|finite set]], and every base ''b'' ≥ 2 has only finitely many Athena primes, e.g. in [[:w:Decimal|decimal]] (base ''b'' = 10), the Athena set has exactly 77 [[:w:Element of a set|element]]s (they are exactly the Athena primes in decimal (base ''b'' = 10)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}.

Determining the set of the minimal elements of a arbitrary set of strings under the subsequence ordering is in general [[:w:List of unsolved problems in mathematics|unsolvable]], and can be difficult even when this set is relatively simple (such as the base ''b'' representations of the prime numbers &gt; ''b'', whose set is exactly the Athena set in base ''b'').

Although the set ''M''(''S'') of minimal strings is necessarily [[:w:Finite set|finite]], determining it explicitly for a given ''S'' can be a difficult computational problem. We use some [[:w:Number theory|numbertheoretic]] [[:w:Heuristic argument|heuristic]]s to [[:w:Computing|compute]] ''M''(''L''&lt;sub&gt;''b''&lt;/sub&gt;) (i.e. to compute the Athena set in base ''b''), where ''L''&lt;sub&gt;''b''&lt;/sub&gt; is the [[:w:Formal language|language]] of [[:w:Radix|base]]-''b'' representations of the [[:w:Prime number|prime number]]s which are [[:w:Greater than|&gt;]] ''b'', for 2 ≤ ''b'' ≤ 36.

For bases 2 ≤ ''b'' ≤ 36, Athena problem is fully solved in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24, and also solved in bases ''b'' = 11, 13, 16, 22, 30 if [[:w:Probable prime|probable prime]]s are allowed. For the unsolved bases ''b'' = 17, 19, 21, 23, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, Athena problem is solved (if probable primes are allowed) except 771 [[:w:Indexed family|families]] of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be [[:w:Empty string|empty]]) of digits in base ''b'', ''y'' is a digit in base ''b'') = sequence {''xz'', ''xyz'', ''xyyz'', ''xyyyz'', ''xyyyyz'', ''xyyyyyz'', ...} (i.e. &quot;''xy''&lt;sup&gt;+&lt;/sup&gt;''z''&quot; in [[:w:Regular expression|regular expression]]), all of these 771 families contain no primes &gt; ''b'' or probable primes &gt; ''b'' with length ≤ 100000. (The chance that an unproven probable prime in these sets is in fact composite is less than 10&lt;sup&gt;−2000&lt;/sup&gt;, see https://t5k.org/notes/prp_prob.html)

== Solve the problem ==

To solve the Athena problem for a given base ''b'', we must [[:w:Computing|compute]] the elements up to families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), and find the smallest prime &gt; ''b'' in all such families.

We call families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') &quot;linear&quot; families, and we reduce these families by removing all trailing digits ''y'' from ''x'', and removing all leading digits ''y'' from ''z'', to make the families be easier, e.g. family 12333{3}33345 in base ''b'' is reduced to family 12{3}45 in base ''b'', since they are in fact the same family. Our [[:w:Algorithm|algorithm]] then proceeds as follows:

* 1. ''M'' := {minimal primes in base ''b'' of length 2 or 3}, ''L'' := union of all ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'') such that ''x'' ≠ 0 and ''gcd''(''z'', ''b'') = 1 and ''Y'' is the set of digits ''y'' in base ''b'' such that ''xyz'' has no subsequence in ''M''.
* 2. While ''L'' contains nonlinear families (families which are not linear families): Explore each family of ''L'', and update ''L''. Examine each family of ''L'' by:
* 2.1. Let ''w'' be the shortest string in the family. If ''w'' has a subsequence in ''M'', then remove the family from ''L''. If ''w'' represents a prime, then add ''w'' to ''M'' and remove the family from ''L''.
* 2.2. If possible, simplify the family.
* 2.3. Using the techniques below (covering congruence, algebraic factorization, or combine of them), check if the family can be proven to only contain composites (only count the numbers &gt; ''b''), and if so then remove the family from ''L''.
* 3. Update ''L'', after each split examine the new families as in step 2.

e.g. in decimal (base ''b'' = 10):

''M'' := {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991}

''L'' := {2{0,2}1, 2{0,8}7, 3{0,3,6,9}3, 3{0,3,6,9}9, 4{6}9, 5{0,5,8}1, 5{0,2}7, 6{0,3,6,9}3, 6{0,3,4,6,9}9, 7{0,7}7, 8{0,5}1, 8{0}7, 9{0,2,5,8}1, 9{0,3,6,9}3, 9{0,3,4,6,9}9}

and since 2221 is prime, it follows that the family 2{0,2}1 splits into the families 2{0}1 and 2{0}2{0}1

and since the family 2{0}1 can be proven to contain no primes &gt; base (since all numbers in this family are divisible by 3), it can be removed

and since 20201 is prime, it follows that the family 2{0}2{0}1 splits into the families 2{0}21 and 22{0}1

221 and 2021 are composites, but 20021 is prime, thus add 20021 to ''L''

none of 221, 2201, 22001, 220001, 2200001 are primes, but 22000001 is prime, thus add 22000001 to ''L''

and since the family 3{0,3,6,9}3 can be proven to contain no primes &gt; base (since all numbers in this family are divisible by 3), it can be removed

etc.

Since the number of possible (first digit,last digit) (also called (initial digit,final digit)) combos ([[:w:Ordered pair|ordered pair]]s) of a prime &gt; ''b'' in base ''b'' is (''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(''b'') (all digits except 0 can be the first digit of a prime &gt; ''b'' in base ''b'' (thus ''b''−1 possible digits), but only the digits coprime to ''b'' can be the last digit of a prime &gt; ''b'' in base ''b'' (thus ''eulerphi''(''b'') possible digits), and by the [[:w:Rule of product|rule of product]], there are (''b''−1)×''eulerphi''(''b'') choices of the (first digit,last digit) combo, also, both &quot;numbers of Athena primes in base ''b''&quot; and &quot;length of the largest Athena prime in base ''b''&quot; are [[:w:Asymptotic analysis|roughly]] ''[[:w:E (mathematical_constant)|e]]''&lt;sup&gt;''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)&lt;/sup&gt;.

Shrinking the family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'')

* If ''y'' ∈ ''Y'' and the string ''xyyz'' represents a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''}''z'' ∪ ''x''{''Y'' \ ''y''}''y''{''Y'' \ ''y''}''z''.
* If ''y''&lt;sub&gt;1&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;2&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;1&lt;/sub&gt; ≠ ''y''&lt;sub&gt;2&lt;/sub&gt; and the string ''xy''&lt;sub&gt;1&lt;/sub&gt;''y''&lt;sub&gt;2&lt;/sub&gt;''z'' represents a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''&lt;sub&gt;1&lt;/sub&gt;}{''Y'' \ ''y''&lt;sub&gt;2&lt;/sub&gt;}''z''.
* If ''y''&lt;sub&gt;1&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;2&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;1&lt;/sub&gt; ≠ ''y''&lt;sub&gt;2&lt;/sub&gt; and both the strings ''xy''&lt;sub&gt;1&lt;/sub&gt;''y''&lt;sub&gt;2&lt;/sub&gt;''z'' and ''xy''&lt;sub&gt;2&lt;/sub&gt;''y''&lt;sub&gt;1&lt;/sub&gt;''z'' represent a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or have a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''&lt;sub&gt;1&lt;/sub&gt;}''z'' ∪ ''x''{''Y'' \ ''y''&lt;sub&gt;2&lt;/sub&gt;}''z''.

e.g. in decimal (base ''b'' = 10):

* 2221 is a prime &gt; 10, thus the family 2{0,2}1 splits into the two families 2{0}1 and 2{0}2{0}1.
* 227 is a prime &gt; 10, and it is a subsequence of 5227, thus the family 5{0,2}7 splits into the two families 5{0}7 and 5{0}2{0}7.
* 449 is a prime &gt; 10, and it is a subsequence of 6449, thus the family 6{0,3,4,6,9}9 splits into the two families 6{0,3,6,9}9 and 6{0,3,6,9}4{0,3,6,9}9.
* Both 5051 and 5501 are primes &gt; 10, thus the family 5{0,5}1 splits into the two families 5{0}1 and 5{5}1 = {5}1.
* 8501 is a prime &gt; 10, thus the family 8{0,5}1 splits into the family 8{0}{5}1.
* 887 is a prime &gt; 10, and it is a subsequence of 2887, also 2087 is a prime &gt; 10, thus the family 2{0,8}7 splits into the two families 2{0}7 and 28{0}7.
* 349 and 449 are primes &gt; 10, and they are subsequences of 9349 and 9449, respectively, also 9049, 9649, 9949 are primes &gt; 10, thus the family 9{0,3,4,6,9}9 splits into the two families 9{0,3,6,9}9 and 94{0,3,6,9}9.
* 251, 281, 521, 821, 881 are primes &gt; 10, and they are subsequences of 9251, 9281, 9521, 9821, 9881, respectively, also 9001, 9221, 9551, 9851 are primes &gt; 10, thus the family 9{0,2,5,8}1 splits into the numbers {91, 901, 921, 951, 981, 9021, 9051, 9081, 9201, 9501, 9581, 9801, 90581, 95081, 95801}.

If the methods we have discussed cannot be used to rule out or shrink ''x''{''Y''}''z'' where ''Y'' = {''y''&lt;sub&gt;1&lt;/sub&gt;, ''y''&lt;sub&gt;2&lt;/sub&gt;, ..., ''y''&lt;sub&gt;''n''&lt;/sub&gt;}, then we can replace ''x''{''Y''}''z'' by ''xy''&lt;sub&gt;1&lt;/sub&gt;{''Y''}''z'' ∪ ''xy''&lt;sub&gt;2&lt;/sub&gt;{''Y''}''z'' ∪ ... ∪ ''xy''&lt;sub&gt;''n''&lt;/sub&gt;{''Y''}''z'' and re-run the methods on this new [[:w:Formal language|language]].

If all remain families are linear families (i.e. of the form ''x''{''y''}''z'', where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), then we search the smallest (probable) primes in these families and add these primes to the list.

e.g. in decimal (base ''b'' = 10):

* The smallest prime in the family 5{0}27 is 5000000000000000000000000000027.
* The smallest prime in the family {5}1 is 555555555551.
* The smallest prime in the family 8{5}1 is 8555555555555555555551, but 8555555555555555555551 is not a minimal element since 555555555551 is a subsequence of 8555555555555555555551.

There is no guarantee that the techniques discussed will ever terminate, but in practice they often do. They are able to determine the Athena set in base ''b'' for 2 ≤ ''b'' ≤ 16 and ''b'' = 18, 20, 22, 24, 30. The bases ''b'' = 17, 19, 21, 23, 25 ≤ ''b'' ≤ 29, 31 ≤ ''b'' ≤ 36 are solved with the exception of 771 families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'').

The following is a &quot;[[:w:Semi-algorithm|semi-algorithm]]&quot; that is guaranteed to solve the Athena problem for a given base ''b'', but it is not so easy to implement:

# ''M'' = ''[[:w:Empty string|∅]]''
# while (''L'' ≠ ''∅'') do
# choose ''x'', a shortest string in ''L''
# ''M'' := ''M'' ∪ {''x''}
# ''L'' := ''L'' − ''sup''({''x''})

In practice, for arbitrary ''L'', we cannot feasibly carry out step 5. Instead, we work with ''L''&amp;#39;, some regular overapproximation to ''L'', until we can show ''L''&amp;#39; = ''∅'' (which implies ''L'' = ''∅''). In practice, ''L''&amp;#39; is usually chosen to be a finite [[:w:Union (set theory)|union]] of sets of the form ''L''&lt;sub&gt;1&lt;/sub&gt;{''L''&lt;sub&gt;2&lt;/sub&gt;}''L''&lt;sub&gt;3&lt;/sub&gt;, where each of ''L''&lt;sub&gt;1&lt;/sub&gt;, ''L''&lt;sub&gt;2&lt;/sub&gt;, ''L''&lt;sub&gt;3&lt;/sub&gt; is finite. In the case we consider in this project, we then have to determine whether such a family contains a prime or not.

Thus, the [[:w:Time complexity|time complexity]] of the Athena problem in base ''b'' may be ''[[:w:Big O notation|O]]''(''[[:w:E (mathematical_constant)|e]]''&lt;sup&gt;''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)&lt;/sup&gt;), and the [[:w:CPU time|CPU time]] of the Athena problem in base ''b'' may be longer than [[:w:Age of the universe|the age of the universe]] for bases ''b'' = 19, 23, 25, 27, 29, 31, 32, 33, 34, 35, also, Athena problem in bases ''b'' around 500 may be [[:w:NP-complete|NP-complete]] or [[:w:NP-hard|NP-hard]], or an [[:w:Undecidable problem|undecidable problem]], or an example of [[:w:Gödel's incompleteness theorems|Gödel's incompleteness theorems]] (like the [[:w:Continuum hypothesis|continuum hypothesis]] and the [[:w:Halting problem|halting problem]]).

To solve the Athena problem (i.e. to compute the Athena set), we need to determine whether a given family contains a prime. In practice, if family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'') could not be ruled out as only containing composites and ''Y'' contains two or more digits, then a relatively small prime &gt; ''b'' could always be found in this family. Intuitively, this is because there are a large number of small strings in such a family, and at least one is likely to be prime (e.g. there are 2&lt;sup&gt;''n''−2&lt;/sup&gt; strings of length ''n'' in the family 1{3,7}9, and there are over a thousand strings of length 12 in the family 1{3,7}9, thus it is very impossible that these numbers are all composite). In the case ''Y'' contains only one digit, this family is of the form ''x''{''y''}''z'', and there is only a single string of each length &gt; (the length of ''x'' + the length of ''z''), and it is not known if the following [[:w:Decision problem|decision problem]] is recursively solvable (just like [[:w:Sierpiński number|Sierpiński problem]] and [[:w:Riesel number|Riesel problem]], Sierpiński problem and Riesel problem can be generalized to other bases ''b'' (references: http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm), in fact, Athena problem base ''b'' covers the Sierpiński problem base ''b'' and the Riesel problem base ''b'' with ''k'' &lt; ''b'', i.e. finding the smallest prime of the form ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 and ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (or prove such prime does not exist) with ''k'' &lt; ''b'' (specially, for bases ''b'' such that the conjectured smallest Sierpiński number or the conjectured smallest Riesel number is &lt; ''b'', Athena problem base ''b'' covers the Sierpiński problem base ''b'' or the Riesel problem base ''b'', respectively), since the smallest prime of the form ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 and ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (if exists) must be a minimal element in base ''b'', also, Athena problem base ''b'' covers finding the smallest prime of these forms in base ''b'' (or proving that such prime does not exist) (in fact, it is known that exactly what bases 2 ≤ ''b'' ≤ 1024 have the families listed in the table below as unsolved families, all of these families in all bases 2 ≤ ''b'' ≤ 1024 have been searched to length ≥ 10000 (for the family (''sqrt''(''b'')×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''sqrt''(''b'')+1), bases 2 ≤ ''b'' ≤ 1048576, searched to length ≥ 5000)): (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1) (for this form, ''n'' must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepu.txt, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379, https://pzktupel.de/Primetables/TableRepunitGen.php, https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A128164, https://oeis.org/A285642; or for prime bases ''b'': https://oeis.org/A065854, https://oeis.org/A279068), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 1) (references of this form: http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A228101), (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/2 (for odd ''b'') (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 2) (reference of this form: http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt), (''sqrt''(''b'')×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''sqrt''(''b'')+1) (for square ''b'') (for this form, 2×''n''+1 must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepuP.txt, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/488, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://oeis.org/A084742, https://oeis.org/A084741; or for bases ''b'' with ''sqrt''(''b'') prime: https://oeis.org/A065507), ((''b''−2)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''−1) (''n'' ≥ 2) (reference of this form: https://oeis.org/A243404), 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://oeis.org/A119624), 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&amp;d=1567314217, https://oeis.org/A119591), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+2 (''n'' ≥ 1) (references of this form: https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067), ''b''&lt;sup&gt;''n''&lt;/sup&gt;−2 (''n'' ≥ 2) (references of this form: https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A250200, https://oeis.org/A255707, https://oeis.org/A084714; or for prime bases ''b'': https://oeis.org/A292201), (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (''n'' ≥ 1) (references of this form: http://www.noprimeleftbehind.net/Williams-primes-MP.htm, http://www.bitman.name/math/table/477, https://pzktupel.de/Primetables/TableWilliams2.php, https://oeis.org/A305531; or for prime bases ''b'': https://oeis.org/A087139), (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (''n'' ≥ 1) (references of this form: https://harvey563.tripod.com/wills.txt, http://www.noprimeleftbehind.net/Williams-primes-MM.htm, http://www.bitman.name/math/table/484, https://pzktupel.de/Primetables/TableWilliams1.php; or for prime bases ''b'': https://oeis.org/A122396), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''−1) (''n'' ≥ 1) (references of this form: http://www.bitman.name/math/table/795, https://pzktupel.de/Primetables/TableWilliams6.php, https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179), ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''−1) (''n'' ≥ 2) (references of this form: http://www.bitman.name/math/table/792, https://pzktupel.de/Primetables/TableWilliams5.php, https://oeis.org/A113516, https://oeis.org/A343589; or for prime bases ''b'': https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/435)):

'''Problem: Given strings ''x'', ''z'' (may be empty), a digit ''y'', and a base ''b'' (''x'' does not [[:w:Leading zero|start with the digit 0]], ''z'' ends with a digit which [[:w:Coprime integers|coprime]] to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty), does there exist a prime number whose base-''b'' expansion is of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' for some ''n'' ≥ 0?'''

An [[:w:Algorithm|algorithm]] to solve this problem, for example, would allow us to decide if there are any additional [[:w:Fermat prime|Fermat prime]]s other than the known ones (corresponding to ''n'' = 0, 1, 2, 3, 4). To see this, take ''b'' = 2, ''x'' = 1, ''y'' = 0, and ''z'' = 0&lt;sub&gt;16&lt;/sub&gt;1. Since if 2&lt;sup&gt;''n''&lt;/sup&gt;+1 is prime then ''n'' must be a [[:w:Power of 2|power of two]], a prime of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' must be a new Fermat prime. Besides, it would allow us to decide if there are infinitely many [[:w:Mersenne prime|Mersenne prime]]s (of the form 2&lt;sup&gt;''p''&lt;/sup&gt;−1 with prime ''p''). To see this, take ''b'' = 2, ''x'' = ''𝜆'' (the [[:w:Empty string|empty string]]), ''y'' = 1, and ''z'' = 1&lt;sub&gt;''n''+1&lt;/sub&gt;, where ''n'' is the exponent of the Mersenne prime which we want to know whether it is the largest Mersenne prime or not. Since if 2&lt;sup&gt;''n''&lt;/sup&gt;−1 is prime then ''n'' must be a [[:w:Prime number|prime]], a prime of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' must be a new Mersenne prime. Also, it would allow us to decide whether 78557 is the smallest [[:w:Sierpinski number|Sierpinski number]] (i.e. odd numbers ''k'' such that ''k''×2&lt;sup&gt;''n''&lt;/sup&gt;+1 is composite for all ''n'' ≥ 1) and whether 509203 is the smallest [[:w:Riesel number|Riesel number]] (i.e. odd numbers ''k'' such that ''k''×2&lt;sup&gt;*n*&lt;/sup&gt;−1 is composite for all ''n'' ≥ 1), etc.

'''Conjecture (this conjecture is very important for the Athena problem): If family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' (with fixed strings ''x'', ''z'' (may be empty), fixed digit ''y'', and variable ''n'') in base ''b'' (with fixed ''b'' ≥ 2) (''x'' does not start with the digit 0, ''z'' ends with a digit which coprime to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty) cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' contains infinitely many primes (this is equivalent to: If form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) (with fixed integers ''a'' ≥ 1, ''b'' ≥ 2, ''c'' ≠ 0 (with ''gcd''(''a'',''c'') = 1 and ''gcd''(''b'',''c'') = 1), and variable ''n'') cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) contains infinitely many primes).'''

(in fact, this conjecture is equivalent to the conjecture (to prove this, by change the base (''b'') to a power of ''b'' which is larger than the largest prime in a given family (in base ''b'') which only contains finitely many primes): If family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' (with fixed strings ''x'', ''z'' (may be empty), fixed digit ''y'', and variable ''n'') in base ''b'' (with fixed ''b'' ≥ 2) (''x'' does not start with the digit 0, ''z'' ends with a digit which coprime to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty) cannot be proven to only contain composites (by covering congruence, algebraic factorization, or combine of them), then family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' contains at least one prime (this is equivalent to: If form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) (with fixed integers ''a'' ≥ 1, ''b'' ≥ 2, ''c'' ≠ 0 (with ''gcd''(''a'',''c'') = 1 and ''gcd''(''b'',''c'') = 1), and variable ''n'') cannot be proven to only contain composites (by covering congruence, algebraic factorization, or combine of them), then form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) contains at least one prime), like the [[:w:Bunyakovsky conjecture|Bunyakovsky conjecture]] and the [[:w:Dickson's conjecture|Dickson's conjecture]] and the [[:w:Schinzel's hypothesis H|Schinzel's hypothesis ''H'']], if such ''n'' always exists, then there must be always infinitely many such ''n'', to prove this, add another polynomial for the cases of the Dickson's conjecture and the Schinzel's hypothesis ''H'', also, change the polynomial (e.g. change ''n'' to ''r''×''n'' or ''n''&lt;sup&gt;''r''&lt;/sup&gt; for all integers ''r'' &gt; 1) for the cases of the Bunyakovsky conjecture and the Schinzel's hypothesis ''H'')

Some families can be ruled out to contain no prime &gt; ''b'' by [[:w:Covering set|covering congruence]], [[:w:Factorization of polynomials|algebraic factorization]] (e.g. [[:w:Difference of two squares|difference of two squares]], [[:w:Sum of two cubes|sum of two cubes]], [[:w:Sophie Germain's identity|Sophie Germain's identity of ''x''&lt;sup&gt;4&lt;/sup&gt;+4×''y''&lt;sup&gt;4&lt;/sup&gt;]]), or combine of them, e.g.

* The base 9 family 2{7}: Always divisible by 2 or 5
* The base 11 family 2{5}: Always divisible by 2 or 3
* The base 14 family B{0}1: Always divisible by 3 or 5
* The base 13 family 95{0}3: Always divisible by 5, 7, or 17
* The base 16 family {4}D: Always divisible by 3, 7, or 13
* The base 16 family {8}F: Always divisible by 3, 7, or 13
* The base 21 family {7}D: Always divisible by 2, 13, or 17
* The base 23 family {D}GA: Always divisible by 2, 5, 7, 37, or 79
* The base 9 family {1}: Can be written as (9&lt;sup&gt;''n''&lt;/sup&gt;−1)/8 and can be factored as (3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (3&lt;sup&gt;''n''&lt;/sup&gt;+1) / 8
* The base 8 family 1{0}1: Can be written as 8&lt;sup&gt;''n''&lt;/sup&gt;+1 and can be factored as (2&lt;sup&gt;''n''&lt;/sup&gt;+1) × (4&lt;sup&gt;''n''&lt;/sup&gt;−2&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 9 family 3{8}: Can be written as 4×9&lt;sup&gt;''n''&lt;/sup&gt;−1 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 16 family 1{5}: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;−1)/3 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+1) / 3
* The base 16 family {4}1: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;−49)/15 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−7) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+7) / 15
* The base 27 family 7{Q}: Can be written as 8×27&lt;sup&gt;''n''&lt;/sup&gt;−1 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (4×9&lt;sup&gt;''n''&lt;/sup&gt;+2×3&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 27 family 9{G}: Can be written as (125×27&lt;sup&gt;''n''&lt;/sup&gt;−8)/13 and can be factored as (5×3&lt;sup&gt;''n''&lt;/sup&gt;−2) × (25×9&lt;sup&gt;''n''&lt;/sup&gt;+10×3&lt;sup&gt;''n''&lt;/sup&gt;+4)
* The base 16 family {C}D: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;+1)/5 and can be factored as (2×4&lt;sup&gt;''n''&lt;/sup&gt;−2×2&lt;sup&gt;''n''&lt;/sup&gt;+1) × (2×4&lt;sup&gt;''n''&lt;/sup&gt;+2×2&lt;sup&gt;''n''&lt;/sup&gt;+1) / 5
* The base 14 family 8{D}: Can be written as 9×14&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is odd and can be factored as (3×14&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (3×14&lt;sup&gt;''n''/2&lt;/sup&gt;+1) if ''n'' is even
* The base 12 family {B}9B: Can be written as 12&lt;sup&gt;''n''&lt;/sup&gt;−25, it is divisible by 13 if ''n'' is odd and can be factored as (12&lt;sup&gt;''n''/2&lt;/sup&gt;−5) × (12&lt;sup&gt;''n''/2&lt;/sup&gt;+5) if ''n'' is even
* The base 14 family {D}5: Can be written as 14&lt;sup&gt;''n''&lt;/sup&gt;−9, it is divisible by 5 if ''n'' is odd and can be factored as (14&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (14&lt;sup&gt;''n''/2&lt;/sup&gt;+3) if ''n'' is even
* The base 17 family 1{9}: Can be written as (25×17&lt;sup&gt;''n''&lt;/sup&gt;−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (5×17&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (5×17&lt;sup&gt;''n''/2&lt;/sup&gt;+3) / 16 if ''n'' is even
* The base 17 family 7{9}: Can be written as (121×17&lt;sup&gt;''n''&lt;/sup&gt;−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (11×17&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (11×17&lt;sup&gt;''n''/2&lt;/sup&gt;+3) / 16 if ''n'' is even
* The base 19 family 1{6}: Can be written as (4×19&lt;sup&gt;''n''&lt;/sup&gt;−1)/3, it is divisible by 5 if ''n'' is odd and can be factored as (2×19&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (2×19&lt;sup&gt;''n''/2&lt;/sup&gt;+1) / 3 if ''n'' is even
* The base 24 family 3{N}: Can be written as 4×24&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is odd and can be factored as (2×24&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (2×24&lt;sup&gt;''n''/2&lt;/sup&gt;+1) if ''n'' is even
* The base 24 family 5{N}: Can be written as 6×24&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is even and can be factored as (12×24&lt;sup&gt;(''n''−1)/2&lt;/sup&gt;−1) × (12×24&lt;sup&gt;(''n''−1)/2&lt;/sup&gt;+1) if ''n'' is odd

If the conjecture above is true, then the [[:w:Sierpiński number|Sierpiński conjecture]] and [[:w:Riesel number|Riesel conjecture]] are also true, and the [https://www.mersenneforum.org/showthread.php?t=10761 dual Sierpiński conjecture] and the [https://www.mersenneforum.org/showthread.php?t=6545 dual Riesel conjecture] are also true, and the [http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm Sierpiński conjectures] and the [http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm Riesel conjectures] in all bases ''b'' are also true, and the [http://www.noprimeleftbehind.net/crus/SNOB-Sierp-conjectures.htm real Sierpiński conjectures] and the [http://www.noprimeleftbehind.net/crus/Real-Riesel-conjectures.htm real Riesel conjectures] are also true, also, if the Athena conjecture is true, then there are infinitely many primes of these forms for fixed bases ''b'' ≥ 2 and variable exponents ''n'':

* (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1) for all bases ''b'' which are not [[:w:Perfect power|perfect power]]s (for this form, ''n'' must be prime) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepu.txt, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379, https://pzktupel.de/Primetables/TableRepunitGen.php, https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A128164, https://oeis.org/A285642; or for prime bases ''b'': https://oeis.org/A065854, https://oeis.org/A279068)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' which are not of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 (for this form, ''n'' must be power of 2) (references of this form: http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A228101)
* (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/2 for all odd bases ''b'' which are not of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 (for this form, ''n'' must be power of 2) (reference of this form: http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt)
* (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''+1) for all bases ''b'' which are neither of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 nor of the form 4×''m''&lt;sup&gt;4&lt;/sup&gt; (for this form, ''n'' must be prime) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepuP.txt, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/488, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://oeis.org/A084742, https://oeis.org/A084741; or for prime bases ''b'': https://oeis.org/A065507)
* ((''b''−2)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''−1) for all bases ''b'' &gt; 2 (reference of this form: https://oeis.org/A243404)
* 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' &lt; 201446503145165177, not == 1 mod 3 (references of this form: https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://oeis.org/A119624)
* 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&amp;d=1567314217, https://oeis.org/A119591)
* 3×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b''
* 3×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b''
* 4×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 5, not == 14 mod 15, not [[:w:Fourth power|fourth power]]s
* 4×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 3, not == 4 mod 5, not [[:w:Square number|square]]s
* 5×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' &lt; 140324348, not == 1 mod 3
* 5×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b''
* 6×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 7, not == 34 mod 35
* 6×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 5, not == 34 mod 35, not of the form 6×''m''&lt;sup&gt;2&lt;/sup&gt; with ''m'' == 2, 3 mod 5
* 7×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b''
* 7×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' &lt; 9162668342, not == 1 mod 3
* 8×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 3, not == 20 mod 21, not == 47, 83 mod 195, not == 467, 4343, 9887, 25448, 35978, 41522, 42647, 57083 mod 73815, not == 722, 83813, 206672, 239432, 322523, 1283843, 1519577, 1522553 mod 1551615, ..., not [[:w:Cube (algebra)|cube]]s
* 8×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 7, not == 20 mod 21, not == 83, 307 mod 455, not == 1266, 13593, 27292, 46353 mod 63973, ..., not [[:w:Cube (algebra)|cube]]s
* 9×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' &lt; 177744, not == 1 mod 5
* 9×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' not == 4 mod 5, not [[:w:Square number|square]]s
* 10×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 11, not == 32 mod 33 (references of this form: https://oeis.org/A088782)
* 10×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 3, not == 32 mod 33
* 11×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' not == 1 mod 3, not == 14 mod 15
* 11×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' not == 1 mod 5, not == 14 mod 15, not of the form 11×''m''&lt;sup&gt;2&lt;/sup&gt; with ''m'' == 2, 3 mod 5
* 12×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 13, not == 142 mod 143, not == 562, 828, 900, 1166 mod 1729, not == 597, 1143 mod 1885, not == 296, 901, 1759, 3090, 4553, 5521, 5807, 6016, 6984, 7094, 7270, 7380, 7479, 8447, 8557, 8733, 8843, 9910, 10020, 10196, 10306, 11483, 11769, 12737, 14200, 15531, 16994, 18457 mod 19019, not == 563, 1433, 13212, 15097, 19848, 20718, 32497, 34382, 39133, 51782, 53667, 58418, 58452, 60337, 60883, 71067, 72952, 77737, 79622, 80168, 94267, 97022, 98583, 98907, 113552, 116307, 117868, 118192, 131967, 132513, 132837, 134398, 151252, 151798, 152122, 153683, 170537, 171083, 172968, 177753, 179638, 189822, 190368, 192253, 192287, 197038, 198923, 211572, 213568, 216323, 218208, 229987, 232853, 235608, 237493, 249272 mod 250705, ...
* 12×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 11, not == 142 mod 143, not == 307, 1143 mod 1595, not == 901, 6016, 7479, 18457 mod 19019, ...
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+2 for all odd bases ''b'' &lt; 201446503145165177, not == 1 mod 3 (references of this form: https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−2 for all odd bases ''b'' (references of this form: https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A250200, https://oeis.org/A255707, https://oeis.org/A084714; or for prime bases ''b'': https://oeis.org/A292201)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+3 for all even bases ''b'' not divisible by 3
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−3 for all even bases ''b'' not divisible by 3
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+4 for all odd bases ''b'' not == 1 mod 5, not == 14 mod 15, not [[:w:Fourth power|fourth power]]s
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−4 for all odd bases ''b'' not == 1 mod 3, not == 4 mod 5, not [[:w:Square number|square]]s
* (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' (references of this form: http://www.noprimeleftbehind.net/Williams-primes-MP.htm, http://www.bitman.name/math/table/477, https://pzktupel.de/Primetables/TableWilliams2.php, https://oeis.org/A305531; or for prime bases ''b'': https://oeis.org/A087139)
* (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: https://harvey563.tripod.com/wills.txt, http://www.noprimeleftbehind.net/Williams-primes-MM.htm, http://www.bitman.name/math/table/484, https://pzktupel.de/Primetables/TableWilliams1.php; or for prime bases ''b'': https://oeis.org/A122396)
* (''b''+1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 3 (references of this form: http://www.noprimeleftbehind.net/Williams-primes-PP.htm, http://www.bitman.name/math/table/474, https://pzktupel.de/Primetables/TableWilliams4.php)
* (''b''+1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: http://www.noprimeleftbehind.net/Williams-primes-PM.htm, http://www.bitman.name/math/table/471, https://pzktupel.de/Primetables/TableWilliams3.php)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''−1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/795, https://pzktupel.de/Primetables/TableWilliams6.php, https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''−1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/792, https://pzktupel.de/Primetables/TableWilliams5.php, https://oeis.org/A113516, https://oeis.org/A343589; or for prime bases ''b'': https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/435)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''+1) for all bases ''b'' not == 1 mod 3 (references of this form: http://www.bitman.name/math/table/801, https://pzktupel.de/Primetables/TableWilliams8.php, https://oeis.org/A346149, https://oeis.org/A346154)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''+1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/798, https://pzktupel.de/Primetables/TableWilliams7.php, https://oeis.org/A178250)

By the [[:w:Prime number theorem|prime number theorem]], the [[:w:Probability|chance]] that a [[:w:Random number|random]] ''n''-digit base ''b'' number is prime is [[:w:Asymptotic analysis|approximately]] 1/''n'' (more accurately, the chance is approximately 1/(''n''×''ln''(''b'')), where ''ln'' is the [[:w:Natural logarithm|natural logarithm]]). If one conjectures the numbers ''x''{''y''}''z'' behave similarly (i.e. the numbers ''x''{''y''}''z'' is a [[:w:Pseudorandomness|pseudorandom sequence]]) you would expect [[:w:Harmonic_series (mathematics)|1/1 + 1/2 + 1/3 + 1/4 + ... = ∞]] primes of the form ''x''{''y''}''z'' (of course, this does not always happen, since some ''x''{''y''}''z'' families can be ruled out to contain no prime &gt; ''b'' (by covering congruence, algebraic factorization, or combine of them), but it is at least a reasonable conjecture in the absence of evidence to the contrary. Hence, the [[:w:Heuristic argument|heuristic argument]] suggests there are always infinitely many primes in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') if it cannot be ruled out to contain no prime or only contain finitely many primes, by covering congruence, algebraic factorization, or combine of them. However, some families ''x''{''y''}''z'' could not be proven to contain no primes &gt; ''b'' (by covering congruence, algebraic factorization, or combine of them) but no primes &gt; ''b'' could be found in the family, even after searching through numbers with over 100000 digits. In such a case, the only way to proceed is to [[:w:Primality test|test the primality]] of larger and larger numbers of such form and hope a prime is eventually discovered. e.g. the smallest (probable) prime in the family A{3}A in base ''b'' = 13 is A3&lt;sub&gt;592197&lt;/sub&gt;A, its algebraic form is (41×13&lt;sup&gt;592198&lt;/sup&gt;+27)/4, when written in decimal contains 659677 digits (it is only probable prime, i.e. not definitely prime, since technically, probable primality tests were used to show this (which have a ''very'' small chance of making an error, see https://t5k.org/notes/prp_prob.html) because all known primality tests run far too slowly to run on numbers of this size unless either [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] (or both) can be ≥ 1/3 factored).

The numbers in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') are of the form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) for some fixed ''a'', ''b'', ''c'' such that ''a'' ≥ 1, ''b'' ≥ 2 (''b'' is the base), ''c'' ≠ 0, ''gcd''(''a'',''c'') = 1, ''gcd''(''b'',''c'') = 1. Except in the [[:w:Special case|special case]] ''c'' = ±1 and ''gcd''(''a''+''c'',''b''−1) = 1 (the only case which [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] is [[:w:Triviality (mathematics)|trivially]] fully factored), when ''n'' is large the known [[:w:Primality test|primality test]]s for such a number are too inefficient to run (since they are [https://t5k.org/glossary/xpage/OrdinaryPrime.html ordinary primes]). In this case one must resort to a [[:w:Probabilistic algorithm|probable]] primality test such as a [[:w:Miller–Rabin primality test|Miller–Rabin primality test]] or a [[:w:Baillie–PSW primality test|Baillie–PSW primality test]], unless a divisor of the number can be found. Since we are testing many numbers in an [[:w:Exponential growth|exponential sequence]], it is possible to use a sieving process to find divisors rather than using [[:w:Trial division|trial division]].

To do this, we made use of Geoffrey Reynolds' ''srsieve'' software (download: https://pzktupel.de/Software/srsieve_1.1.4.7z). This program uses the [[:w:Baby-step giant-step|baby-step giant-step]] [[:w:Algorithm|algorithm]] to find all primes ''p'' which divide ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'' where ''p'' and ''n'' lie in a [[:w:Interval_(mathematics)|specified range]]. Since this program cannot handle the general case (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) &gt; 1 we only used it to sieve the sequence ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'' for primes ''p'' not dividing ''gcd''(''a''+''c'',''b''−1), and initialized the list of candidates to not include ''n'' for which there is some prime ''p'' dividing ''gcd''(''a''+''c'',''b''−1) for which ''p'' dividing (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1). The program had to be modified slightly to remove a check which would prevent it from running in the case when ''a'', ''b'', and ''c'' were all odd (since then 2 divides ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'', but 2 may not divide (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1)).

Once the numbers with small divisors had been removed, it remained to test the remaining numbers using a probable primality test. For this we used the software ''LLR'' by Jean Penné. (download: http://jpenne.free.fr/index2.html). Although undocumented, it is possible to run this program on numbers of the form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) &gt; 1, so this program required no modifications. A script was also written which allowed one to run ''srsieve'' while ''LLR'' was testing the remaining candidates, so that when a divisor was found by srsieve on a number which had not yet been tested by ''LLR'' it would be removed from the list of candidates.

For the primes &lt; 10&lt;sup&gt;25000&lt;/sup&gt; for the &quot;easy&quot; bases (bases ''b'' with ≤ 150 primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; (base ''b'' = 26 has 83 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 3 unsolved families, base ''b'' = 36 has 75 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 4 unsolved families, base ''b'' = 17 has 99 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 18 unsolved families, base ''b'' = 21 has 80 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 12 unsolved families, base ''b'' = 19 has 201 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 23 unsolved families), i.e. bases *b* = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36), we employed ''CM'' by Andreas Enge (download: https://www.multiprecision.org/cm/download.html), an elliptic curve primality proving implementation.

Currently, the final goal of the Athena problem project is finding the Athena set (i.e. finding all Athena primes) and proving that this set is exactly the Athena set (i.e. proving that these are all Athena primes (including the primality proving for the probable primes)) in all bases 2 ≤ ''b'' ≤ 36, i.e. solving all families in all bases 2 ≤ ''b'' ≤ 36. Solving all (unsolved) families in all bases 2 ≤ ''b'' ≤ 36 (and proving the primality of all probable primes in the sets of all bases 2 ≤ ''b'' ≤ 36) is not possible but we aim to solve many of them (and proving the primality of many of them), at least find a ''probable'' prime for many of them (since the smallest prime in a family may be too large (&gt; 10&lt;sup&gt;25000&lt;/sup&gt;) to be proved primality, unless its *N*−1 or/and *N*+1 can be ≥ 25% factored).

== Data ==

These are the results of the Athena problem in bases 2 ≤ ''b'' ≤ 36 (we stop at base 36 since this base is the maximum base for which it is possible to write the numbers with the [[:w:Symbol|symbol]]s 0, 1, 2, ..., 9 and A, B, C, ..., Z (i.e. the 10 [[:w:Arabic numerals|Arabic numerals]] and the 26 [[:w:Latin script|Latin letters]]): (some large Athena primes are only probable primes, i.e. not definitely primes, since they are too large to be [[:w:Elliptic curve primality|ECPP proved]] and [[:w:Pocklington primality test#Extensions and variants|neither ''N''−1 nor ''N''+1 can be ≥ 1/3 factored]], all of them pass the [[:w:Baillie–PSW primality test|Baillie–PSW primality test]] and the [[:w:Strong pseudoprime|strong primality test]] (i.e. the [[:w:Miller–Rabin primality test|Miller–Rabin primality test]]) with all prime bases ''p'' ≤ 61, however, all Athena primes &lt; 10&lt;sup&gt;25000&lt;/sup&gt; for bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 36 are definitely primes, most of them &gt; 10&lt;sup&gt;299&lt;/sup&gt; are proven primes with [[:w:Elliptic curve primality|ECPP proving]], others &gt; 10&lt;sup&gt;299&lt;/sup&gt; are proven primes with [[:w:Pocklington primality test#Extensions and variants|''N''−1 or ''N''+1 proving]])

The Athena primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 which are proven primes with ''N''−1 or ''N''+1 proving includes the Athena primes whose ''N''−1 or ''N''+1 is trivially fully factored:

* the 3176th Athena prime in base 13, 81010&lt;sub&gt;415&lt;/sub&gt;1, which equals 17746×13&lt;sup&gt;416&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003590431555, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003590431556&amp;open=ecm
* the 3177th Athena prime in base 13, 8110&lt;sub&gt;435&lt;/sub&gt;1, which equals 1366×13&lt;sup&gt;436&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000002373259109, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000002373259124&amp;open=ecm
* the 3188th Athena prime in base 13, 930&lt;sub&gt;1551&lt;/sub&gt;1, which equals 120×13&lt;sup&gt;1552&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961452, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961453&amp;open=ecm
* the 3191st Athena prime in base 13, 390&lt;sub&gt;6266&lt;/sub&gt;1, which equals 48×13&lt;sup&gt;6267&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961441, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961451&amp;open=ecm
* the 649th Athena prime in base 14, 34D&lt;sub&gt;708&lt;/sub&gt;, which equals 47×14&lt;sup&gt;708&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001540144903, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001540144907&amp;open=ecm
* the 650th Athena prime in base 14, 4D&lt;sub&gt;19698&lt;/sub&gt;, which equals 5×14&lt;sup&gt;19698&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000884560233, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000884560625&amp;open=ecm
* the 2335th Athena prime in base 16, 88F&lt;sub&gt;545&lt;/sub&gt;, which equals 137×16&lt;sup&gt;545&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000413679658, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000413877337&amp;open=ecm
* the 10317th Athena prime in base 17, 5A70&lt;sub&gt;274&lt;/sub&gt;1, which equals 1622×17&lt;sup&gt;275&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003782940709, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003782941930&amp;open=ecm
* the 10359th Athena prime in base 17, 9D0&lt;sub&gt;1067&lt;/sub&gt;1, which equals 166×17&lt;sup&gt;1068&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961369, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961370&amp;open=ecm
* the 10370th Athena prime in base 17, A0&lt;sub&gt;1355&lt;/sub&gt;1, which equals 10×17&lt;sup&gt;1356&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000034167087, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000271866825&amp;open=ecm
* the 10386th Athena prime in base 17, 530&lt;sub&gt;4867&lt;/sub&gt;1, which equals 88×17&lt;sup&gt;4868&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000762660735, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000762660737&amp;open=ecm
* the 10408th Athena prime in base 17, 570&lt;sub&gt;51310&lt;/sub&gt;1, which equals 92×17&lt;sup&gt;51311&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961389, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469616&amp;open=ecm
* the 10412th Athena prime in base 17, 970&lt;sub&gt;166047&lt;/sub&gt;1, which equals 160×17&lt;sup&gt;166048&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (&gt;10&lt;sup&gt;199999&lt;/sup&gt;) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817312&amp;open=ecm
* the 10413th Athena prime in base 17, F70&lt;sub&gt;186767&lt;/sub&gt;1, which equals 262×17&lt;sup&gt;186768&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (&gt;10&lt;sup&gt;199999&lt;/sup&gt;) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817317&amp;open=ecm
* the 3310th Athena prime in base 20, JCJ&lt;sub&gt;629&lt;/sub&gt;, which equals 393×20&lt;sup&gt;629&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001559454258, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001559454271&amp;open=ecm
* the 13373rd Athena prime in base 21, 5D0&lt;sub&gt;19848&lt;/sub&gt;1, which equals 118×21&lt;sup&gt;19849&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000777265872, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469310&amp;open=ecm
* the 3408th Athena prime in base 24, 88N&lt;sub&gt;5951&lt;/sub&gt;, which equals 201×24&lt;sup&gt;5951&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003593275880, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000003593373246&amp;open=ecm
* the 25509th Athena prime in base 28, EB0&lt;sub&gt;405&lt;/sub&gt;1, which equals 403×28&lt;sup&gt;406&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001534442374, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000001534442380&amp;open=ecm
* the 2616th Athena prime in base 30, C0&lt;sub&gt;1022&lt;/sub&gt;1, which equals 12×30&lt;sup&gt;1023&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000785448736, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785448737&amp;open=ecm
* the 2619th Athena prime in base 30, OT&lt;sub&gt;34205&lt;/sub&gt;, which equals 25×30&lt;sup&gt;34205&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000800812865, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000819405041&amp;open=ecm
* the 35237th Athena prime in base 36, P8Z&lt;sub&gt;390&lt;/sub&gt;, which equals 909×36&lt;sup&gt;390&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000764100228, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000764100231&amp;open=ecm

and the Athena primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 whose ''N''−1 or ''N''+1 is ≥ 1/3 factored: (''R''&lt;sub&gt;''n''&lt;/sub&gt;(''b'') means the [[:w:Repunit|repunit]] in base ''b'' with length ''n''), i.e. ''R''&lt;sub&gt;''n''&lt;/sub&gt;(''b'') = (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1), &quot;''S''&lt;sub&gt;''n''&lt;/sub&gt;(''b'')&quot; means ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)

* the 3168th Athena prime in base 13, 9&lt;sub&gt;308&lt;/sub&gt;1, ''N''−1 is 117×''R''&lt;sub&gt;308&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;308&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;308&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=308&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;308&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=308&amp;c0=-&amp;EN=&amp;LM=
* the 3179th Athena prime in base 13, B&lt;sub&gt;563&lt;/sub&gt;C, ''N''−1 is 11×''R''&lt;sub&gt;564&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;564&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;564&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=564&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;564&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=564&amp;c0=-&amp;EN=&amp;LM=
* the 3180th Athena prime in base 13, 1B&lt;sub&gt;576&lt;/sub&gt;, ''N''−1 is 23×''R''&lt;sub&gt;576&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;576&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;576&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=576&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;576&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=576&amp;c0=-&amp;EN=&amp;LM=
* the 10320th Athena prime in base 17, 9&lt;sub&gt;292&lt;/sub&gt;1, ''N''−1 is 153×''R''&lt;sub&gt;292&lt;/sub&gt;(17), thus factor ''N''−1 is equivalent to factor the Cunningham number 17&lt;sup&gt;292&lt;/sup&gt;−1, and for the algebraic factors of 17&lt;sup&gt;292&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=17&amp;Exp=292&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 17&lt;sup&gt;292&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=17&amp;Exp=292&amp;c0=-&amp;EN=&amp;LM=
* the 13304th Athena prime in base 21, 7&lt;sub&gt;230&lt;/sub&gt;1, ''N''−1 is 147×''R''&lt;sub&gt;230&lt;/sub&gt;(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21&lt;sup&gt;230&lt;/sup&gt;−1, and for the algebraic factors of 21&lt;sup&gt;230&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&amp;Exp=230&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 21&lt;sup&gt;230&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&amp;Exp=230&amp;c0=-&amp;EN=&amp;LM=
* the 13355th Athena prime in base 21, 3&lt;sub&gt;1063&lt;/sub&gt;2, ''N''+1 is 3×''R''&lt;sub&gt;1064&lt;/sub&gt;(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21&lt;sup&gt;1064&lt;/sup&gt;−1, and for the algebraic factors of 21&lt;sup&gt;1064&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&amp;Exp=1064&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 21&lt;sup&gt;1064&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&amp;Exp=1064&amp;c0=-&amp;EN=&amp;LM=
* the 25199th Athena prime in base 26, 9K&lt;sub&gt;343&lt;/sub&gt;AP, ''N''+1 is 6370×''R''&lt;sub&gt;344&lt;/sub&gt;(26), thus factor ''N''+1 is equivalent to factor the Cunningham number 26&lt;sup&gt;344&lt;/sup&gt;−1, and for the algebraic factors of 26&lt;sup&gt;344&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&amp;Exp=344&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 26&lt;sup&gt;344&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&amp;Exp=344&amp;c0=-&amp;EN=&amp;LM=
* the 25200th Athena prime in base 26, 8&lt;sub&gt;354&lt;/sub&gt;1, ''N''−1 is 208×''R''&lt;sub&gt;354&lt;/sub&gt;(26), thus factor ''N''−1 is equivalent to factor the Cunningham number 26&lt;sup&gt;354&lt;/sup&gt;−1, and for the algebraic factors of 26&lt;sup&gt;354&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&amp;Exp=354&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 26&lt;sup&gt;354&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&amp;Exp=354&amp;c0=-&amp;EN=&amp;LM=

All numbers are written in base ''b'', [[:w:Senary#Base 36 as senary compression|using A to Z to represent digit values 10 to 35]], &quot;{}&quot; means repeating, e.g. family 12{3}45 means the sequence {1245, 12345, 123345, 1233345, 12333345, 123333345, ...} (where the members are expressed as base ''b'' strings), subscripts are used to indicate repetitions of digits, e.g. 123&lt;sub&gt;4&lt;/sub&gt;567 means 123333567 (all subscripts are written in decimal).

Base 2: 1 Athena prime (the largest of which has 2 digits (it is 11, and its value is 3 in decimal)): {11}

Base 3: 3 Athena primes (the largest of which has 3 digits (it is 111, and its value is 13 in decimal)): {12, 21, 111}

Base 4: 5 Athena primes (the largest of which has 3 digits (it is 221, and its value is 41 in decimal)): {11, 13, 23, 31, 221}

Base 5: 22 Athena primes (the largest of which has 96 digits (it is 10&lt;sub&gt;93&lt;/sub&gt;13, and its algebraic form is 5&lt;sup&gt;95&lt;/sup&gt;+8)): {12, 21, 23, 32, 34, 43, 104, 111, 131, 133, 313, 401, 414, 3101, 10103, 14444, 30301, 33001, 33331, 44441, 300031, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013}

Base 6: 11 Athena primes (the largest of which has 5 digits (it is 40041, and its value is 5209 in decimal)): {11, 15, 21, 25, 31, 35, 45, 51, 4401, 4441, 40041}

Base 7: 71 Athena primes (the largest of which has 17 digits (it is 3&lt;sub&gt;16&lt;/sub&gt;1, and its algebraic form is (7&lt;sup&gt;17&lt;/sup&gt;−5)/2)): {14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 113, 115, 131, 133, 155, 212, 221, 304, 313, 335, 344, 346, 364, 445, 515, 533, 535, 544, 551, 553, 1022, 1051, 1112, 1202, 1211, 1222, 2111, 3031, 3055, 3334, 3503, 3505, 3545, 4504, 4555, 5011, 5455, 5545, 5554, 6034, 6634, 11111, 11201, 30011, 30101, 31001, 31111, 33001, 33311, 35555, 40054, 100121, 150001, 300053, 351101, 531101, 1100021, 33333301, 5100000001, 33333333333333331}

Base 8: 75 Athena primes (the largest of which has 221 digits (it is 4&lt;sub&gt;220&lt;/sub&gt;7, and its algebraic form is (4×8&lt;sup&gt;221&lt;/sup&gt;+17)/7)): {13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 107, 111, 117, 141, 147, 161, 177, 225, 255, 301, 343, 361, 401, 407, 417, 431, 433, 463, 467, 471, 631, 643, 661, 667, 701, 711, 717, 747, 767, 3331, 3411, 4043, 4443, 4611, 5205, 6007, 6101, 6441, 6477, 6707, 6777, 7461, 7641, 47777, 60171, 60411, 60741, 444641, 500025, 505525, 3344441, 4444477, 5500525, 5550525, 55555025, 444444441, 744444441, 77774444441, 7777777777771, 555555555555525, 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447}

Base 9: 151 Athena primes (the largest of which has 1161 digits (it is 30&lt;sub&gt;1158&lt;/sub&gt;11, and its algebraic form is 3×9&lt;sup&gt;1160&lt;/sup&gt;+10)): {12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 117, 131, 135, 151, 155, 175, 177, 238, 272, 308, 315, 331, 337, 355, 371, 375, 377, 438, 504, 515, 517, 531, 537, 557, 564, 601, 638, 661, 702, 711, 722, 735, 737, 751, 755, 757, 771, 805, 838, 1011, 1015, 1101, 1701, 2027, 2207, 3017, 3057, 3101, 3501, 3561, 3611, 3688, 3868, 5035, 5051, 5071, 5101, 5501, 5554, 5705, 5707, 7017, 7075, 7105, 7301, 8535, 8544, 8555, 8854, 20777, 22227, 22777, 30161, 33388, 50161, 50611, 53335, 55111, 55535, 55551, 57061, 57775, 70631, 71007, 77207, 100037, 100071, 100761, 105007, 270707, 301111, 305111, 333035, 333385, 333835, 338885, 350007, 500075, 530005, 555611, 631111, 720707, 2770007, 3030335, 7776662, 30300005, 30333335, 38333335, 51116111, 70000361, 300030005, 300033305, 351111111, 1300000007, 5161111111, 8333333335, 300000000035, 311111111161, 544444444444, 2000000000007, 5700000000001, 7270000000007, 88888888833335, 100000000000507, 5111111111111161, 7277777777777777707, 8888888888888888888335, 30000000000000000000051, 1000000000000000000000000057, 56111111111111111111111111111111111111, 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666662, 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777707, 300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011}

Base 10: 77 Athena primes (the largest of which has 31 digits (it is 50&lt;sub&gt;28&lt;/sub&gt;27, and its algebraic form is 5×10&lt;sup&gt;30&lt;/sup&gt;+27)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}

Base 11: 1068 Athena (probable) primes (including 1 unproven probable prime: 57&lt;sub&gt;62668&lt;/sub&gt;), the largest of which has 62669 digits (it is 57&lt;sub&gt;62668&lt;/sub&gt;, and its algebraic form is (57×11&lt;sup&gt;62668&lt;/sup&gt;−7)/10), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel11 Data of Athena (probable) primes base 11]

Base 12: 106 Athena primes (the largest of which has 42 digits (it is 40&lt;sub&gt;39&lt;/sub&gt;77, and its algebraic form is 4×12&lt;sup&gt;41&lt;/sup&gt;+91)): {11, 15, 17, 1B, 25, 27, 31, 35, 37, 3B, 45, 4B, 51, 57, 5B, 61, 67, 6B, 75, 81, 85, 87, 8B, 91, 95, A7, AB, B5, B7, 221, 241, 2A1, 2B1, 2BB, 401, 421, 447, 471, 497, 565, 655, 665, 701, 70B, 721, 747, 771, 77B, 797, 7A1, 7BB, 907, 90B, 9BB, A41, B21, B2B, 2001, 200B, 202B, 222B, 229B, 292B, 299B, 4441, 4707, 4777, 6A05, 6AA5, 729B, 7441, 7B41, 929B, 9777, 992B, 9947, 997B, 9997, A0A1, A201, A605, A6A5, AA65, B001, B0B1, BB01, BB41, 600A5, 7999B, 9999B, AAAA1, B04A1, B0B9B, BAA01, BAAA1, BB09B, BBBB1, 44AAA1, A00065, BBBAA1, AAA0001, B00099B, AA000001, BBBBBB99B, B0000000000000000000000000009B, 400000000000000000000000000000000000000077}

Base 13: 3197 Athena (probable) primes (including 4 unproven probable primes: C5&lt;sub&gt;23755&lt;/sub&gt;C, 80&lt;sub&gt;32017&lt;/sub&gt;111, 95&lt;sub&gt;197420&lt;/sub&gt;, A3&lt;sub&gt;592197&lt;/sub&gt;A), the largest of which has 592199 digits (it is A3&lt;sub&gt;592197&lt;/sub&gt;A, and its algebraic form is (41×13&lt;sup&gt;592198&lt;/sup&gt;+27)/4), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel13 Data of Athena (probable) primes base 13]

Base 14: 650 Athena primes, the largest of which has 19699 digits (it is 4D&lt;sub&gt;19698&lt;/sub&gt;, and its algebraic form is 5×14&lt;sup&gt;19698&lt;/sup&gt;−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel14 Data of Athena primes base 14]

Base 15: 1284 Athena primes, the largest of which has 157 digits (it is 7&lt;sub&gt;155&lt;/sub&gt;97, and its algebraic form is (15&lt;sup&gt;157&lt;/sup&gt;+59)/2), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel15 Data of Athena primes base 15]

Base 16: 2347 Athena (probable) primes (including 3 unproven probable primes: DB&lt;sub&gt;32234&lt;/sub&gt;, 4&lt;sub&gt;72785&lt;/sub&gt;DD, 3&lt;sub&gt;116137&lt;/sub&gt;AF), the largest of which has 116139 digits (it is 3&lt;sub&gt;116137&lt;/sub&gt;AF, and its algebraic form is (16&lt;sup&gt;116139&lt;/sup&gt;+619)/5), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel16 Data of Athena (probable) primes base 16]

Base 17: 10415 known Athena (probable) primes (including many unproven probable primes) and 12 unsolved families (1{7}, 1F{0}7, 4{7}A, 70F{0}D, 8{B}9, 9{5}9, A{D}F, B{0}B3, {B}E9, {B}EE, F1{9}, FD0{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel17 Data of known Athena (probable) primes base 17]

Base 18: 549 Athena primes, the largest of which has 6271 digits (it is C0&lt;sub&gt;6268&lt;/sub&gt;C5, and its algebraic form is 12×18&lt;sup&gt;6270&lt;/sup&gt;+221), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel18 Data of Athena primes base 18]

Base 19: 31417 known Athena (probable) primes (including many unproven probable primes) and 17 unsolved families (4B5{0}H, {5}3, 5{H}05, 5{H}0H, 5{H}5, 66{B}, 71{0}177, 7AF{0}H, 97{0}3, C{H}C, EE1{6}, F{7}5, F{B}G, F{D}F, H0F{0}7A, HB{0}5B5, II{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel19 Data of known Athena (probable) primes base 19]

Base 20: 3314 Athena primes, the largest of which has 6271 digits (it is G0&lt;sub&gt;6269&lt;/sub&gt;D, and its algebraic form is 16×20&lt;sup&gt;6270&lt;/sup&gt;+13), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel20 Data of Athena primes base 20]

Base 21: 13386 known Athena (probable) primes (including many unproven probable primes) and 8 unsolved families (5{0}DJ, {9}D, B3{0}EB, B{H}6H, C{F}0K, {F}35, G{0}FK, H{0}7771, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel21 Data of known Athena (probable) primes base 21]

Base 22: 8003 Athena (probable) primes (including 1 unproven probable prime: BK&lt;sub&gt;22001&lt;/sub&gt;5), the largest of which has 22003 digits (it is BK&lt;sub&gt;22001&lt;/sub&gt;5, and its algebraic form is (251×22&lt;sup&gt;22002&lt;/sup&gt;−335)/21), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel22 Data of Athena (probable) primes base 22]

Base 23: 65178 known Athena (probable) primes (including many unproven probable primes) and 87 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel23 Data of known Athena (probable) primes base 23] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left23 Data of unsolved families for Athena problem base 23]

Base 24: 3409 Athena primes, the largest of which has 8134 digits (it is N00N&lt;sub&gt;8129&lt;/sub&gt;LN, and its algebraic form is 13249×24&lt;sup&gt;8131&lt;/sup&gt;−49), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel24 Data of Athena primes base 24]

Base 25: 133639 known Athena (probable) primes (including many unproven probable primes) and 85 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel25 Data of known Athena (probable) primes base 25] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left25 Data of unsolved families for Athena problem base 25]

Base 26: 25256 known Athena (probable) primes (including 7 unproven probable primes: 5&lt;sub&gt;19391&lt;/sub&gt;6F, 7&lt;sub&gt;20279&lt;/sub&gt;OL, LD0&lt;sub&gt;20975&lt;/sub&gt;7, 6K&lt;sub&gt;23300&lt;/sub&gt;5, J0&lt;sub&gt;44303&lt;/sub&gt;KCB, M0&lt;sub&gt;61186&lt;/sub&gt;2BB, 85M&lt;sub&gt;197060&lt;/sub&gt;B) and 3 unsolved families ({A}6F, {H}MH, {I}GL, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel26 Data of known Athena (probable) primes base 26]

Base 27: 102852 known Athena (probable) primes (including many unproven probable primes) and 44 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel27 Data of known Athena (probable) primes base 27] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left27 Data of unsolved families for Athena problem base 27]

Base 28: 25528 known Athena (probable) primes (including 3 unproven probable primes: N6&lt;sub&gt;24051&lt;/sub&gt;LR, 5OA&lt;sub&gt;31238&lt;/sub&gt;F, O4O&lt;sub&gt;94535&lt;/sub&gt;9) and 1 unsolved family (O{A}F, no primes or probable primes with length ≤ 900000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel28 Data of known Athena (probable) primes base 28]

Base 29: 355242 known Athena (probable) primes (including many unproven probable primes) and 125 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel29 Data of known Athena (probable) primes base 29] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left29 Data of unsolved families for Athena problem base 29]

Base 30: 2619 Athena (probable) primes (including 1 unproven probable prime: I0&lt;sub&gt;24608&lt;/sub&gt;D), the largest of which has 34206 digits (it is OT&lt;sub&gt;34205&lt;/sub&gt;, and its algebraic form is 25×30&lt;sup&gt;34205&lt;/sup&gt;−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel30 Data of Athena (probable) primes base 30]

Base 31: 569323 known Athena (probable) primes (including many unproven probable primes) and 77 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel31 Data of known Athena (probable) primes base 31] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left31 Data of unsolved families for Athena problem base 31]

Base 32: 168882 known Athena (probable) primes (including many unproven probable primes) and 120 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel32 Data of known Athena (probable) primes base 32] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left32 Data of unsolved families for Athena problem base 32]

Base 33: 280012 known Athena (probable) primes (including many unproven probable primes) and 81 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel33 Data of known Athena (probable) primes base 33] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left33 Data of unsolved families for Athena problem base 33]

Base 34: 184785 known Athena (probable) primes (including many unproven probable primes) and 47 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel34 Data of known Athena (probable) primes base 34] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left34 Data of unsolved families for Athena problem base 34]

Base 35: 720002 known Athena (probable) primes (including many unproven probable primes) and 60 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel35 Data of known Athena (probable) primes base 35] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left35 Data of unsolved families for Athena problem base 35]

Base 36: 35286 known Athena (probable) primes (including 3 unproven probable primes: 7K&lt;sub&gt;26567&lt;/sub&gt;Z, S0&lt;sub&gt;75007&lt;/sub&gt;8H, P&lt;sub&gt;81993&lt;/sub&gt;SZ) and 4 unsolved families (B{0}EUV, HM{0}N, N{0}YYN, O{L}Z, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel36 Data of known Athena (probable) primes base 36]

== Condensed table for bases 2 ≤ ''b'' ≤ 36 ==

{|class=&quot;wikitable&quot;
||''b''||number of Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||base-''b'' form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' (write &quot;''d''&lt;sub&gt;''n''&lt;/sub&gt;&quot; if there are 5 or more (''n'') consecutive same digits ''d'')||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' in decimal||algebraic ((''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1)) form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||''factordb'' entry of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' written in base ''b'' (use lower case letters instead of upper case letters)||number of unsolved families in the Athena problem in base ''b'' (all of these left families are linear families)||searching limit of length for the unsolved families in the Athena problem in base ''b'' (if there are different searching limits for the unsolved families in the Athena problem in base ''b'', choose the lowest searching limit)||
|-
||2||1||11||2||1||3||http://factordb.com/index.php?id=3&amp;open=ecm||http://factordb.com/index.php?showid=3&amp;base=2||0||–||
|-
||3||3||111&lt;br&gt;21&lt;br&gt;12||3&lt;br&gt;2&lt;br&gt;2||2&lt;br&gt;1&lt;br&gt;1||13&lt;br&gt;7&lt;br&gt;5||http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=7&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=5&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=13&amp;base=3&lt;br&gt;http://factordb.com/index.php?showid=7&amp;base=3&lt;br&gt;http://factordb.com/index.php?showid=5&amp;base=3&lt;nowiki/&gt;||0||–||
|-
||4||5||221&lt;br&gt;31&lt;br&gt;23&lt;br&gt;13&lt;br&gt;11||3&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;1&lt;br&gt;1||41&lt;br&gt;13&lt;br&gt;11&lt;br&gt;7&lt;br&gt;5||http://factordb.com/index.php?id=41&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=11&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=7&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=5&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=41&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=13&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=11&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=7&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=5&amp;base=4&lt;nowiki/&gt;||0||–||
|-
||5||22||10&lt;sub&gt;93&lt;/sub&gt;13&lt;br&gt;300031&lt;br&gt;44441&lt;br&gt;33331&lt;br&gt;33001&lt;br&gt;30301&lt;br&gt;14444&lt;br&gt;10103&lt;br&gt;3101&lt;br&gt;414||96&lt;br&gt;6&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;4&lt;br&gt;3||67&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;3&lt;br&gt;3&lt;br&gt;3||5&lt;sup&gt;95&lt;/sup&gt;+8&lt;br&gt;9391&lt;br&gt;3121&lt;br&gt;2341&lt;br&gt;2251&lt;br&gt;1951&lt;br&gt;1249&lt;br&gt;653&lt;br&gt;401&lt;br&gt;109||http://factordb.com/index.php?id=1100000000034686071&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=9391&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=3121&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2341&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2251&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1951&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1249&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=653&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=401&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=109&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000000034686071&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=9391&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=3121&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=2341&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=2251&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=1951&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=1249&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=653&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=401&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=109&amp;base=5&lt;nowiki/&gt;||0||–||
|-
||6||11||40041&lt;br&gt;4441&lt;br&gt;4401&lt;br&gt;51&lt;br&gt;45&lt;br&gt;35&lt;br&gt;31&lt;br&gt;25&lt;br&gt;21&lt;br&gt;15||5&lt;br&gt;4&lt;br&gt;4&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||5209&lt;br&gt;1033&lt;br&gt;1009&lt;br&gt;31&lt;br&gt;29&lt;br&gt;23&lt;br&gt;19&lt;br&gt;17&lt;br&gt;13&lt;br&gt;11||http://factordb.com/index.php?id=5209&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1033&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1009&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=31&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=29&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=23&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=19&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=17&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=11&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=5209&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=1033&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=1009&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=31&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=29&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=23&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=19&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=17&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=13&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=11&amp;base=6&lt;nowiki/&gt;||0||–||
|-
||7||71||3&lt;sub&gt;16&lt;/sub&gt;1&lt;br&gt;510&lt;sub&gt;7&lt;/sub&gt;1&lt;br&gt;3&lt;sub&gt;6&lt;/sub&gt;01&lt;br&gt;1100021&lt;br&gt;531101&lt;br&gt;351101&lt;br&gt;300053&lt;br&gt;150001&lt;br&gt;100121&lt;br&gt;40054||17&lt;br&gt;10&lt;br&gt;8&lt;br&gt;7&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;5||15&lt;br&gt;9&lt;br&gt;7&lt;br&gt;6&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;4||(7&lt;sup&gt;17&lt;/sup&gt;−5)/2&lt;br&gt;36×7&lt;sup&gt;8&lt;/sup&gt;+1&lt;br&gt;(7&lt;sup&gt;8&lt;/sup&gt;−47)/2&lt;br&gt;134471&lt;br&gt;91631&lt;br&gt;62819&lt;br&gt;50459&lt;br&gt;28813&lt;br&gt;16871&lt;br&gt;9643||http://factordb.com/index.php?id=116315256993601&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=207532837&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2882377&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=134471&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=91631&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=62819&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=50459&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=28813&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=16871&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=9643&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=116315256993601&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=207532837&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=2882377&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=134471&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=91631&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=62819&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=50459&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=28813&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=16871&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=9643&amp;base=7&lt;nowiki/&gt;||0||–||
|-
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||33||280012~280093||DP&lt;sub&gt;95093&lt;/sub&gt;M5&lt;br&gt;HJ0&lt;sub&gt;94295&lt;/sub&gt;J&lt;br&gt;90&lt;sub&gt;93597&lt;/sub&gt;Q&lt;br&gt;9F0&lt;sub&gt;93157&lt;/sub&gt;N&lt;br&gt;7&lt;sub&gt;89449&lt;/sub&gt;333H&lt;br&gt;K3&lt;sub&gt;80751&lt;/sub&gt;6K&lt;br&gt;D&lt;sub&gt;80107&lt;/sub&gt;9UD&lt;br&gt;VFU&lt;sub&gt;72204&lt;/sub&gt;FK&lt;br&gt;J&lt;sub&gt;68715&lt;/sub&gt;2BJ&lt;br&gt;DF0&lt;sub&gt;68367&lt;/sub&gt;J||95096&lt;br&gt;94298&lt;br&gt;93599&lt;br&gt;93160&lt;br&gt;89453&lt;br&gt;80754&lt;br&gt;80110&lt;br&gt;72208&lt;br&gt;68718&lt;br&gt;68370||144405&lt;br&gt;143193&lt;br&gt;142131&lt;br&gt;141465&lt;br&gt;135835&lt;br&gt;122626&lt;br&gt;121648&lt;br&gt;109649&lt;br&gt;104350&lt;br&gt;103821||(441×33&lt;sup&gt;95095&lt;/sup&gt;−3833)/32&lt;br&gt;580×33&lt;sup&gt;94296&lt;/sup&gt;+19&lt;br&gt;9×33&lt;sup&gt;93598&lt;/sup&gt;+26&lt;br&gt;312×33&lt;sup&gt;93158&lt;/sup&gt;+23&lt;br&gt;(7×33&lt;sup&gt;89453&lt;/sup&gt;−4743239)/32&lt;br&gt;(643×33&lt;sup&gt;80753&lt;/sup&gt;+3709)/32&lt;br&gt;(13×33&lt;sup&gt;80110&lt;/sup&gt;−121453)/32&lt;br&gt;(16623×33&lt;sup&gt;72206&lt;/sup&gt;−8095)/16&lt;br&gt;(19×33&lt;sup&gt;68718&lt;/sup&gt;−600883)/32&lt;br&gt;444×33&lt;sup&gt;68368&lt;/sup&gt;+19||http://factordb.com/index.php?id=1100000005652348775&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652362811&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652375073&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652389776&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652430746&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652446200&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652461592&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614764298&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614770536&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614784274&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000005652348775&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652362811&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652375073&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652389776&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652430746&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652446200&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652461592&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614764298&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614770536&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614784274&amp;base=33&lt;nowiki/&gt;||81||100000||
|-
||34||184785~184832||GFGC&lt;sub&gt;99996&lt;/sub&gt;5&lt;br&gt;90&lt;sub&gt;97950&lt;/sub&gt;FJ&lt;br&gt;NM0&lt;sub&gt;85218&lt;/sub&gt;KX&lt;br&gt;F&lt;sub&gt;83189&lt;/sub&gt;H2HP&lt;br&gt;P&lt;sub&gt;79441&lt;/sub&gt;444P&lt;br&gt;6&lt;sub&gt;77027&lt;/sub&gt;8X&lt;br&gt;XQIQ&lt;sub&gt;72241&lt;/sub&gt;D&lt;br&gt;T&lt;sub&gt;66530&lt;/sub&gt;IF&lt;br&gt;4&lt;sub&gt;66152&lt;/sub&gt;B&lt;br&gt;2EEC&lt;sub&gt;66039&lt;/sub&gt;7||100000&lt;br&gt;97953&lt;br&gt;85222&lt;br&gt;83193&lt;br&gt;79445&lt;br&gt;77029&lt;br&gt;72245&lt;br&gt;66532&lt;br&gt;66153&lt;br&gt;66043||153148&lt;br&gt;150013&lt;br&gt;130516&lt;br&gt;127408&lt;br&gt;121669&lt;br&gt;117968&lt;br&gt;110642&lt;br&gt;101893&lt;br&gt;101312&lt;br&gt;101143||(209246×34&lt;sup&gt;99997&lt;/sup&gt;−81)/11&lt;br&gt;9×34&lt;sup&gt;97952&lt;/sup&gt;+529&lt;br&gt;804×34&lt;sup&gt;85220&lt;/sup&gt;+713&lt;br&gt;(5×34&lt;sup&gt;83193&lt;/sup&gt;+700233)/11&lt;br&gt;(25×34&lt;sup&gt;79445&lt;/sup&gt;−28062367)/33&lt;br&gt;(2×34&lt;sup&gt;77029&lt;/sup&gt;+1043)/11&lt;br&gt;(1288676×34&lt;sup&gt;72242&lt;/sup&gt;−455)/33&lt;br&gt;(29×34&lt;sup&gt;66532&lt;/sup&gt;−12833)/33&lt;br&gt;(4×34&lt;sup&gt;66153&lt;/sup&gt;+227)/33&lt;br&gt;(30826×34&lt;sup&gt;66040&lt;/sup&gt;−59)/11||http://factordb.com/index.php?id=1100000004702891268&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702894713&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702900996&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702910376&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702913746&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702918600&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399656529&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399657696&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399658651&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399659716&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000004702891268&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702894713&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702900996&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702910376&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702913746&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702918600&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399656529&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399657696&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399658651&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399659716&amp;base=34&lt;nowiki/&gt;||47||100000||
|-
||35||720002~720062||N0N&lt;sub&gt;99971&lt;/sub&gt;9&lt;br&gt;V0&lt;sub&gt;83669&lt;/sub&gt;E73&lt;br&gt;N&lt;sub&gt;81563&lt;/sub&gt;K7N&lt;br&gt;BJ0&lt;sub&gt;81279&lt;/sub&gt;N&lt;br&gt;J0&lt;sub&gt;80062&lt;/sub&gt;FUH&lt;br&gt;43V&lt;sub&gt;79754&lt;/sub&gt;&lt;br&gt;9&lt;sub&gt;76600&lt;/sub&gt;K3&lt;br&gt;LB&lt;sub&gt;71366&lt;/sub&gt;PB&lt;br&gt;Q&lt;sub&gt;64150&lt;/sub&gt;H&lt;br&gt;50&lt;sub&gt;63397&lt;/sub&gt;5R||99974&lt;br&gt;83673&lt;br&gt;81566&lt;br&gt;81282&lt;br&gt;80066&lt;br&gt;79756&lt;br&gt;76602&lt;br&gt;71369&lt;br&gt;64151&lt;br&gt;63400||154367&lt;br&gt;129197&lt;br&gt;125944&lt;br&gt;125505&lt;br&gt;123628&lt;br&gt;123148&lt;br&gt;118279&lt;br&gt;110199&lt;br&gt;99054&lt;br&gt;97894||(27393×35&lt;sup&gt;99972&lt;/sup&gt;−499)/34&lt;br&gt;31×35&lt;sup&gt;83672&lt;/sup&gt;+17398&lt;br&gt;(23×35&lt;sup&gt;81566&lt;/sup&gt;−144013)/34&lt;br&gt;404×35&lt;sup&gt;81280&lt;/sup&gt;+23&lt;br&gt;19×35&lt;sup&gt;80065&lt;/sup&gt;+19442&lt;br&gt;(4893×35&lt;sup&gt;79754&lt;/sup&gt;−31)/34&lt;br&gt;(9×35&lt;sup&gt;76602&lt;/sup&gt;+12877)/34&lt;br&gt;(725×35&lt;sup&gt;71368&lt;/sup&gt;+16649)/34&lt;br&gt;(13×35&lt;sup&gt;64151&lt;/sup&gt;−166)/17&lt;br&gt;5×35&lt;sup&gt;63399&lt;/sup&gt;+202||http://factordb.com/index.php?id=1100000008248342445&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248353306&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248375642&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248397018&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248412468&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248418540&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248423670&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192119974&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192126630&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192129294&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000008248342445&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248353306&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248375642&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248397018&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248412468&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248418540&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248423670&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192119974&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192126630&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192129294&amp;base=35&lt;nowiki/&gt;||60||100000||
|-
||36||35286~35290||P&lt;sub&gt;81993&lt;/sub&gt;SZ&lt;br&gt;S0&lt;sub&gt;75007&lt;/sub&gt;8H&lt;br&gt;7K&lt;sub&gt;26567&lt;/sub&gt;Z&lt;br&gt;J&lt;sub&gt;10117&lt;/sub&gt;LJ&lt;br&gt;VL0&lt;sub&gt;7258&lt;/sub&gt;J&lt;br&gt;EO0&lt;sub&gt;6177&lt;/sub&gt;V&lt;br&gt;FZ&lt;sub&gt;5777&lt;/sub&gt;3P&lt;br&gt;T09&lt;sub&gt;4618&lt;/sub&gt;1&lt;br&gt;RY&lt;sub&gt;4562&lt;/sub&gt;H&lt;br&gt;OZ&lt;sub&gt;3932&lt;/sub&gt;AZ||81995&lt;br&gt;75010&lt;br&gt;26569&lt;br&gt;10119&lt;br&gt;7261&lt;br&gt;6180&lt;br&gt;5780&lt;br&gt;4621&lt;br&gt;4564&lt;br&gt;3935||127609&lt;br&gt;116739&lt;br&gt;41349&lt;br&gt;15748&lt;br&gt;11301&lt;br&gt;9618&lt;br&gt;8996&lt;br&gt;7192&lt;br&gt;7103&lt;br&gt;6124||(5×36&lt;sup&gt;81995&lt;/sup&gt;+821)/7&lt;br&gt;28×36&lt;sup&gt;75009&lt;/sup&gt;+305&lt;br&gt;(53×36&lt;sup&gt;26568&lt;/sup&gt;+101)/7&lt;br&gt;(19×36&lt;sup&gt;10119&lt;/sup&gt;+2501)/35&lt;br&gt;1137×36&lt;sup&gt;7259&lt;/sup&gt;+19&lt;br&gt;528×36&lt;sup&gt;6178&lt;/sup&gt;+31&lt;br&gt;16×36&lt;sup&gt;5779&lt;/sup&gt;−1163&lt;br&gt;(36549×36&lt;sup&gt;4619&lt;/sup&gt;−289)/35&lt;br&gt;(979×36&lt;sup&gt;4563&lt;/sup&gt;−629)/35&lt;br&gt;25×36&lt;sup&gt;3934&lt;/sup&gt;−901||http://factordb.com/index.php?id=1100000002394962083&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004020085177&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003896952461&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362491&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362489&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362488&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362487&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362486&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362485&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000000840634476&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000002394962083&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000004020085177&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003896952461&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362491&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362489&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362488&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362487&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362486&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362485&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000000840634476&amp;base=36&lt;nowiki/&gt;||4||200000||
|}

== The fully proof of Athena problem in decimal (base ''b'' = 10) ==

'''Bold''' for the Athena primes, ''x'' ◁ ''y'' means ''x'' is a subsequence of ''y''.

Assume ''p'' is a prime &gt; 10, and the last digit of ''p'' must lie in {1,3,7,9}.

Case 1: ''p'' ends with 1.

In this case we can write ''p'' = ''x''1. If ''x'' contains 1, 3, 4, 6, or 7, then (respectively) '''11''' ◁ ''p'', '''31''' ◁ ''p'', '''41''' ◁ ''p'', '''61''' ◁ ''p'', or '''71''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 8, or 9.

Case 1.1: ''p'' begins with 2.

In this case we can write ''p'' = 2''y''1. If 5 ◁ ''y'', then '''251''' ◁ ''p''. If 8 ◁ ''y'', then '''281''' ◁ ''p''. If 9 ◁ ''y'', then 29 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2.

If 22 ◁ ''y'', then '''2221''' ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's.

If ''y'' contains no 2's, then ''p'' ∈ 2{0}1. But then, since the sum of the digits of ''p'' is 3, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' contains exactly one 2, then we can write ''p'' = 2''z''2''w''1, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''20201''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty.

If ''z'' is empty, then ''p'' ∈ 22{0}1, and the smallest prime ''p'' ∈ 22{0}1 is '''22000001'''.

If ''w'' is empty, then ''p'' ∈ 2{0}21, and the smallest prime ''p'' ∈ 2{0}21 is '''20021'''.

Case 1.2: ''p'' begins with 5.

In this case we can write ''p'' = 5''y''1. If 2 ◁ ''y'', then '''521''' ◁ ''p''. If 9 ◁ ''y'', then 59 ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 5, or 8.

If 05 ◁ ''y'', then '''5051''' ◁ ''p''. If 08 ◁ ''y'', then '''5081''' ◁ ''p''. If 50 ◁ ''y'', then '''5501''' ◁ ''p''. If 58 ◁ ''y'', then '''5581''' ◁ ''p''. If 80 ◁ ''y'', then '''5801''' ◁ ''p''. If 85 ◁ ''y'', then '''5851''' ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ {5} ∪ {8}.

If ''y'' ∈ {0}, then ''p'' ∈ 5{0}1. But then, since the sum of the digits of ''p'' is 6, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' ∈ {5}, then ''p'' ∈ 5{5}1, and the smallest prime ''p'' ∈ 5{5}1 is '''555555555551'''.

If ''y'' ∈ {8}, since if 88 ◁ ''y'', then 881 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'',8}, and thus ''p'' ∈ {51,581}, but 51 and 581 are both composite.

Case 1.3: ''p'' begins with 8.

In this case we can write p = 8''y''1. If 2 ◁ ''y'', then '''821''' ◁ ''p''. If 8 ◁ ''y'', then '''881''' ◁ ''p''. If 9 ◁ ''y'', then 89 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 5.

If 50 ◁ ''y'', then '''8501''' ◁ ''p''. Hence we may assume y ∈ {0}{5}.

If 005 ◁ ''y'', then '''80051''' ◁ p. Hence we may assume y ∈ {0} ∪ {5} ∪ 0{5}.

If y ∈ {0}, then ''p'' ∈ 8{0}1. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime.

If y ∈ {5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'', 5, 55, 555, 5555, 55555, 555555, 5555555, 55555555, 555555555, 5555555555}, and thus ''p'' ∈ {81, 851, 8551, 85551, 855551, 8555551, 85555551, 855555551, 8555555551, 85555555551, 855555555551}, but all of these numbers are composite.

If y ∈ 0{5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {0, 05, 055, 0555, 05555, 055555, 0555555, 05555555, 055555555, 0555555555, 05555555555}, and thus ''p'' ∈ {801, 8051, 80551, 805551, 8055551, 80555551, 805555551, 8055555551, 80555555551, 805555555551, 8055555555551}, and of these numbers only 80555551 and 8055555551 are primes, but 80555551 ◁ 8055555551, thus only '''80555551''' is a minimal element.

Case 1.4: ''p'' begins with 9.

In this case we can write p = 9''y''1. If 9 ◁ ''y'', then '''991''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 2, 5, or 8.

If 00 ◁ ''y'', then '''9001''' ◁ ''p''. If 22 ◁ ''y'', then '''9221''' ◁ ''p''. If 55 ◁ ''y'', then '''9551''' ◁ ''p''. If 88 ◁ ''y'', then 881 ◁ ''p''. Hence we may assume ''y'' contains at most one 0, at most one 2, at most one 5, and at most one 8.

If ''y'' only contains at most one 0 and does not contain any of {2,5,8}, then ''y'' ∈ {''𝜆'',0}, and thus ''p'' ∈ {91,901}, but 91 and 901 are both composite. If ''y'' only contains at most one 0 and only one of {2,5,8}, then the sum of the digits of ''p'' is divisible by 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume ''y'' contains at least two of {2,5,8}.

If 25 ◁ ''y'', then 251 ◁ ''p''. If 28 ◁ ''y'', then 281 ◁ ''p''. If 52 ◁ ''y'', then 521 ◁ ''p''. If 82 ◁ ''y'', then 821 ◁ ''p''. Hence we may assume ''y'' contains no 2's (since if ''y'' contains 2, then ''y'' cannot contain either 5's or 8's, which is a contradiction).

If 85 ◁ ''y'', then '''9851''' ◁ ''p''. Hence we may assume ''y'' ∈ {58,580,508,058}, and thus ''p'' ∈ {9581,95801,95081,90581}, and of these numbers only 95801 is prime, but 95801 is not a minimal element since 5801 ◁ 95801.

Case 2: ''p'' ends with 3.

In this case we can write p = ''x''3. If ''x'' contains 1, 2, 4, 5, 7, or 8, then (respectively) '''13''' ◁ ''p'', '''23''' ◁ ''p'', '''43''' ◁ ''p'', '''53''' ◁ ''p'', '''73''' ◁ ''p'', or '''83''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime.

Case 3: ''p'' ends with 7.

In this case we can write ''p'' = ''x''7. If ''x'' contains 1, 3, 4, 6, or 9, then (respectively) '''17''' ◁ ''p'', '''37''' ◁ ''p'', '''47''' ◁ ''p'', '''67''' ◁ ''p'', or '''97''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 7, or 8.

Case 3.1: ''p'' begins with 2.

In this case we can write ''p'' = 2''y''7. If 2 ◁ ''y'', then '''227''' ◁ ''p''. If 5 ◁ ''y'', then '''257''' ◁ ''p''. If 7 ◁ ''y'', then '''277''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 8.

If 08 ◁ ''y'', then '''2087''' ◁ ''p''. If 88 ◁ ''y'', then 887 ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ 8{0}.

If ''y'' ∈ {0}, then ''p'' ∈ 2{0}7. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime.

If y ∈ 8{0}, then ''p'' ∈ 28{0}7. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 40&lt;sub&gt;''n''&lt;/sub&gt;1 = 280&lt;sub&gt;''n''&lt;/sub&gt;7.

Case 3.2: ''p'' begins with 5.

In this case we can write ''p'' = 5''y''7. If 5 ◁ ''y'', then '''557''' ◁ ''p''. If 7 ◁ ''y'', then '''577''' ◁ ''p''. If 8 ◁ ''y'', then '''587''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2.

If 22 ◁ ''y'', then 227 ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's.

If ''y'' contains no 2's, then ''p'' ∈ 5{0}7. But then, since the sum of the digits of ''p'' is 12, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' contains exactly one 2, then we can write ''p'' = 5''z''2''w''7, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''50207''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty.

If ''z'' is empty, then ''p'' ∈ 52{0}7, and the smallest prime ''p'' ∈ 52{0}7 is '''5200007'''.

If ''w'' is empty, then ''p'' ∈ 5{0}27, and the smallest prime ''p'' ∈ 5{0}27 is '''5000000000000000000000000000027'''.

Case 3.3: ''p'' begins with 7.

In this case we can write ''p'' = 7''y''7. If 2 ◁ ''y'', then '''727''' ◁ ''p''. If 5 ◁ ''y'', then '''757''' ◁ ''p''. If 8 ◁ ''y'', then '''787''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 7, and thus all digits of ''p'' are 0 or 7. But then, since the digits of ''p'' all have a common factor 7, ''p'' is divisible by 7, so ''p'' cannot be prime.

Case 3.4: ''p'' begins with 8.

In this case we can write ''p'' = 8''y''7. If 2 ◁ ''y'', then '''827''' ◁ ''p''. If 5 ◁ ''y'', then '''857''' ◁ ''p''. If 7 ◁ ''y'', then '''877''' ◁ ''p''. If 8 ◁ ''y'', then '''887''' ◁ ''p''. Hence we may assume ''y'' ∈ {0}, and thus ''p'' ∈ 8{0}7. But then, since the sum of the digits of ''p'' is 15, ''p'' is divisible by 3, so ''p'' cannot be prime.

Case 4: ''p'' ends with 9.

In this case we can write ''p'' = ''x''9. If ''x'' contains 1, 2, 5, 7, or 8, then (respectively) '''19''' ◁ ''p'', '''29''' ◁ ''p'', '''59''' ◁ ''p'', '''79''' ◁ ''p'', or '''89''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 4, 6, or 9.

If 44 ◁ ''x'', then '''449''' ◁ ''p''. Hence we may assume ''x'' contains zero or one 4's.

If x contains no 4's, then all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume that ''x'' contains exactly one 4.

Case 4.1: ''p'' begins with 3.

In this case we can write ''p'' = 3''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. We must have '''349''' ◁ ''p''.

Case 4.2: ''p'' begins with 4.

In this case we can write ''p'' = 4''y''9, where all digits of ''y'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''409''' ◁ ''p''. If 3 ◁ ''y'', then 43 ◁ ''p''. If 9 ◁ ''y'', then '''499''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}, and thus ''p'' ∈ 4{6}9. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 6&lt;sub&gt;''n''&lt;/sub&gt;7 = 46&lt;sub&gt;''n''&lt;/sub&gt;9.

Case 4.3: ''p'' begins with 6.

In this case we can write p = 6''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 6 ◁ ''z'', then '''6469''' ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' is empty.

If 3 ◁ ''y'', then 349 ◁ ''p''. If 9 ◁ ''y'', then '''6949''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 6.

If 06 ◁ ''y'', then '''60649''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}{0}.

If 666 ◁ ''y'', then '''666649''' ◁ ''p''. If 00000 ◁ ''y'', then '''60000049''' ◁ ''p''. Hence we may assume ''y'' ∈ {''𝜆'', 0, 00, 000, 0000, 6, 60, 600, 6000, 60000, 66, 660, 6600, 66000, 660000}, and thus ''p'' ∈ {649, 6049, 60049, 600049, 6000049, 6649, 66049, 660049, 6600049, 66000049, 66649, 666049, 6660049, 66600049, 666000049}, and of these numbers only '''66000049''' and '''66600049''' are primes.

Case 4.4: ''p'' begins with 9.

In this case we can write p = 9''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''9049''' ◁ ''p''. If 3 ◁ ''y'', then 349 ◁ ''p''. If 6 ◁ ''y'', then '''9649''' ◁ ''p''. If 9 ◁ ''y'', then '''9949''' ◁ ''p''. Hence we may assume ''y'' is empty.

If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' ∈ {6}, and thus ''p'' ∈ 94{6}9, and the smallest prime ''p'' ∈ 94{6}9 is 946669.

[[Category:Number theory]]</text>
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'''Athena problem''' is an [[:w:List of unsolved problems in mathematics|unsolved problem]] in [[:w:Number theory|number theory]] and [[:w:Formal language theory|formal language theory]] and [[:w:Order theory|order theory]], this problem is named after the ancient Greek goddess [[:w:Athena|Athena]] (which is associated with [[:w:Wisdom|wisdom]]). Athena problem is: Give a [[:w:Natural number|natural number]] ''b'' &gt; 1, find the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the set of the &quot;[[:w:Prime number|prime number]] [[:w:Greater than|&gt;]] ''b''&quot; [[:w:Numerical digit|digit]] [[:w:String (computer science)|string]]s in the [[:w:Positional numeral system|positional numeral system]] with [[:w:Radix|base]] ''b'' for the [[:w:Subsequence|subsequence]] [[:w:Partially ordered set|ordering]]. (A string ''x'' is a subsequence of another string ''y'', if ''x'' can be obtained from ''y'' by deleting zero or more of the [[:w:Character (computing)|character]]s in ''y''. For example, 514 is a subsequence of 352148, &quot;string&quot; is a subsequence of &quot;meistersinger&quot;. In contrast, 758 is not a subsequence of 378259, &quot;abc&quot; is not a subsequence of &quot;cbacacba&quot;, since the characters must be in the same order) (Unlike [[:w:Substring|substring]], subsequence is not required to occupy consecutive positions within the original sequences, e.g. the [[:w:Longest common subsequence|longest common subsequence problem]] is different from the [[:w:Longest common substring|longest common substring problem]])

Using [[:w:Formal language theory|formal language theory]] terminology, Athena problem is finding the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the [[:w:Formal language|language]] of base-''b'' [[:w:Representation (mathematics)|representation]]s of the [[:w:Prime number|prime number]]s [[:w:Greater than|&gt;]] ''b'' (which is a set of [[:w:String (computer science)|string]]s of [[:w:Symbol|symbol]]s over the [[:w:Alphabet (formal languages)|alphabet]] ''Σ''&lt;sub&gt;''b''&lt;/sub&gt; := {0, 1, ..., ''b''−1}), under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] &quot;is a subsequence of&quot;, which is a [[:w:Partially ordered set|partial ordering]]), for a given natural number ''b'' &gt; 1 (You can draw this partial ordering as a [[:w:Hasse diagram|Hasse diagram]] to find all [[:w:Minimal element|minimal element]]s), this set is called '''Athena set''', and the prime numbers in this set are called '''Athena primes'''.

By [[:w:Higman's lemma|Higman's lemma]], there are no [[:w:Infinite set|infinite]] [[:w:Antichain|antichain]]s for the subsequence ordering (i.e. the subsequence ordering is always a [[:w:Well-quasi-ordering|well quasi order]]) (i.e. under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] &quot;is a subsequence of&quot;, which is a [[:w:Partially ordered set|partial ordering]]), every set of pairwise incomparable (i.e. not [[:w:Comparability|comparable]]) strings is finite), thus there must be only finitely many such minimal elements. In other words, the Athena set in every base ''b'' must be a [[:w:Finite set|finite set]], and every base ''b'' ≥ 2 has only finitely many Athena primes, e.g. in [[:w:Decimal|decimal]] (base ''b'' = 10), the Athena set has exactly 77 [[:w:Element of a set|element]]s (they are exactly the Athena primes in decimal (base ''b'' = 10)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}.

Determining the set of the minimal elements of a arbitrary set of strings under the subsequence ordering is in general [[:w:List of unsolved problems in mathematics|unsolvable]], and can be difficult even when this set is relatively simple (such as the base ''b'' representations of the prime numbers &gt; ''b'', whose set is exactly the Athena set in base ''b'').

Although the set ''M''(''S'') of minimal strings is necessarily [[:w:Finite set|finite]], determining it explicitly for a given ''S'' can be a difficult computational problem. We use some [[:w:Number theory|numbertheoretic]] [[:w:Heuristic argument|heuristic]]s to [[:w:Computing|compute]] ''M''(''L''&lt;sub&gt;''b''&lt;/sub&gt;) (i.e. to compute the Athena set in base ''b''), where ''L''&lt;sub&gt;''b''&lt;/sub&gt; is the [[:w:Formal language|language]] of [[:w:Radix|base]]-''b'' representations of the [[:w:Prime number|prime number]]s which are [[:w:Greater than|&gt;]] ''b'', for 2 ≤ ''b'' ≤ 36.

For bases 2 ≤ ''b'' ≤ 36, Athena problem is fully solved in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24, and also solved in bases ''b'' = 11, 13, 16, 22, 30 if [[:w:Probable prime|probable prime]]s are allowed. For the unsolved bases ''b'' = 17, 19, 21, 23, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, Athena problem is solved (if probable primes are allowed) except 771 [[:w:Indexed family|families]] of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be [[:w:Empty string|empty]]) of digits in base ''b'', ''y'' is a digit in base ''b'') = sequence {''xz'', ''xyz'', ''xyyz'', ''xyyyz'', ''xyyyyz'', ''xyyyyyz'', ...} (i.e. &quot;''xy''&lt;sup&gt;+&lt;/sup&gt;''z''&quot; in [[:w:Regular expression|regular expression]]), all of these 771 families contain no primes &gt; ''b'' or probable primes &gt; ''b'' with length ≤ 100000. (The chance that an unproven probable prime in these sets is in fact composite is less than 10&lt;sup&gt;−2000&lt;/sup&gt;, see https://t5k.org/notes/prp_prob.html)

== Solve the problem ==

To solve the Athena problem for a given base ''b'', we must [[:w:Computing|compute]] the elements up to families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), and find the smallest prime &gt; ''b'' in all such families.

We call families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') &quot;linear&quot; families, and we reduce these families by removing all trailing digits ''y'' from ''x'', and removing all leading digits ''y'' from ''z'', to make the families be easier, e.g. family 12333{3}33345 in base ''b'' is reduced to family 12{3}45 in base ''b'', since they are in fact the same family. Our [[:w:Algorithm|algorithm]] then proceeds as follows:

* 1. ''M'' := {minimal primes in base ''b'' of length 2 or 3}, ''L'' := union of all ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'') such that ''x'' ≠ 0 and ''gcd''(''z'', ''b'') = 1 and ''Y'' is the set of digits ''y'' in base ''b'' such that ''xyz'' has no subsequence in ''M''.
* 2. While ''L'' contains nonlinear families (families which are not linear families): Explore each family of ''L'', and update ''L''. Examine each family of ''L'' by:
* 2.1. Let ''w'' be the shortest string in the family. If ''w'' has a subsequence in ''M'', then remove the family from ''L''. If ''w'' represents a prime, then add ''w'' to ''M'' and remove the family from ''L''.
* 2.2. If possible, simplify the family.
* 2.3. Using the techniques below (covering congruence, algebraic factorization, or combine of them), check if the family can be proven to only contain composites (only count the numbers &gt; ''b''), and if so then remove the family from ''L''.
* 3. Update ''L'', after each split examine the new families as in step 2.

e.g. in decimal (base ''b'' = 10):

''M'' := {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991}

''L'' := {2{0,2}1, 2{0,8}7, 3{0,3,6,9}3, 3{0,3,6,9}9, 4{6}9, 5{0,5,8}1, 5{0,2}7, 6{0,3,6,9}3, 6{0,3,4,6,9}9, 7{0,7}7, 8{0,5}1, 8{0}7, 9{0,2,5,8}1, 9{0,3,6,9}3, 9{0,3,4,6,9}9}

and since 2221 is prime, it follows that the family 2{0,2}1 splits into the families 2{0}1 and 2{0}2{0}1

and since the family 2{0}1 can be proven to contain no primes &gt; base (since all numbers in this family are divisible by 3), it can be removed

and since 20201 is prime, it follows that the family 2{0}2{0}1 splits into the families 2{0}21 and 22{0}1

221 and 2021 are composites, but 20021 is prime, thus add 20021 to ''L''

none of 221, 2201, 22001, 220001, 2200001 are primes, but 22000001 is prime, thus add 22000001 to ''L''

and since the family 3{0,3,6,9}3 can be proven to contain no primes &gt; base (since all numbers in this family are divisible by 3), it can be removed

etc.

Since the number of possible (first digit,last digit) (also called (initial digit,final digit)) combos ([[:w:Ordered pair|ordered pair]]s) of a prime &gt; ''b'' in base ''b'' is (''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(''b'') (all digits except 0 can be the first digit of a prime &gt; ''b'' in base ''b'' (thus ''b''−1 possible digits), but only the digits coprime to ''b'' can be the last digit of a prime &gt; ''b'' in base ''b'' (thus ''eulerphi''(''b'') possible digits), and by the [[:w:Rule of product|rule of product]], there are (''b''−1)×''eulerphi''(''b'') choices of the (first digit,last digit) combo, also, both &quot;numbers of Athena primes in base ''b''&quot; and &quot;length of the largest Athena prime in base ''b''&quot; are [[:w:Asymptotic analysis|roughly]] ''[[:w:E (mathematical_constant)|e]]''&lt;sup&gt;''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)&lt;/sup&gt;.

Shrinking the family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'')

* If ''y'' ∈ ''Y'' and the string ''xyyz'' represents a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''}''z'' ∪ ''x''{''Y'' \ ''y''}''y''{''Y'' \ ''y''}''z''.
* If ''y''&lt;sub&gt;1&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;2&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;1&lt;/sub&gt; ≠ ''y''&lt;sub&gt;2&lt;/sub&gt; and the string ''xy''&lt;sub&gt;1&lt;/sub&gt;''y''&lt;sub&gt;2&lt;/sub&gt;''z'' represents a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''&lt;sub&gt;1&lt;/sub&gt;}{''Y'' \ ''y''&lt;sub&gt;2&lt;/sub&gt;}''z''.
* If ''y''&lt;sub&gt;1&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;2&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;1&lt;/sub&gt; ≠ ''y''&lt;sub&gt;2&lt;/sub&gt; and both the strings ''xy''&lt;sub&gt;1&lt;/sub&gt;''y''&lt;sub&gt;2&lt;/sub&gt;''z'' and ''xy''&lt;sub&gt;2&lt;/sub&gt;''y''&lt;sub&gt;1&lt;/sub&gt;''z'' represent a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or have a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''&lt;sub&gt;1&lt;/sub&gt;}''z'' ∪ ''x''{''Y'' \ ''y''&lt;sub&gt;2&lt;/sub&gt;}''z''.

e.g. in decimal (base ''b'' = 10):

* 2221 is a prime &gt; 10, thus the family 2{0,2}1 splits into the two families 2{0}1 and 2{0}2{0}1.
* 227 is a prime &gt; 10, and it is a subsequence of 5227, thus the family 5{0,2}7 splits into the two families 5{0}7 and 5{0}2{0}7.
* 449 is a prime &gt; 10, and it is a subsequence of 6449, thus the family 6{0,3,4,6,9}9 splits into the two families 6{0,3,6,9}9 and 6{0,3,6,9}4{0,3,6,9}9.
* Both 5051 and 5501 are primes &gt; 10, thus the family 5{0,5}1 splits into the two families 5{0}1 and 5{5}1 = {5}1.
* 8501 is a prime &gt; 10, thus the family 8{0,5}1 splits into the family 8{0}{5}1.
* 887 is a prime &gt; 10, and it is a subsequence of 2887, also 2087 is a prime &gt; 10, thus the family 2{0,8}7 splits into the two families 2{0}7 and 28{0}7.
* 349 and 449 are primes &gt; 10, and they are subsequences of 9349 and 9449, respectively, also 9049, 9649, 9949 are primes &gt; 10, thus the family 9{0,3,4,6,9}9 splits into the two families 9{0,3,6,9}9 and 94{0,3,6,9}9.
* 251, 281, 521, 821, 881 are primes &gt; 10, and they are subsequences of 9251, 9281, 9521, 9821, 9881, respectively, also 9001, 9221, 9551, 9851 are primes &gt; 10, thus the family 9{0,2,5,8}1 splits into the numbers {91, 901, 921, 951, 981, 9021, 9051, 9081, 9201, 9501, 9581, 9801, 90581, 95081, 95801}.

If the methods we have discussed cannot be used to rule out or shrink ''x''{''Y''}''z'' where ''Y'' = {''y''&lt;sub&gt;1&lt;/sub&gt;, ''y''&lt;sub&gt;2&lt;/sub&gt;, ..., ''y''&lt;sub&gt;''n''&lt;/sub&gt;}, then we can replace ''x''{''Y''}''z'' by ''xy''&lt;sub&gt;1&lt;/sub&gt;{''Y''}''z'' ∪ ''xy''&lt;sub&gt;2&lt;/sub&gt;{''Y''}''z'' ∪ ... ∪ ''xy''&lt;sub&gt;''n''&lt;/sub&gt;{''Y''}''z'' and re-run the methods on this new [[:w:Formal language|language]].

If all remain families are linear families (i.e. of the form ''x''{''y''}''z'', where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), then we search the smallest (probable) primes in these families and add these primes to the list.

e.g. in decimal (base ''b'' = 10):

* The smallest prime in the family 5{0}27 is 5000000000000000000000000000027.
* The smallest prime in the family {5}1 is 555555555551.
* The smallest prime in the family 8{5}1 is 8555555555555555555551, but 8555555555555555555551 is not a minimal element since 555555555551 is a subsequence of 8555555555555555555551.

There is no guarantee that the techniques discussed will ever terminate, but in practice they often do. They are able to determine the Athena set in base ''b'' for 2 ≤ ''b'' ≤ 16 and ''b'' = 18, 20, 22, 24, 30. The bases ''b'' = 17, 19, 21, 23, 25 ≤ ''b'' ≤ 29, 31 ≤ ''b'' ≤ 36 are solved with the exception of 771 families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'').

The following is a &quot;[[:w:Semi-algorithm|semi-algorithm]]&quot; that is guaranteed to solve the Athena problem for a given base ''b'', but it is not so easy to implement:

# ''M'' = ''[[:w:Empty string|∅]]''
# while (''L'' ≠ ''∅'') do
# choose ''x'', a shortest string in ''L''
# ''M'' := ''M'' ∪ {''x''}
# ''L'' := ''L'' − ''sup''({''x''})

In practice, for arbitrary ''L'', we cannot feasibly carry out step 5. Instead, we work with ''L''&amp;#39;, some regular overapproximation to ''L'', until we can show ''L''&amp;#39; = ''∅'' (which implies ''L'' = ''∅''). In practice, ''L''&amp;#39; is usually chosen to be a finite [[:w:Union (set theory)|union]] of sets of the form ''L''&lt;sub&gt;1&lt;/sub&gt;{''L''&lt;sub&gt;2&lt;/sub&gt;}''L''&lt;sub&gt;3&lt;/sub&gt;, where each of ''L''&lt;sub&gt;1&lt;/sub&gt;, ''L''&lt;sub&gt;2&lt;/sub&gt;, ''L''&lt;sub&gt;3&lt;/sub&gt; is finite. In the case we consider in this project, we then have to determine whether such a family contains a prime or not.

Thus, the [[:w:Time complexity|time complexity]] of the Athena problem in base ''b'' may be ''[[:w:Big O notation|O]]''(''[[:w:E (mathematical_constant)|e]]''&lt;sup&gt;''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)&lt;/sup&gt;), and the [[:w:CPU time|CPU time]] of the Athena problem in base ''b'' may be longer than [[:w:Age of the universe|the age of the universe]] for bases ''b'' = 19, 23, 25, 27, 29, 31, 32, 33, 34, 35, also, Athena problem in bases ''b'' around 500 may be [[:w:NP-complete|NP-complete]] or [[:w:NP-hard|NP-hard]], or an [[:w:Undecidable problem|undecidable problem]], or an example of [[:w:Gödel's incompleteness theorems|Gödel's incompleteness theorems]] (like the [[:w:Continuum hypothesis|continuum hypothesis]] and the [[:w:Halting problem|halting problem]]).

To solve the Athena problem (i.e. to compute the Athena set), we need to determine whether a given family contains a prime. In practice, if family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'') could not be ruled out as only containing composites and ''Y'' contains two or more digits, then a relatively small prime &gt; ''b'' could always be found in this family. Intuitively, this is because there are a large number of small strings in such a family, and at least one is likely to be prime (e.g. there are 2&lt;sup&gt;''n''−2&lt;/sup&gt; strings of length ''n'' in the family 1{3,7}9, and there are over a thousand strings of length 12 in the family 1{3,7}9, thus it is very impossible that these numbers are all composite). In the case ''Y'' contains only one digit, this family is of the form ''x''{''y''}''z'', and there is only a single string of each length &gt; (the length of ''x'' + the length of ''z''), and it is not known if the following [[:w:Decision problem|decision problem]] is recursively solvable (just like [[:w:Sierpiński number|Sierpiński problem]] and [[:w:Riesel number|Riesel problem]], Sierpiński problem and Riesel problem can be generalized to other bases ''b'' (references: http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm), in fact, Athena problem base ''b'' covers the Sierpiński problem base ''b'' and the Riesel problem base ''b'' with ''k'' &lt; ''b'', i.e. finding the smallest prime of the form ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 and ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (or prove such prime does not exist) with ''k'' &lt; ''b'' (specially, for bases ''b'' such that the conjectured smallest Sierpiński number or the conjectured smallest Riesel number is &lt; ''b'', Athena problem base ''b'' covers the Sierpiński problem base ''b'' or the Riesel problem base ''b'', respectively), since the smallest prime of the form ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 and ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (if exists) must be a minimal element in base ''b'', also, Athena problem base ''b'' covers finding the smallest prime of these forms in base ''b'' (or proving that such prime does not exist) (in fact, it is known that exactly what bases 2 ≤ ''b'' ≤ 1024 have the families listed in the table below as unsolved families, all of these families in all bases 2 ≤ ''b'' ≤ 1024 have been searched to length ≥ 10000 (for the family (''sqrt''(''b'')×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''sqrt''(''b'')+1), bases 2 ≤ ''b'' ≤ 1048576, searched to length ≥ 5000)): (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1) (for this form, ''n'' must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepu.txt, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379, https://pzktupel.de/Primetables/TableRepunitGen.php, https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A128164, https://oeis.org/A285642; or for prime bases ''b'': https://oeis.org/A065854, https://oeis.org/A279068), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 1) (references of this form: http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A228101), (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/2 (for odd ''b'') (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 2) (reference of this form: http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt), (''sqrt''(''b'')×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''sqrt''(''b'')+1) (for square ''b'') (for this form, 2×''n''+1 must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepuP.txt, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/488, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://oeis.org/A084742, https://oeis.org/A084741; or for bases ''b'' with ''sqrt''(''b'') prime: https://oeis.org/A065507), ((''b''−2)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''−1) (''n'' ≥ 2) (reference of this form: https://oeis.org/A243404), 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://oeis.org/A119624), 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&amp;d=1567314217, https://oeis.org/A119591), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+2 (''n'' ≥ 1) (references of this form: https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067), ''b''&lt;sup&gt;''n''&lt;/sup&gt;−2 (''n'' ≥ 2) (references of this form: https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A250200, https://oeis.org/A255707, https://oeis.org/A084714; or for prime bases ''b'': https://oeis.org/A292201), (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (''n'' ≥ 1) (references of this form: http://www.noprimeleftbehind.net/Williams-primes-MP.htm, http://www.bitman.name/math/table/477, https://pzktupel.de/Primetables/TableWilliams2.php, https://oeis.org/A305531; or for prime bases ''b'': https://oeis.org/A087139), (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (''n'' ≥ 1) (references of this form: https://harvey563.tripod.com/wills.txt, http://www.noprimeleftbehind.net/Williams-primes-MM.htm, http://www.bitman.name/math/table/484, https://pzktupel.de/Primetables/TableWilliams1.php; or for prime bases ''b'': https://oeis.org/A122396), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''−1) (''n'' ≥ 1) (references of this form: http://www.bitman.name/math/table/795, https://pzktupel.de/Primetables/TableWilliams6.php, https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179), ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''−1) (''n'' ≥ 2) (references of this form: http://www.bitman.name/math/table/792, https://pzktupel.de/Primetables/TableWilliams5.php, https://oeis.org/A113516, https://oeis.org/A343589; or for prime bases ''b'': https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/435)):

'''Problem: Given strings ''x'', ''z'' (may be empty), a digit ''y'', and a base ''b'' (''x'' does not [[:w:Leading zero|start with the digit 0]], ''z'' ends with a digit which [[:w:Coprime integers|coprime]] to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty), does there exist a prime number whose base-''b'' expansion is of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' for some ''n'' ≥ 0?'''

An [[:w:Algorithm|algorithm]] to solve this problem, for example, would allow us to decide if there are any additional [[:w:Fermat prime|Fermat prime]]s other than the known ones (corresponding to ''n'' = 0, 1, 2, 3, 4). To see this, take ''b'' = 2, ''x'' = 1, ''y'' = 0, and ''z'' = 0&lt;sub&gt;16&lt;/sub&gt;1. Since if 2&lt;sup&gt;''n''&lt;/sup&gt;+1 is prime then ''n'' must be a [[:w:Power of 2|power of two]], a prime of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' must be a new Fermat prime. Besides, it would allow us to decide if there are infinitely many [[:w:Mersenne prime|Mersenne prime]]s (of the form 2&lt;sup&gt;''p''&lt;/sup&gt;−1 with prime ''p''). To see this, take ''b'' = 2, ''x'' = ''𝜆'' (the [[:w:Empty string|empty string]]), ''y'' = 1, and ''z'' = 1&lt;sub&gt;''n''+1&lt;/sub&gt;, where ''n'' is the exponent of the Mersenne prime which we want to know whether it is the largest Mersenne prime or not. Since if 2&lt;sup&gt;''n''&lt;/sup&gt;−1 is prime then ''n'' must be a [[:w:Prime number|prime]], a prime of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' must be a new Mersenne prime. Also, it would allow us to decide whether 78557 is the smallest [[:w:Sierpinski number|Sierpinski number]] (i.e. odd numbers ''k'' such that ''k''×2&lt;sup&gt;''n''&lt;/sup&gt;+1 is composite for all ''n'' ≥ 1) and whether 509203 is the smallest [[:w:Riesel number|Riesel number]] (i.e. odd numbers ''k'' such that ''k''×2&lt;sup&gt;*n*&lt;/sup&gt;−1 is composite for all ''n'' ≥ 1), etc.

'''Conjecture (this conjecture is very important for the Athena problem): If family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' (with fixed strings ''x'', ''z'' (may be empty), fixed digit ''y'', and variable ''n'') in base ''b'' (with fixed ''b'' ≥ 2) (''x'' does not start with the digit 0, ''z'' ends with a digit which coprime to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty) cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' contains infinitely many primes (this is equivalent to: If form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) (with fixed integers ''a'' ≥ 1, ''b'' ≥ 2, ''c'' ≠ 0 (with ''gcd''(''a'',''c'') = 1 and ''gcd''(''b'',''c'') = 1), and variable ''n'') cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) contains infinitely many primes).'''

(in fact, this conjecture is equivalent to the conjecture (to prove this, by change the base (''b'') to a power of ''b'' which is larger than the largest prime in a given family (in base ''b'') which only contains finitely many primes): If family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' (with fixed strings ''x'', ''z'' (may be empty), fixed digit ''y'', and variable ''n'') in base ''b'' (with fixed ''b'' ≥ 2) (''x'' does not start with the digit 0, ''z'' ends with a digit which coprime to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty) cannot be proven to only contain composites (by covering congruence, algebraic factorization, or combine of them), then family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' contains at least one prime (this is equivalent to: If form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) (with fixed integers ''a'' ≥ 1, ''b'' ≥ 2, ''c'' ≠ 0 (with ''gcd''(''a'',''c'') = 1 and ''gcd''(''b'',''c'') = 1), and variable ''n'') cannot be proven to only contain composites (by covering congruence, algebraic factorization, or combine of them), then form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) contains at least one prime), like the [[:w:Bunyakovsky conjecture|Bunyakovsky conjecture]] and the [[:w:Dickson's conjecture|Dickson's conjecture]] and the [[:w:Schinzel's hypothesis H|Schinzel's hypothesis ''H'']], if such ''n'' always exists, then there must be always infinitely many such ''n'', to prove this, add another polynomial for the cases of the Dickson's conjecture and the Schinzel's hypothesis ''H'', also, change the polynomial (e.g. change ''n'' to ''r''×''n'' or ''n''&lt;sup&gt;''r''&lt;/sup&gt; for all integers ''r'' &gt; 1) for the cases of the Bunyakovsky conjecture and the Schinzel's hypothesis ''H'')

Some families can be ruled out to contain no prime &gt; ''b'' by [[:w:Covering set|covering congruence]], [[:w:Factorization of polynomials|algebraic factorization]] (e.g. [[:w:Difference of two squares|difference of two squares]], [[:w:Sum of two cubes|sum of two cubes]], [[:w:Sophie Germain's identity|Sophie Germain's identity of ''x''&lt;sup&gt;4&lt;/sup&gt;+4×''y''&lt;sup&gt;4&lt;/sup&gt;]]), or combine of them, e.g.

* The base 9 family 2{7}: Always divisible by 2 or 5
* The base 11 family 2{5}: Always divisible by 2 or 3
* The base 14 family B{0}1: Always divisible by 3 or 5
* The base 13 family 95{0}3: Always divisible by 5, 7, or 17
* The base 16 family {4}D: Always divisible by 3, 7, or 13
* The base 16 family {8}F: Always divisible by 3, 7, or 13
* The base 21 family {7}D: Always divisible by 2, 13, or 17
* The base 23 family {D}GA: Always divisible by 2, 5, 7, 37, or 79
* The base 9 family {1}: Can be written as (9&lt;sup&gt;''n''&lt;/sup&gt;−1)/8 and can be factored as (3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (3&lt;sup&gt;''n''&lt;/sup&gt;+1) / 8
* The base 8 family 1{0}1: Can be written as 8&lt;sup&gt;''n''&lt;/sup&gt;+1 and can be factored as (2&lt;sup&gt;''n''&lt;/sup&gt;+1) × (4&lt;sup&gt;''n''&lt;/sup&gt;−2&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 9 family 3{8}: Can be written as 4×9&lt;sup&gt;''n''&lt;/sup&gt;−1 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 16 family 1{5}: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;−1)/3 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+1) / 3
* The base 16 family {4}1: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;−49)/15 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−7) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+7) / 15
* The base 27 family 7{Q}: Can be written as 8×27&lt;sup&gt;''n''&lt;/sup&gt;−1 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (4×9&lt;sup&gt;''n''&lt;/sup&gt;+2×3&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 27 family 9{G}: Can be written as (125×27&lt;sup&gt;''n''&lt;/sup&gt;−8)/13 and can be factored as (5×3&lt;sup&gt;''n''&lt;/sup&gt;−2) × (25×9&lt;sup&gt;''n''&lt;/sup&gt;+10×3&lt;sup&gt;''n''&lt;/sup&gt;+4)
* The base 16 family {C}D: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;+1)/5 and can be factored as (2×4&lt;sup&gt;''n''&lt;/sup&gt;−2×2&lt;sup&gt;''n''&lt;/sup&gt;+1) × (2×4&lt;sup&gt;''n''&lt;/sup&gt;+2×2&lt;sup&gt;''n''&lt;/sup&gt;+1) / 5
* The base 14 family 8{D}: Can be written as 9×14&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is odd and can be factored as (3×14&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (3×14&lt;sup&gt;''n''/2&lt;/sup&gt;+1) if ''n'' is even
* The base 12 family {B}9B: Can be written as 12&lt;sup&gt;''n''&lt;/sup&gt;−25, it is divisible by 13 if ''n'' is odd and can be factored as (12&lt;sup&gt;''n''/2&lt;/sup&gt;−5) × (12&lt;sup&gt;''n''/2&lt;/sup&gt;+5) if ''n'' is even
* The base 14 family {D}5: Can be written as 14&lt;sup&gt;''n''&lt;/sup&gt;−9, it is divisible by 5 if ''n'' is odd and can be factored as (14&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (14&lt;sup&gt;''n''/2&lt;/sup&gt;+3) if ''n'' is even
* The base 17 family 1{9}: Can be written as (25×17&lt;sup&gt;''n''&lt;/sup&gt;−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (5×17&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (5×17&lt;sup&gt;''n''/2&lt;/sup&gt;+3) / 16 if ''n'' is even
* The base 17 family 7{9}: Can be written as (121×17&lt;sup&gt;''n''&lt;/sup&gt;−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (11×17&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (11×17&lt;sup&gt;''n''/2&lt;/sup&gt;+3) / 16 if ''n'' is even
* The base 19 family 1{6}: Can be written as (4×19&lt;sup&gt;''n''&lt;/sup&gt;−1)/3, it is divisible by 5 if ''n'' is odd and can be factored as (2×19&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (2×19&lt;sup&gt;''n''/2&lt;/sup&gt;+1) / 3 if ''n'' is even
* The base 24 family 3{N}: Can be written as 4×24&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is odd and can be factored as (2×24&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (2×24&lt;sup&gt;''n''/2&lt;/sup&gt;+1) if ''n'' is even
* The base 24 family 5{N}: Can be written as 6×24&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is even and can be factored as (12×24&lt;sup&gt;(''n''−1)/2&lt;/sup&gt;−1) × (12×24&lt;sup&gt;(''n''−1)/2&lt;/sup&gt;+1) if ''n'' is odd

If the conjecture above is true, then the [[:w:Sierpiński number|Sierpiński conjecture]] and [[:w:Riesel number|Riesel conjecture]] are also true, and the [https://www.mersenneforum.org/showthread.php?t=10761 dual Sierpiński conjecture] and the [https://www.mersenneforum.org/showthread.php?t=6545 dual Riesel conjecture] are also true, and the [http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm Sierpiński conjectures] and the [http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm Riesel conjectures] in all bases ''b'' are also true, and the [http://www.noprimeleftbehind.net/crus/SNOB-Sierp-conjectures.htm real Sierpiński conjectures] and the [http://www.noprimeleftbehind.net/crus/Real-Riesel-conjectures.htm real Riesel conjectures] are also true, also, if the Athena conjecture is true, then there are infinitely many primes of these forms for fixed bases ''b'' ≥ 2 and variable exponents ''n'':

* (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1) for all bases ''b'' which are not [[:w:Perfect power|perfect power]]s (for this form, ''n'' must be prime) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepu.txt, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379, https://pzktupel.de/Primetables/TableRepunitGen.php, https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A128164, https://oeis.org/A285642; or for prime bases ''b'': https://oeis.org/A065854, https://oeis.org/A279068)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' which are not of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 (for this form, ''n'' must be power of 2) (references of this form: http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A228101)
* (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/2 for all odd bases ''b'' which are not of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 (for this form, ''n'' must be power of 2) (reference of this form: http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt)
* (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''+1) for all bases ''b'' which are neither of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 nor of the form 4×''m''&lt;sup&gt;4&lt;/sup&gt; (for this form, ''n'' must be prime) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepuP.txt, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/488, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://oeis.org/A084742, https://oeis.org/A084741; or for prime bases ''b'': https://oeis.org/A065507)
* ((''b''−2)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''−1) for all bases ''b'' &gt; 2 (reference of this form: https://oeis.org/A243404)
* 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' &lt; 201446503145165177, not == 1 mod 3 (references of this form: https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://oeis.org/A119624)
* 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&amp;d=1567314217, https://oeis.org/A119591)
* 3×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b''
* 3×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b''
* 4×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 5, not == 14 mod 15, not [[:w:Fourth power|fourth power]]s
* 4×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 3, not == 4 mod 5, not [[:w:Square number|square]]s
* 5×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' &lt; 140324348, not == 1 mod 3
* 5×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b''
* 6×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 7, not == 34 mod 35
* 6×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 5, not == 34 mod 35, not of the form 6×''m''&lt;sup&gt;2&lt;/sup&gt; with ''m'' == 2, 3 mod 5
* 7×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b''
* 7×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' &lt; 9162668342, not == 1 mod 3
* 8×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 3, not == 20 mod 21, not == 47, 83 mod 195, not == 467, 4343, 9887, 25448, 35978, 41522, 42647, 57083 mod 73815, not == 722, 83813, 206672, 239432, 322523, 1283843, 1519577, 1522553 mod 1551615, ..., not [[:w:Cube (algebra)|cube]]s
* 8×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 7, not == 20 mod 21, not == 83, 307 mod 455, not == 1266, 13593, 27292, 46353 mod 63973, ..., not [[:w:Cube (algebra)|cube]]s
* 9×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' &lt; 177744, not == 1 mod 5
* 9×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' not == 4 mod 5, not [[:w:Square number|square]]s
* 10×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 11, not == 32 mod 33 (references of this form: https://oeis.org/A088782)
* 10×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 3, not == 32 mod 33
* 11×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' not == 1 mod 3, not == 14 mod 15
* 11×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' not == 1 mod 5, not == 14 mod 15, not of the form 11×''m''&lt;sup&gt;2&lt;/sup&gt; with ''m'' == 2, 3 mod 5
* 12×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 13, not == 142 mod 143, not == 562, 828, 900, 1166 mod 1729, not == 597, 1143 mod 1885, not == 296, 901, 1759, 3090, 4553, 5521, 5807, 6016, 6984, 7094, 7270, 7380, 7479, 8447, 8557, 8733, 8843, 9910, 10020, 10196, 10306, 11483, 11769, 12737, 14200, 15531, 16994, 18457 mod 19019, not == 563, 1433, 13212, 15097, 19848, 20718, 32497, 34382, 39133, 51782, 53667, 58418, 58452, 60337, 60883, 71067, 72952, 77737, 79622, 80168, 94267, 97022, 98583, 98907, 113552, 116307, 117868, 118192, 131967, 132513, 132837, 134398, 151252, 151798, 152122, 153683, 170537, 171083, 172968, 177753, 179638, 189822, 190368, 192253, 192287, 197038, 198923, 211572, 213568, 216323, 218208, 229987, 232853, 235608, 237493, 249272 mod 250705, ...
* 12×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 11, not == 142 mod 143, not == 307, 1143 mod 1595, not == 901, 6016, 7479, 18457 mod 19019, ...
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+2 for all odd bases ''b'' &lt; 201446503145165177, not == 1 mod 3 (references of this form: https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−2 for all odd bases ''b'' (references of this form: https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A250200, https://oeis.org/A255707, https://oeis.org/A084714; or for prime bases ''b'': https://oeis.org/A292201)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+3 for all even bases ''b'' not divisible by 3
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−3 for all even bases ''b'' not divisible by 3
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+4 for all odd bases ''b'' not == 1 mod 5, not == 14 mod 15, not [[:w:Fourth power|fourth power]]s
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−4 for all odd bases ''b'' not == 1 mod 3, not == 4 mod 5, not [[:w:Square number|square]]s
* (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' (references of this form: http://www.noprimeleftbehind.net/Williams-primes-MP.htm, http://www.bitman.name/math/table/477, https://pzktupel.de/Primetables/TableWilliams2.php, https://oeis.org/A305531; or for prime bases ''b'': https://oeis.org/A087139)
* (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: https://harvey563.tripod.com/wills.txt, http://www.noprimeleftbehind.net/Williams-primes-MM.htm, http://www.bitman.name/math/table/484, https://pzktupel.de/Primetables/TableWilliams1.php; or for prime bases ''b'': https://oeis.org/A122396)
* (''b''+1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 3 (references of this form: http://www.noprimeleftbehind.net/Williams-primes-PP.htm, http://www.bitman.name/math/table/474, https://pzktupel.de/Primetables/TableWilliams4.php)
* (''b''+1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: http://www.noprimeleftbehind.net/Williams-primes-PM.htm, http://www.bitman.name/math/table/471, https://pzktupel.de/Primetables/TableWilliams3.php)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''−1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/795, https://pzktupel.de/Primetables/TableWilliams6.php, https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''−1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/792, https://pzktupel.de/Primetables/TableWilliams5.php, https://oeis.org/A113516, https://oeis.org/A343589; or for prime bases ''b'': https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/435)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''+1) for all bases ''b'' not == 1 mod 3 (references of this form: http://www.bitman.name/math/table/801, https://pzktupel.de/Primetables/TableWilliams8.php, https://oeis.org/A346149, https://oeis.org/A346154)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''+1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/798, https://pzktupel.de/Primetables/TableWilliams7.php, https://oeis.org/A178250)

By the [[:w:Prime number theorem|prime number theorem]], the [[:w:Probability|chance]] that a [[:w:Random number|random]] ''n''-digit base ''b'' number is prime is [[:w:Asymptotic analysis|approximately]] 1/''n'' (more accurately, the chance is approximately 1/(''n''×''ln''(''b'')), where ''ln'' is the [[:w:Natural logarithm|natural logarithm]]). If one conjectures the numbers ''x''{''y''}''z'' behave similarly (i.e. the numbers ''x''{''y''}''z'' is a [[:w:Pseudorandomness|pseudorandom sequence]]) you would expect [[:w:Harmonic_series (mathematics)|1/1 + 1/2 + 1/3 + 1/4 + ... = ∞]] primes of the form ''x''{''y''}''z'' (of course, this does not always happen, since some ''x''{''y''}''z'' families can be ruled out to contain no prime &gt; ''b'' (by covering congruence, algebraic factorization, or combine of them), but it is at least a reasonable conjecture in the absence of evidence to the contrary. Hence, the [[:w:Heuristic argument|heuristic argument]] suggests there are always infinitely many primes in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') if it cannot be ruled out to contain no prime or only contain finitely many primes, by covering congruence, algebraic factorization, or combine of them. However, some families ''x''{''y''}''z'' could not be proven to contain no primes &gt; ''b'' (by covering congruence, algebraic factorization, or combine of them) but no primes &gt; ''b'' could be found in the family, even after searching through numbers with over 100000 digits. In such a case, the only way to proceed is to [[:w:Primality test|test the primality]] of larger and larger numbers of such form and hope a prime is eventually discovered. e.g. the smallest (probable) prime in the family A{3}A in base ''b'' = 13 is A3&lt;sub&gt;592197&lt;/sub&gt;A, its algebraic form is (41×13&lt;sup&gt;592198&lt;/sup&gt;+27)/4, when written in decimal contains 659677 digits (it is only probable prime, i.e. not definitely prime, since technically, probable primality tests were used to show this (which have a ''very'' small chance of making an error, see https://t5k.org/notes/prp_prob.html) because all known primality tests run far too slowly to run on numbers of this size unless either [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] (or both) can be ≥ 1/3 factored).

The numbers in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') are of the form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) for some fixed ''a'', ''b'', ''c'' such that ''a'' ≥ 1, ''b'' ≥ 2 (''b'' is the base), ''c'' ≠ 0, ''gcd''(''a'',''c'') = 1, ''gcd''(''b'',''c'') = 1. Except in the [[:w:Special case|special case]] ''c'' = ±1 and ''gcd''(''a''+''c'',''b''−1) = 1 (the only case which [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] is [[:w:Triviality (mathematics)|trivially]] fully factored), when ''n'' is large the known [[:w:Primality test|primality test]]s for such a number are too inefficient to run (since they are [https://t5k.org/glossary/xpage/OrdinaryPrime.html ordinary primes]). In this case one must resort to a [[:w:Probabilistic algorithm|probable]] primality test such as a [[:w:Miller–Rabin primality test|Miller–Rabin primality test]] or a [[:w:Baillie–PSW primality test|Baillie–PSW primality test]], unless a divisor of the number can be found. Since we are testing many numbers in an [[:w:Exponential growth|exponential sequence]], it is possible to use a sieving process to find divisors rather than using [[:w:Trial division|trial division]].

To do this, we made use of Geoffrey Reynolds' ''srsieve'' software (download: https://pzktupel.de/Software/srsieve_1.1.4.7z). This program uses the [[:w:Baby-step giant-step|baby-step giant-step]] [[:w:Algorithm|algorithm]] to find all primes ''p'' which divide ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'' where ''p'' and ''n'' lie in a [[:w:Interval_(mathematics)|specified range]]. Since this program cannot handle the general case (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) &gt; 1 we only used it to sieve the sequence ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'' for primes ''p'' not dividing ''gcd''(''a''+''c'',''b''−1), and initialized the list of candidates to not include ''n'' for which there is some prime ''p'' dividing ''gcd''(''a''+''c'',''b''−1) for which ''p'' dividing (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1). The program had to be modified slightly to remove a check which would prevent it from running in the case when ''a'', ''b'', and ''c'' were all odd (since then 2 divides ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'', but 2 may not divide (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1)).

Once the numbers with small divisors had been removed, it remained to test the remaining numbers using a probable primality test. For this we used the software ''LLR'' by Jean Penné. (download: http://jpenne.free.fr/index2.html). Although undocumented, it is possible to run this program on numbers of the form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) &gt; 1, so this program required no modifications. A script was also written which allowed one to run ''srsieve'' while ''LLR'' was testing the remaining candidates, so that when a divisor was found by srsieve on a number which had not yet been tested by ''LLR'' it would be removed from the list of candidates.

For the primes &lt; 10&lt;sup&gt;25000&lt;/sup&gt; for the &quot;easy&quot; bases (bases ''b'' with ≤ 150 primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; (base ''b'' = 26 has 83 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 3 unsolved families, base ''b'' = 36 has 75 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 4 unsolved families, base ''b'' = 17 has 99 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 18 unsolved families, base ''b'' = 21 has 80 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 12 unsolved families, base ''b'' = 19 has 201 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 23 unsolved families), i.e. bases *b* = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36), we employed ''CM'' by Andreas Enge (download: https://www.multiprecision.org/cm/download.html), an elliptic curve primality proving implementation.

Currently, the final goal of the Athena problem project is finding the Athena set (i.e. finding all Athena primes) and proving that this set is exactly the Athena set (i.e. proving that these are all Athena primes (including the primality proving for the probable primes)) in all bases 2 ≤ ''b'' ≤ 36, i.e. solving all families in all bases 2 ≤ ''b'' ≤ 36. Solving all (unsolved) families in all bases 2 ≤ ''b'' ≤ 36 (and proving the primality of all probable primes in the sets of all bases 2 ≤ ''b'' ≤ 36) is not possible but we aim to solve many of them (and proving the primality of many of them), at least find a ''probable'' prime for many of them (since the smallest prime in a family may be too large (&gt; 10&lt;sup&gt;25000&lt;/sup&gt;) to be proved primality, unless its *N*−1 or/and *N*+1 can be ≥ 25% factored).

== Data ==

These are the results of the Athena problem in bases 2 ≤ ''b'' ≤ 36 (we stop at base 36 since this base is the maximum base for which it is possible to write the numbers with the [[:w:Symbol|symbol]]s 0, 1, 2, ..., 9 and A, B, C, ..., Z (i.e. the 10 [[:w:Arabic numerals|Arabic numerals]] and the 26 [[:w:Latin script|Latin letters]]): (some large Athena primes are only probable primes, i.e. not definitely primes, since they are too large to be [[:w:Elliptic curve primality|ECPP proved]] and [[:w:Pocklington primality test#Extensions and variants|neither ''N''−1 nor ''N''+1 can be ≥ 1/3 factored]] (Brillhart-Lehmer-Selfridge primality test), all of them pass the [[:w:Baillie–PSW primality test|Baillie–PSW primality test]] and the [[:w:Strong pseudoprime|strong primality test]] (i.e. the [[:w:Miller–Rabin primality test|Miller–Rabin primality test]]) with all prime bases ''p'' ≤ 61, however, all Athena primes &lt; 10&lt;sup&gt;25000&lt;/sup&gt; for bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 36 are definitely primes, most of them &gt; 10&lt;sup&gt;299&lt;/sup&gt; are proven primes with [[:w:Elliptic curve primality|ECPP proving]], others &gt; 10&lt;sup&gt;299&lt;/sup&gt; are proven primes with [[:w:Pocklington primality test#Extensions and variants|''N''−1 or ''N''+1 proving]])

The Athena primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 which are proven primes with ''N''−1 or ''N''+1 proving includes the Athena primes whose ''N''−1 or ''N''+1 is trivially fully factored:

* the 3176th Athena prime in base 13, 81010&lt;sub&gt;415&lt;/sub&gt;1, which equals 17746×13&lt;sup&gt;416&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003590431555, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003590431556&amp;open=ecm
* the 3177th Athena prime in base 13, 8110&lt;sub&gt;435&lt;/sub&gt;1, which equals 1366×13&lt;sup&gt;436&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000002373259109, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000002373259124&amp;open=ecm
* the 3188th Athena prime in base 13, 930&lt;sub&gt;1551&lt;/sub&gt;1, which equals 120×13&lt;sup&gt;1552&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961452, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961453&amp;open=ecm
* the 3191st Athena prime in base 13, 390&lt;sub&gt;6266&lt;/sub&gt;1, which equals 48×13&lt;sup&gt;6267&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961441, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961451&amp;open=ecm
* the 649th Athena prime in base 14, 34D&lt;sub&gt;708&lt;/sub&gt;, which equals 47×14&lt;sup&gt;708&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001540144903, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001540144907&amp;open=ecm
* the 650th Athena prime in base 14, 4D&lt;sub&gt;19698&lt;/sub&gt;, which equals 5×14&lt;sup&gt;19698&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000884560233, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000884560625&amp;open=ecm
* the 2335th Athena prime in base 16, 88F&lt;sub&gt;545&lt;/sub&gt;, which equals 137×16&lt;sup&gt;545&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000413679658, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000413877337&amp;open=ecm
* the 10317th Athena prime in base 17, 5A70&lt;sub&gt;274&lt;/sub&gt;1, which equals 1622×17&lt;sup&gt;275&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003782940709, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003782941930&amp;open=ecm
* the 10359th Athena prime in base 17, 9D0&lt;sub&gt;1067&lt;/sub&gt;1, which equals 166×17&lt;sup&gt;1068&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961369, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961370&amp;open=ecm
* the 10370th Athena prime in base 17, A0&lt;sub&gt;1355&lt;/sub&gt;1, which equals 10×17&lt;sup&gt;1356&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000034167087, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000271866825&amp;open=ecm
* the 10386th Athena prime in base 17, 530&lt;sub&gt;4867&lt;/sub&gt;1, which equals 88×17&lt;sup&gt;4868&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000762660735, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000762660737&amp;open=ecm
* the 10408th Athena prime in base 17, 570&lt;sub&gt;51310&lt;/sub&gt;1, which equals 92×17&lt;sup&gt;51311&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961389, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469616&amp;open=ecm
* the 10412th Athena prime in base 17, 970&lt;sub&gt;166047&lt;/sub&gt;1, which equals 160×17&lt;sup&gt;166048&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (&gt;10&lt;sup&gt;199999&lt;/sup&gt;) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817312&amp;open=ecm
* the 10413th Athena prime in base 17, F70&lt;sub&gt;186767&lt;/sub&gt;1, which equals 262×17&lt;sup&gt;186768&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (&gt;10&lt;sup&gt;199999&lt;/sup&gt;) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817317&amp;open=ecm
* the 3310th Athena prime in base 20, JCJ&lt;sub&gt;629&lt;/sub&gt;, which equals 393×20&lt;sup&gt;629&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001559454258, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001559454271&amp;open=ecm
* the 13373rd Athena prime in base 21, 5D0&lt;sub&gt;19848&lt;/sub&gt;1, which equals 118×21&lt;sup&gt;19849&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000777265872, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469310&amp;open=ecm
* the 3408th Athena prime in base 24, 88N&lt;sub&gt;5951&lt;/sub&gt;, which equals 201×24&lt;sup&gt;5951&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003593275880, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000003593373246&amp;open=ecm
* the 25509th Athena prime in base 28, EB0&lt;sub&gt;405&lt;/sub&gt;1, which equals 403×28&lt;sup&gt;406&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001534442374, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000001534442380&amp;open=ecm
* the 2616th Athena prime in base 30, C0&lt;sub&gt;1022&lt;/sub&gt;1, which equals 12×30&lt;sup&gt;1023&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000785448736, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785448737&amp;open=ecm
* the 2619th Athena prime in base 30, OT&lt;sub&gt;34205&lt;/sub&gt;, which equals 25×30&lt;sup&gt;34205&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000800812865, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000819405041&amp;open=ecm
* the 35237th Athena prime in base 36, P8Z&lt;sub&gt;390&lt;/sub&gt;, which equals 909×36&lt;sup&gt;390&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000764100228, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000764100231&amp;open=ecm

and the Athena primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 whose ''N''−1 or ''N''+1 is ≥ 1/3 factored: (''R''&lt;sub&gt;''n''&lt;/sub&gt;(''b'') means the [[:w:Repunit|repunit]] in base ''b'' with length ''n''), i.e. ''R''&lt;sub&gt;''n''&lt;/sub&gt;(''b'') = (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1), &quot;''S''&lt;sub&gt;''n''&lt;/sub&gt;(''b'')&quot; means ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)

* the 3168th Athena prime in base 13, 9&lt;sub&gt;308&lt;/sub&gt;1, ''N''−1 is 117×''R''&lt;sub&gt;308&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;308&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;308&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=308&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;308&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=308&amp;c0=-&amp;EN=&amp;LM=
* the 3179th Athena prime in base 13, B&lt;sub&gt;563&lt;/sub&gt;C, ''N''−1 is 11×''R''&lt;sub&gt;564&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;564&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;564&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=564&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;564&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=564&amp;c0=-&amp;EN=&amp;LM=
* the 3180th Athena prime in base 13, 1B&lt;sub&gt;576&lt;/sub&gt;, ''N''−1 is 23×''R''&lt;sub&gt;576&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;576&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;576&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=576&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;576&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=576&amp;c0=-&amp;EN=&amp;LM=
* the 10320th Athena prime in base 17, 9&lt;sub&gt;292&lt;/sub&gt;1, ''N''−1 is 153×''R''&lt;sub&gt;292&lt;/sub&gt;(17), thus factor ''N''−1 is equivalent to factor the Cunningham number 17&lt;sup&gt;292&lt;/sup&gt;−1, and for the algebraic factors of 17&lt;sup&gt;292&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=17&amp;Exp=292&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 17&lt;sup&gt;292&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=17&amp;Exp=292&amp;c0=-&amp;EN=&amp;LM=
* the 13304th Athena prime in base 21, 7&lt;sub&gt;230&lt;/sub&gt;1, ''N''−1 is 147×''R''&lt;sub&gt;230&lt;/sub&gt;(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21&lt;sup&gt;230&lt;/sup&gt;−1, and for the algebraic factors of 21&lt;sup&gt;230&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&amp;Exp=230&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 21&lt;sup&gt;230&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&amp;Exp=230&amp;c0=-&amp;EN=&amp;LM=
* the 13355th Athena prime in base 21, 3&lt;sub&gt;1063&lt;/sub&gt;2, ''N''+1 is 3×''R''&lt;sub&gt;1064&lt;/sub&gt;(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21&lt;sup&gt;1064&lt;/sup&gt;−1, and for the algebraic factors of 21&lt;sup&gt;1064&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&amp;Exp=1064&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 21&lt;sup&gt;1064&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&amp;Exp=1064&amp;c0=-&amp;EN=&amp;LM=
* the 25199th Athena prime in base 26, 9K&lt;sub&gt;343&lt;/sub&gt;AP, ''N''+1 is 6370×''R''&lt;sub&gt;344&lt;/sub&gt;(26), thus factor ''N''+1 is equivalent to factor the Cunningham number 26&lt;sup&gt;344&lt;/sup&gt;−1, and for the algebraic factors of 26&lt;sup&gt;344&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&amp;Exp=344&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 26&lt;sup&gt;344&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&amp;Exp=344&amp;c0=-&amp;EN=&amp;LM=
* the 25200th Athena prime in base 26, 8&lt;sub&gt;354&lt;/sub&gt;1, ''N''−1 is 208×''R''&lt;sub&gt;354&lt;/sub&gt;(26), thus factor ''N''−1 is equivalent to factor the Cunningham number 26&lt;sup&gt;354&lt;/sup&gt;−1, and for the algebraic factors of 26&lt;sup&gt;354&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&amp;Exp=354&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 26&lt;sup&gt;354&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&amp;Exp=354&amp;c0=-&amp;EN=&amp;LM=

All numbers are written in base ''b'', [[:w:Senary#Base 36 as senary compression|using A to Z to represent digit values 10 to 35]], &quot;{}&quot; means repeating, e.g. family 12{3}45 means the sequence {1245, 12345, 123345, 1233345, 12333345, 123333345, ...} (where the members are expressed as base ''b'' strings), subscripts are used to indicate repetitions of digits, e.g. 123&lt;sub&gt;4&lt;/sub&gt;567 means 123333567 (all subscripts are written in decimal).

Base 2: 1 Athena prime (the largest of which has 2 digits (it is 11, and its value is 3 in decimal)): {11}

Base 3: 3 Athena primes (the largest of which has 3 digits (it is 111, and its value is 13 in decimal)): {12, 21, 111}

Base 4: 5 Athena primes (the largest of which has 3 digits (it is 221, and its value is 41 in decimal)): {11, 13, 23, 31, 221}

Base 5: 22 Athena primes (the largest of which has 96 digits (it is 10&lt;sub&gt;93&lt;/sub&gt;13, and its algebraic form is 5&lt;sup&gt;95&lt;/sup&gt;+8)): {12, 21, 23, 32, 34, 43, 104, 111, 131, 133, 313, 401, 414, 3101, 10103, 14444, 30301, 33001, 33331, 44441, 300031, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013}

Base 6: 11 Athena primes (the largest of which has 5 digits (it is 40041, and its value is 5209 in decimal)): {11, 15, 21, 25, 31, 35, 45, 51, 4401, 4441, 40041}

Base 7: 71 Athena primes (the largest of which has 17 digits (it is 3&lt;sub&gt;16&lt;/sub&gt;1, and its algebraic form is (7&lt;sup&gt;17&lt;/sup&gt;−5)/2)): {14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 113, 115, 131, 133, 155, 212, 221, 304, 313, 335, 344, 346, 364, 445, 515, 533, 535, 544, 551, 553, 1022, 1051, 1112, 1202, 1211, 1222, 2111, 3031, 3055, 3334, 3503, 3505, 3545, 4504, 4555, 5011, 5455, 5545, 5554, 6034, 6634, 11111, 11201, 30011, 30101, 31001, 31111, 33001, 33311, 35555, 40054, 100121, 150001, 300053, 351101, 531101, 1100021, 33333301, 5100000001, 33333333333333331}

Base 8: 75 Athena primes (the largest of which has 221 digits (it is 4&lt;sub&gt;220&lt;/sub&gt;7, and its algebraic form is (4×8&lt;sup&gt;221&lt;/sup&gt;+17)/7)): {13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 107, 111, 117, 141, 147, 161, 177, 225, 255, 301, 343, 361, 401, 407, 417, 431, 433, 463, 467, 471, 631, 643, 661, 667, 701, 711, 717, 747, 767, 3331, 3411, 4043, 4443, 4611, 5205, 6007, 6101, 6441, 6477, 6707, 6777, 7461, 7641, 47777, 60171, 60411, 60741, 444641, 500025, 505525, 3344441, 4444477, 5500525, 5550525, 55555025, 444444441, 744444441, 77774444441, 7777777777771, 555555555555525, 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447}

Base 9: 151 Athena primes (the largest of which has 1161 digits (it is 30&lt;sub&gt;1158&lt;/sub&gt;11, and its algebraic form is 3×9&lt;sup&gt;1160&lt;/sup&gt;+10)): {12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 117, 131, 135, 151, 155, 175, 177, 238, 272, 308, 315, 331, 337, 355, 371, 375, 377, 438, 504, 515, 517, 531, 537, 557, 564, 601, 638, 661, 702, 711, 722, 735, 737, 751, 755, 757, 771, 805, 838, 1011, 1015, 1101, 1701, 2027, 2207, 3017, 3057, 3101, 3501, 3561, 3611, 3688, 3868, 5035, 5051, 5071, 5101, 5501, 5554, 5705, 5707, 7017, 7075, 7105, 7301, 8535, 8544, 8555, 8854, 20777, 22227, 22777, 30161, 33388, 50161, 50611, 53335, 55111, 55535, 55551, 57061, 57775, 70631, 71007, 77207, 100037, 100071, 100761, 105007, 270707, 301111, 305111, 333035, 333385, 333835, 338885, 350007, 500075, 530005, 555611, 631111, 720707, 2770007, 3030335, 7776662, 30300005, 30333335, 38333335, 51116111, 70000361, 300030005, 300033305, 351111111, 1300000007, 5161111111, 8333333335, 300000000035, 311111111161, 544444444444, 2000000000007, 5700000000001, 7270000000007, 88888888833335, 100000000000507, 5111111111111161, 7277777777777777707, 8888888888888888888335, 30000000000000000000051, 1000000000000000000000000057, 56111111111111111111111111111111111111, 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666662, 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777707, 300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011}

Base 10: 77 Athena primes (the largest of which has 31 digits (it is 50&lt;sub&gt;28&lt;/sub&gt;27, and its algebraic form is 5×10&lt;sup&gt;30&lt;/sup&gt;+27)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}

Base 11: 1068 Athena (probable) primes (including 1 unproven probable prime: 57&lt;sub&gt;62668&lt;/sub&gt;), the largest of which has 62669 digits (it is 57&lt;sub&gt;62668&lt;/sub&gt;, and its algebraic form is (57×11&lt;sup&gt;62668&lt;/sup&gt;−7)/10), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel11 Data of Athena (probable) primes base 11]

Base 12: 106 Athena primes (the largest of which has 42 digits (it is 40&lt;sub&gt;39&lt;/sub&gt;77, and its algebraic form is 4×12&lt;sup&gt;41&lt;/sup&gt;+91)): {11, 15, 17, 1B, 25, 27, 31, 35, 37, 3B, 45, 4B, 51, 57, 5B, 61, 67, 6B, 75, 81, 85, 87, 8B, 91, 95, A7, AB, B5, B7, 221, 241, 2A1, 2B1, 2BB, 401, 421, 447, 471, 497, 565, 655, 665, 701, 70B, 721, 747, 771, 77B, 797, 7A1, 7BB, 907, 90B, 9BB, A41, B21, B2B, 2001, 200B, 202B, 222B, 229B, 292B, 299B, 4441, 4707, 4777, 6A05, 6AA5, 729B, 7441, 7B41, 929B, 9777, 992B, 9947, 997B, 9997, A0A1, A201, A605, A6A5, AA65, B001, B0B1, BB01, BB41, 600A5, 7999B, 9999B, AAAA1, B04A1, B0B9B, BAA01, BAAA1, BB09B, BBBB1, 44AAA1, A00065, BBBAA1, AAA0001, B00099B, AA000001, BBBBBB99B, B0000000000000000000000000009B, 400000000000000000000000000000000000000077}

Base 13: 3197 Athena (probable) primes (including 4 unproven probable primes: C5&lt;sub&gt;23755&lt;/sub&gt;C, 80&lt;sub&gt;32017&lt;/sub&gt;111, 95&lt;sub&gt;197420&lt;/sub&gt;, A3&lt;sub&gt;592197&lt;/sub&gt;A), the largest of which has 592199 digits (it is A3&lt;sub&gt;592197&lt;/sub&gt;A, and its algebraic form is (41×13&lt;sup&gt;592198&lt;/sup&gt;+27)/4), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel13 Data of Athena (probable) primes base 13]

Base 14: 650 Athena primes, the largest of which has 19699 digits (it is 4D&lt;sub&gt;19698&lt;/sub&gt;, and its algebraic form is 5×14&lt;sup&gt;19698&lt;/sup&gt;−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel14 Data of Athena primes base 14]

Base 15: 1284 Athena primes, the largest of which has 157 digits (it is 7&lt;sub&gt;155&lt;/sub&gt;97, and its algebraic form is (15&lt;sup&gt;157&lt;/sup&gt;+59)/2), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel15 Data of Athena primes base 15]

Base 16: 2347 Athena (probable) primes (including 3 unproven probable primes: DB&lt;sub&gt;32234&lt;/sub&gt;, 4&lt;sub&gt;72785&lt;/sub&gt;DD, 3&lt;sub&gt;116137&lt;/sub&gt;AF), the largest of which has 116139 digits (it is 3&lt;sub&gt;116137&lt;/sub&gt;AF, and its algebraic form is (16&lt;sup&gt;116139&lt;/sup&gt;+619)/5), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel16 Data of Athena (probable) primes base 16]

Base 17: 10415 known Athena (probable) primes (including many unproven probable primes) and 12 unsolved families (1{7}, 1F{0}7, 4{7}A, 70F{0}D, 8{B}9, 9{5}9, A{D}F, B{0}B3, {B}E9, {B}EE, F1{9}, FD0{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel17 Data of known Athena (probable) primes base 17]

Base 18: 549 Athena primes, the largest of which has 6271 digits (it is C0&lt;sub&gt;6268&lt;/sub&gt;C5, and its algebraic form is 12×18&lt;sup&gt;6270&lt;/sup&gt;+221), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel18 Data of Athena primes base 18]

Base 19: 31417 known Athena (probable) primes (including many unproven probable primes) and 17 unsolved families (4B5{0}H, {5}3, 5{H}05, 5{H}0H, 5{H}5, 66{B}, 71{0}177, 7AF{0}H, 97{0}3, C{H}C, EE1{6}, F{7}5, F{B}G, F{D}F, H0F{0}7A, HB{0}5B5, II{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel19 Data of known Athena (probable) primes base 19]

Base 20: 3314 Athena primes, the largest of which has 6271 digits (it is G0&lt;sub&gt;6269&lt;/sub&gt;D, and its algebraic form is 16×20&lt;sup&gt;6270&lt;/sup&gt;+13), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel20 Data of Athena primes base 20]

Base 21: 13386 known Athena (probable) primes (including many unproven probable primes) and 8 unsolved families (5{0}DJ, {9}D, B3{0}EB, B{H}6H, C{F}0K, {F}35, G{0}FK, H{0}7771, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel21 Data of known Athena (probable) primes base 21]

Base 22: 8003 Athena (probable) primes (including 1 unproven probable prime: BK&lt;sub&gt;22001&lt;/sub&gt;5), the largest of which has 22003 digits (it is BK&lt;sub&gt;22001&lt;/sub&gt;5, and its algebraic form is (251×22&lt;sup&gt;22002&lt;/sup&gt;−335)/21), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel22 Data of Athena (probable) primes base 22]

Base 23: 65178 known Athena (probable) primes (including many unproven probable primes) and 87 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel23 Data of known Athena (probable) primes base 23] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left23 Data of unsolved families for Athena problem base 23]

Base 24: 3409 Athena primes, the largest of which has 8134 digits (it is N00N&lt;sub&gt;8129&lt;/sub&gt;LN, and its algebraic form is 13249×24&lt;sup&gt;8131&lt;/sup&gt;−49), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel24 Data of Athena primes base 24]

Base 25: 133639 known Athena (probable) primes (including many unproven probable primes) and 85 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel25 Data of known Athena (probable) primes base 25] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left25 Data of unsolved families for Athena problem base 25]

Base 26: 25256 known Athena (probable) primes (including 7 unproven probable primes: 5&lt;sub&gt;19391&lt;/sub&gt;6F, 7&lt;sub&gt;20279&lt;/sub&gt;OL, LD0&lt;sub&gt;20975&lt;/sub&gt;7, 6K&lt;sub&gt;23300&lt;/sub&gt;5, J0&lt;sub&gt;44303&lt;/sub&gt;KCB, M0&lt;sub&gt;61186&lt;/sub&gt;2BB, 85M&lt;sub&gt;197060&lt;/sub&gt;B) and 3 unsolved families ({A}6F, {H}MH, {I}GL, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel26 Data of known Athena (probable) primes base 26]

Base 27: 102852 known Athena (probable) primes (including many unproven probable primes) and 44 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel27 Data of known Athena (probable) primes base 27] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left27 Data of unsolved families for Athena problem base 27]

Base 28: 25528 known Athena (probable) primes (including 3 unproven probable primes: N6&lt;sub&gt;24051&lt;/sub&gt;LR, 5OA&lt;sub&gt;31238&lt;/sub&gt;F, O4O&lt;sub&gt;94535&lt;/sub&gt;9) and 1 unsolved family (O{A}F, no primes or probable primes with length ≤ 900000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel28 Data of known Athena (probable) primes base 28]

Base 29: 355242 known Athena (probable) primes (including many unproven probable primes) and 125 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel29 Data of known Athena (probable) primes base 29] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left29 Data of unsolved families for Athena problem base 29]

Base 30: 2619 Athena (probable) primes (including 1 unproven probable prime: I0&lt;sub&gt;24608&lt;/sub&gt;D), the largest of which has 34206 digits (it is OT&lt;sub&gt;34205&lt;/sub&gt;, and its algebraic form is 25×30&lt;sup&gt;34205&lt;/sup&gt;−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel30 Data of Athena (probable) primes base 30]

Base 31: 569323 known Athena (probable) primes (including many unproven probable primes) and 77 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel31 Data of known Athena (probable) primes base 31] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left31 Data of unsolved families for Athena problem base 31]

Base 32: 168882 known Athena (probable) primes (including many unproven probable primes) and 120 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel32 Data of known Athena (probable) primes base 32] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left32 Data of unsolved families for Athena problem base 32]

Base 33: 280012 known Athena (probable) primes (including many unproven probable primes) and 81 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel33 Data of known Athena (probable) primes base 33] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left33 Data of unsolved families for Athena problem base 33]

Base 34: 184785 known Athena (probable) primes (including many unproven probable primes) and 47 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel34 Data of known Athena (probable) primes base 34] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left34 Data of unsolved families for Athena problem base 34]

Base 35: 720002 known Athena (probable) primes (including many unproven probable primes) and 60 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel35 Data of known Athena (probable) primes base 35] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left35 Data of unsolved families for Athena problem base 35]

Base 36: 35286 known Athena (probable) primes (including 3 unproven probable primes: 7K&lt;sub&gt;26567&lt;/sub&gt;Z, S0&lt;sub&gt;75007&lt;/sub&gt;8H, P&lt;sub&gt;81993&lt;/sub&gt;SZ) and 4 unsolved families (B{0}EUV, HM{0}N, N{0}YYN, O{L}Z, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel36 Data of known Athena (probable) primes base 36]

== Condensed table for bases 2 ≤ ''b'' ≤ 36 ==

{|class=&quot;wikitable&quot;
||''b''||number of Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||base-''b'' form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' (write &quot;''d''&lt;sub&gt;''n''&lt;/sub&gt;&quot; if there are 5 or more (''n'') consecutive same digits ''d'')||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' in decimal||algebraic ((''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1)) form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||''factordb'' entry of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' written in base ''b'' (use lower case letters instead of upper case letters)||number of unsolved families in the Athena problem in base ''b'' (all of these left families are linear families)||searching limit of length for the unsolved families in the Athena problem in base ''b'' (if there are different searching limits for the unsolved families in the Athena problem in base ''b'', choose the lowest searching limit)||
|-
||2||1||11||2||1||3||http://factordb.com/index.php?id=3&amp;open=ecm||http://factordb.com/index.php?showid=3&amp;base=2||0||–||
|-
||3||3||111&lt;br&gt;21&lt;br&gt;12||3&lt;br&gt;2&lt;br&gt;2||2&lt;br&gt;1&lt;br&gt;1||13&lt;br&gt;7&lt;br&gt;5||http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=7&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=5&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=13&amp;base=3&lt;br&gt;http://factordb.com/index.php?showid=7&amp;base=3&lt;br&gt;http://factordb.com/index.php?showid=5&amp;base=3&lt;nowiki/&gt;||0||–||
|-
||4||5||221&lt;br&gt;31&lt;br&gt;23&lt;br&gt;13&lt;br&gt;11||3&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;1&lt;br&gt;1||41&lt;br&gt;13&lt;br&gt;11&lt;br&gt;7&lt;br&gt;5||http://factordb.com/index.php?id=41&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=11&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=7&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=5&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=41&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=13&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=11&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=7&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=5&amp;base=4&lt;nowiki/&gt;||0||–||
|-
||5||22||10&lt;sub&gt;93&lt;/sub&gt;13&lt;br&gt;300031&lt;br&gt;44441&lt;br&gt;33331&lt;br&gt;33001&lt;br&gt;30301&lt;br&gt;14444&lt;br&gt;10103&lt;br&gt;3101&lt;br&gt;414||96&lt;br&gt;6&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;4&lt;br&gt;3||67&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;3&lt;br&gt;3&lt;br&gt;3||5&lt;sup&gt;95&lt;/sup&gt;+8&lt;br&gt;9391&lt;br&gt;3121&lt;br&gt;2341&lt;br&gt;2251&lt;br&gt;1951&lt;br&gt;1249&lt;br&gt;653&lt;br&gt;401&lt;br&gt;109||http://factordb.com/index.php?id=1100000000034686071&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=9391&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=3121&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2341&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2251&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1951&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1249&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=653&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=401&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=109&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000000034686071&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=9391&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=3121&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=2341&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=2251&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=1951&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=1249&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=653&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=401&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=109&amp;base=5&lt;nowiki/&gt;||0||–||
|-
||6||11||40041&lt;br&gt;4441&lt;br&gt;4401&lt;br&gt;51&lt;br&gt;45&lt;br&gt;35&lt;br&gt;31&lt;br&gt;25&lt;br&gt;21&lt;br&gt;15||5&lt;br&gt;4&lt;br&gt;4&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||5209&lt;br&gt;1033&lt;br&gt;1009&lt;br&gt;31&lt;br&gt;29&lt;br&gt;23&lt;br&gt;19&lt;br&gt;17&lt;br&gt;13&lt;br&gt;11||http://factordb.com/index.php?id=5209&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1033&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1009&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=31&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=29&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=23&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=19&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=17&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=11&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=5209&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=1033&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=1009&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=31&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=29&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=23&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=19&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=17&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=13&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=11&amp;base=6&lt;nowiki/&gt;||0||–||
|-
||7||71||3&lt;sub&gt;16&lt;/sub&gt;1&lt;br&gt;510&lt;sub&gt;7&lt;/sub&gt;1&lt;br&gt;3&lt;sub&gt;6&lt;/sub&gt;01&lt;br&gt;1100021&lt;br&gt;531101&lt;br&gt;351101&lt;br&gt;300053&lt;br&gt;150001&lt;br&gt;100121&lt;br&gt;40054||17&lt;br&gt;10&lt;br&gt;8&lt;br&gt;7&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;5||15&lt;br&gt;9&lt;br&gt;7&lt;br&gt;6&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;4||(7&lt;sup&gt;17&lt;/sup&gt;−5)/2&lt;br&gt;36×7&lt;sup&gt;8&lt;/sup&gt;+1&lt;br&gt;(7&lt;sup&gt;8&lt;/sup&gt;−47)/2&lt;br&gt;134471&lt;br&gt;91631&lt;br&gt;62819&lt;br&gt;50459&lt;br&gt;28813&lt;br&gt;16871&lt;br&gt;9643||http://factordb.com/index.php?id=116315256993601&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=207532837&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2882377&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=134471&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=91631&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=62819&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=50459&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=28813&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=16871&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=9643&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=116315256993601&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=207532837&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=2882377&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=134471&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=91631&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=62819&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=50459&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=28813&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=16871&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=9643&amp;base=7&lt;nowiki/&gt;||0||–||
|-
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||33||280012~280093||DP&lt;sub&gt;95093&lt;/sub&gt;M5&lt;br&gt;HJ0&lt;sub&gt;94295&lt;/sub&gt;J&lt;br&gt;90&lt;sub&gt;93597&lt;/sub&gt;Q&lt;br&gt;9F0&lt;sub&gt;93157&lt;/sub&gt;N&lt;br&gt;7&lt;sub&gt;89449&lt;/sub&gt;333H&lt;br&gt;K3&lt;sub&gt;80751&lt;/sub&gt;6K&lt;br&gt;D&lt;sub&gt;80107&lt;/sub&gt;9UD&lt;br&gt;VFU&lt;sub&gt;72204&lt;/sub&gt;FK&lt;br&gt;J&lt;sub&gt;68715&lt;/sub&gt;2BJ&lt;br&gt;DF0&lt;sub&gt;68367&lt;/sub&gt;J||95096&lt;br&gt;94298&lt;br&gt;93599&lt;br&gt;93160&lt;br&gt;89453&lt;br&gt;80754&lt;br&gt;80110&lt;br&gt;72208&lt;br&gt;68718&lt;br&gt;68370||144405&lt;br&gt;143193&lt;br&gt;142131&lt;br&gt;141465&lt;br&gt;135835&lt;br&gt;122626&lt;br&gt;121648&lt;br&gt;109649&lt;br&gt;104350&lt;br&gt;103821||(441×33&lt;sup&gt;95095&lt;/sup&gt;−3833)/32&lt;br&gt;580×33&lt;sup&gt;94296&lt;/sup&gt;+19&lt;br&gt;9×33&lt;sup&gt;93598&lt;/sup&gt;+26&lt;br&gt;312×33&lt;sup&gt;93158&lt;/sup&gt;+23&lt;br&gt;(7×33&lt;sup&gt;89453&lt;/sup&gt;−4743239)/32&lt;br&gt;(643×33&lt;sup&gt;80753&lt;/sup&gt;+3709)/32&lt;br&gt;(13×33&lt;sup&gt;80110&lt;/sup&gt;−121453)/32&lt;br&gt;(16623×33&lt;sup&gt;72206&lt;/sup&gt;−8095)/16&lt;br&gt;(19×33&lt;sup&gt;68718&lt;/sup&gt;−600883)/32&lt;br&gt;444×33&lt;sup&gt;68368&lt;/sup&gt;+19||http://factordb.com/index.php?id=1100000005652348775&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652362811&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652375073&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652389776&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652430746&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652446200&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652461592&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614764298&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614770536&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614784274&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000005652348775&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652362811&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652375073&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652389776&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652430746&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652446200&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652461592&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614764298&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614770536&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614784274&amp;base=33&lt;nowiki/&gt;||81||100000||
|-
||34||184785~184832||GFGC&lt;sub&gt;99996&lt;/sub&gt;5&lt;br&gt;90&lt;sub&gt;97950&lt;/sub&gt;FJ&lt;br&gt;NM0&lt;sub&gt;85218&lt;/sub&gt;KX&lt;br&gt;F&lt;sub&gt;83189&lt;/sub&gt;H2HP&lt;br&gt;P&lt;sub&gt;79441&lt;/sub&gt;444P&lt;br&gt;6&lt;sub&gt;77027&lt;/sub&gt;8X&lt;br&gt;XQIQ&lt;sub&gt;72241&lt;/sub&gt;D&lt;br&gt;T&lt;sub&gt;66530&lt;/sub&gt;IF&lt;br&gt;4&lt;sub&gt;66152&lt;/sub&gt;B&lt;br&gt;2EEC&lt;sub&gt;66039&lt;/sub&gt;7||100000&lt;br&gt;97953&lt;br&gt;85222&lt;br&gt;83193&lt;br&gt;79445&lt;br&gt;77029&lt;br&gt;72245&lt;br&gt;66532&lt;br&gt;66153&lt;br&gt;66043||153148&lt;br&gt;150013&lt;br&gt;130516&lt;br&gt;127408&lt;br&gt;121669&lt;br&gt;117968&lt;br&gt;110642&lt;br&gt;101893&lt;br&gt;101312&lt;br&gt;101143||(209246×34&lt;sup&gt;99997&lt;/sup&gt;−81)/11&lt;br&gt;9×34&lt;sup&gt;97952&lt;/sup&gt;+529&lt;br&gt;804×34&lt;sup&gt;85220&lt;/sup&gt;+713&lt;br&gt;(5×34&lt;sup&gt;83193&lt;/sup&gt;+700233)/11&lt;br&gt;(25×34&lt;sup&gt;79445&lt;/sup&gt;−28062367)/33&lt;br&gt;(2×34&lt;sup&gt;77029&lt;/sup&gt;+1043)/11&lt;br&gt;(1288676×34&lt;sup&gt;72242&lt;/sup&gt;−455)/33&lt;br&gt;(29×34&lt;sup&gt;66532&lt;/sup&gt;−12833)/33&lt;br&gt;(4×34&lt;sup&gt;66153&lt;/sup&gt;+227)/33&lt;br&gt;(30826×34&lt;sup&gt;66040&lt;/sup&gt;−59)/11||http://factordb.com/index.php?id=1100000004702891268&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702894713&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702900996&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702910376&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702913746&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702918600&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399656529&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399657696&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399658651&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399659716&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000004702891268&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702894713&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702900996&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702910376&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702913746&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702918600&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399656529&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399657696&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399658651&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399659716&amp;base=34&lt;nowiki/&gt;||47||100000||
|-
||35||720002~720062||N0N&lt;sub&gt;99971&lt;/sub&gt;9&lt;br&gt;V0&lt;sub&gt;83669&lt;/sub&gt;E73&lt;br&gt;N&lt;sub&gt;81563&lt;/sub&gt;K7N&lt;br&gt;BJ0&lt;sub&gt;81279&lt;/sub&gt;N&lt;br&gt;J0&lt;sub&gt;80062&lt;/sub&gt;FUH&lt;br&gt;43V&lt;sub&gt;79754&lt;/sub&gt;&lt;br&gt;9&lt;sub&gt;76600&lt;/sub&gt;K3&lt;br&gt;LB&lt;sub&gt;71366&lt;/sub&gt;PB&lt;br&gt;Q&lt;sub&gt;64150&lt;/sub&gt;H&lt;br&gt;50&lt;sub&gt;63397&lt;/sub&gt;5R||99974&lt;br&gt;83673&lt;br&gt;81566&lt;br&gt;81282&lt;br&gt;80066&lt;br&gt;79756&lt;br&gt;76602&lt;br&gt;71369&lt;br&gt;64151&lt;br&gt;63400||154367&lt;br&gt;129197&lt;br&gt;125944&lt;br&gt;125505&lt;br&gt;123628&lt;br&gt;123148&lt;br&gt;118279&lt;br&gt;110199&lt;br&gt;99054&lt;br&gt;97894||(27393×35&lt;sup&gt;99972&lt;/sup&gt;−499)/34&lt;br&gt;31×35&lt;sup&gt;83672&lt;/sup&gt;+17398&lt;br&gt;(23×35&lt;sup&gt;81566&lt;/sup&gt;−144013)/34&lt;br&gt;404×35&lt;sup&gt;81280&lt;/sup&gt;+23&lt;br&gt;19×35&lt;sup&gt;80065&lt;/sup&gt;+19442&lt;br&gt;(4893×35&lt;sup&gt;79754&lt;/sup&gt;−31)/34&lt;br&gt;(9×35&lt;sup&gt;76602&lt;/sup&gt;+12877)/34&lt;br&gt;(725×35&lt;sup&gt;71368&lt;/sup&gt;+16649)/34&lt;br&gt;(13×35&lt;sup&gt;64151&lt;/sup&gt;−166)/17&lt;br&gt;5×35&lt;sup&gt;63399&lt;/sup&gt;+202||http://factordb.com/index.php?id=1100000008248342445&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248353306&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248375642&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248397018&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248412468&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248418540&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248423670&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192119974&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192126630&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192129294&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000008248342445&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248353306&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248375642&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248397018&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248412468&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248418540&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248423670&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192119974&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192126630&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192129294&amp;base=35&lt;nowiki/&gt;||60||100000||
|-
||36||35286~35290||P&lt;sub&gt;81993&lt;/sub&gt;SZ&lt;br&gt;S0&lt;sub&gt;75007&lt;/sub&gt;8H&lt;br&gt;7K&lt;sub&gt;26567&lt;/sub&gt;Z&lt;br&gt;J&lt;sub&gt;10117&lt;/sub&gt;LJ&lt;br&gt;VL0&lt;sub&gt;7258&lt;/sub&gt;J&lt;br&gt;EO0&lt;sub&gt;6177&lt;/sub&gt;V&lt;br&gt;FZ&lt;sub&gt;5777&lt;/sub&gt;3P&lt;br&gt;T09&lt;sub&gt;4618&lt;/sub&gt;1&lt;br&gt;RY&lt;sub&gt;4562&lt;/sub&gt;H&lt;br&gt;OZ&lt;sub&gt;3932&lt;/sub&gt;AZ||81995&lt;br&gt;75010&lt;br&gt;26569&lt;br&gt;10119&lt;br&gt;7261&lt;br&gt;6180&lt;br&gt;5780&lt;br&gt;4621&lt;br&gt;4564&lt;br&gt;3935||127609&lt;br&gt;116739&lt;br&gt;41349&lt;br&gt;15748&lt;br&gt;11301&lt;br&gt;9618&lt;br&gt;8996&lt;br&gt;7192&lt;br&gt;7103&lt;br&gt;6124||(5×36&lt;sup&gt;81995&lt;/sup&gt;+821)/7&lt;br&gt;28×36&lt;sup&gt;75009&lt;/sup&gt;+305&lt;br&gt;(53×36&lt;sup&gt;26568&lt;/sup&gt;+101)/7&lt;br&gt;(19×36&lt;sup&gt;10119&lt;/sup&gt;+2501)/35&lt;br&gt;1137×36&lt;sup&gt;7259&lt;/sup&gt;+19&lt;br&gt;528×36&lt;sup&gt;6178&lt;/sup&gt;+31&lt;br&gt;16×36&lt;sup&gt;5779&lt;/sup&gt;−1163&lt;br&gt;(36549×36&lt;sup&gt;4619&lt;/sup&gt;−289)/35&lt;br&gt;(979×36&lt;sup&gt;4563&lt;/sup&gt;−629)/35&lt;br&gt;25×36&lt;sup&gt;3934&lt;/sup&gt;−901||http://factordb.com/index.php?id=1100000002394962083&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004020085177&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003896952461&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362491&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362489&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362488&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362487&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362486&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362485&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000000840634476&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000002394962083&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000004020085177&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003896952461&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362491&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362489&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362488&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362487&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362486&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362485&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000000840634476&amp;base=36&lt;nowiki/&gt;||4||200000||
|}

== The fully proof of Athena problem in decimal (base ''b'' = 10) ==

'''Bold''' for the Athena primes, ''x'' ◁ ''y'' means ''x'' is a subsequence of ''y''.

Assume ''p'' is a prime &gt; 10, and the last digit of ''p'' must lie in {1,3,7,9}.

Case 1: ''p'' ends with 1.

In this case we can write ''p'' = ''x''1. If ''x'' contains 1, 3, 4, 6, or 7, then (respectively) '''11''' ◁ ''p'', '''31''' ◁ ''p'', '''41''' ◁ ''p'', '''61''' ◁ ''p'', or '''71''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 8, or 9.

Case 1.1: ''p'' begins with 2.

In this case we can write ''p'' = 2''y''1. If 5 ◁ ''y'', then '''251''' ◁ ''p''. If 8 ◁ ''y'', then '''281''' ◁ ''p''. If 9 ◁ ''y'', then 29 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2.

If 22 ◁ ''y'', then '''2221''' ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's.

If ''y'' contains no 2's, then ''p'' ∈ 2{0}1. But then, since the sum of the digits of ''p'' is 3, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' contains exactly one 2, then we can write ''p'' = 2''z''2''w''1, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''20201''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty.

If ''z'' is empty, then ''p'' ∈ 22{0}1, and the smallest prime ''p'' ∈ 22{0}1 is '''22000001'''.

If ''w'' is empty, then ''p'' ∈ 2{0}21, and the smallest prime ''p'' ∈ 2{0}21 is '''20021'''.

Case 1.2: ''p'' begins with 5.

In this case we can write ''p'' = 5''y''1. If 2 ◁ ''y'', then '''521''' ◁ ''p''. If 9 ◁ ''y'', then 59 ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 5, or 8.

If 05 ◁ ''y'', then '''5051''' ◁ ''p''. If 08 ◁ ''y'', then '''5081''' ◁ ''p''. If 50 ◁ ''y'', then '''5501''' ◁ ''p''. If 58 ◁ ''y'', then '''5581''' ◁ ''p''. If 80 ◁ ''y'', then '''5801''' ◁ ''p''. If 85 ◁ ''y'', then '''5851''' ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ {5} ∪ {8}.

If ''y'' ∈ {0}, then ''p'' ∈ 5{0}1. But then, since the sum of the digits of ''p'' is 6, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' ∈ {5}, then ''p'' ∈ 5{5}1, and the smallest prime ''p'' ∈ 5{5}1 is '''555555555551'''.

If ''y'' ∈ {8}, since if 88 ◁ ''y'', then 881 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'',8}, and thus ''p'' ∈ {51,581}, but 51 and 581 are both composite.

Case 1.3: ''p'' begins with 8.

In this case we can write p = 8''y''1. If 2 ◁ ''y'', then '''821''' ◁ ''p''. If 8 ◁ ''y'', then '''881''' ◁ ''p''. If 9 ◁ ''y'', then 89 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 5.

If 50 ◁ ''y'', then '''8501''' ◁ ''p''. Hence we may assume y ∈ {0}{5}.

If 005 ◁ ''y'', then '''80051''' ◁ p. Hence we may assume y ∈ {0} ∪ {5} ∪ 0{5}.

If y ∈ {0}, then ''p'' ∈ 8{0}1. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime.

If y ∈ {5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'', 5, 55, 555, 5555, 55555, 555555, 5555555, 55555555, 555555555, 5555555555}, and thus ''p'' ∈ {81, 851, 8551, 85551, 855551, 8555551, 85555551, 855555551, 8555555551, 85555555551, 855555555551}, but all of these numbers are composite.

If y ∈ 0{5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {0, 05, 055, 0555, 05555, 055555, 0555555, 05555555, 055555555, 0555555555, 05555555555}, and thus ''p'' ∈ {801, 8051, 80551, 805551, 8055551, 80555551, 805555551, 8055555551, 80555555551, 805555555551, 8055555555551}, and of these numbers only 80555551 and 8055555551 are primes, but 80555551 ◁ 8055555551, thus only '''80555551''' is a minimal element.

Case 1.4: ''p'' begins with 9.

In this case we can write p = 9''y''1. If 9 ◁ ''y'', then '''991''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 2, 5, or 8.

If 00 ◁ ''y'', then '''9001''' ◁ ''p''. If 22 ◁ ''y'', then '''9221''' ◁ ''p''. If 55 ◁ ''y'', then '''9551''' ◁ ''p''. If 88 ◁ ''y'', then 881 ◁ ''p''. Hence we may assume ''y'' contains at most one 0, at most one 2, at most one 5, and at most one 8.

If ''y'' only contains at most one 0 and does not contain any of {2,5,8}, then ''y'' ∈ {''𝜆'',0}, and thus ''p'' ∈ {91,901}, but 91 and 901 are both composite. If ''y'' only contains at most one 0 and only one of {2,5,8}, then the sum of the digits of ''p'' is divisible by 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume ''y'' contains at least two of {2,5,8}.

If 25 ◁ ''y'', then 251 ◁ ''p''. If 28 ◁ ''y'', then 281 ◁ ''p''. If 52 ◁ ''y'', then 521 ◁ ''p''. If 82 ◁ ''y'', then 821 ◁ ''p''. Hence we may assume ''y'' contains no 2's (since if ''y'' contains 2, then ''y'' cannot contain either 5's or 8's, which is a contradiction).

If 85 ◁ ''y'', then '''9851''' ◁ ''p''. Hence we may assume ''y'' ∈ {58,580,508,058}, and thus ''p'' ∈ {9581,95801,95081,90581}, and of these numbers only 95801 is prime, but 95801 is not a minimal element since 5801 ◁ 95801.

Case 2: ''p'' ends with 3.

In this case we can write p = ''x''3. If ''x'' contains 1, 2, 4, 5, 7, or 8, then (respectively) '''13''' ◁ ''p'', '''23''' ◁ ''p'', '''43''' ◁ ''p'', '''53''' ◁ ''p'', '''73''' ◁ ''p'', or '''83''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime.

Case 3: ''p'' ends with 7.

In this case we can write ''p'' = ''x''7. If ''x'' contains 1, 3, 4, 6, or 9, then (respectively) '''17''' ◁ ''p'', '''37''' ◁ ''p'', '''47''' ◁ ''p'', '''67''' ◁ ''p'', or '''97''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 7, or 8.

Case 3.1: ''p'' begins with 2.

In this case we can write ''p'' = 2''y''7. If 2 ◁ ''y'', then '''227''' ◁ ''p''. If 5 ◁ ''y'', then '''257''' ◁ ''p''. If 7 ◁ ''y'', then '''277''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 8.

If 08 ◁ ''y'', then '''2087''' ◁ ''p''. If 88 ◁ ''y'', then 887 ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ 8{0}.

If ''y'' ∈ {0}, then ''p'' ∈ 2{0}7. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime.

If y ∈ 8{0}, then ''p'' ∈ 28{0}7. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 40&lt;sub&gt;''n''&lt;/sub&gt;1 = 280&lt;sub&gt;''n''&lt;/sub&gt;7.

Case 3.2: ''p'' begins with 5.

In this case we can write ''p'' = 5''y''7. If 5 ◁ ''y'', then '''557''' ◁ ''p''. If 7 ◁ ''y'', then '''577''' ◁ ''p''. If 8 ◁ ''y'', then '''587''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2.

If 22 ◁ ''y'', then 227 ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's.

If ''y'' contains no 2's, then ''p'' ∈ 5{0}7. But then, since the sum of the digits of ''p'' is 12, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' contains exactly one 2, then we can write ''p'' = 5''z''2''w''7, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''50207''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty.

If ''z'' is empty, then ''p'' ∈ 52{0}7, and the smallest prime ''p'' ∈ 52{0}7 is '''5200007'''.

If ''w'' is empty, then ''p'' ∈ 5{0}27, and the smallest prime ''p'' ∈ 5{0}27 is '''5000000000000000000000000000027'''.

Case 3.3: ''p'' begins with 7.

In this case we can write ''p'' = 7''y''7. If 2 ◁ ''y'', then '''727''' ◁ ''p''. If 5 ◁ ''y'', then '''757''' ◁ ''p''. If 8 ◁ ''y'', then '''787''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 7, and thus all digits of ''p'' are 0 or 7. But then, since the digits of ''p'' all have a common factor 7, ''p'' is divisible by 7, so ''p'' cannot be prime.

Case 3.4: ''p'' begins with 8.

In this case we can write ''p'' = 8''y''7. If 2 ◁ ''y'', then '''827''' ◁ ''p''. If 5 ◁ ''y'', then '''857''' ◁ ''p''. If 7 ◁ ''y'', then '''877''' ◁ ''p''. If 8 ◁ ''y'', then '''887''' ◁ ''p''. Hence we may assume ''y'' ∈ {0}, and thus ''p'' ∈ 8{0}7. But then, since the sum of the digits of ''p'' is 15, ''p'' is divisible by 3, so ''p'' cannot be prime.

Case 4: ''p'' ends with 9.

In this case we can write ''p'' = ''x''9. If ''x'' contains 1, 2, 5, 7, or 8, then (respectively) '''19''' ◁ ''p'', '''29''' ◁ ''p'', '''59''' ◁ ''p'', '''79''' ◁ ''p'', or '''89''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 4, 6, or 9.

If 44 ◁ ''x'', then '''449''' ◁ ''p''. Hence we may assume ''x'' contains zero or one 4's.

If x contains no 4's, then all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume that ''x'' contains exactly one 4.

Case 4.1: ''p'' begins with 3.

In this case we can write ''p'' = 3''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. We must have '''349''' ◁ ''p''.

Case 4.2: ''p'' begins with 4.

In this case we can write ''p'' = 4''y''9, where all digits of ''y'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''409''' ◁ ''p''. If 3 ◁ ''y'', then 43 ◁ ''p''. If 9 ◁ ''y'', then '''499''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}, and thus ''p'' ∈ 4{6}9. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 6&lt;sub&gt;''n''&lt;/sub&gt;7 = 46&lt;sub&gt;''n''&lt;/sub&gt;9.

Case 4.3: ''p'' begins with 6.

In this case we can write p = 6''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 6 ◁ ''z'', then '''6469''' ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' is empty.

If 3 ◁ ''y'', then 349 ◁ ''p''. If 9 ◁ ''y'', then '''6949''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 6.

If 06 ◁ ''y'', then '''60649''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}{0}.

If 666 ◁ ''y'', then '''666649''' ◁ ''p''. If 00000 ◁ ''y'', then '''60000049''' ◁ ''p''. Hence we may assume ''y'' ∈ {''𝜆'', 0, 00, 000, 0000, 6, 60, 600, 6000, 60000, 66, 660, 6600, 66000, 660000}, and thus ''p'' ∈ {649, 6049, 60049, 600049, 6000049, 6649, 66049, 660049, 6600049, 66000049, 66649, 666049, 6660049, 66600049, 666000049}, and of these numbers only '''66000049''' and '''66600049''' are primes.

Case 4.4: ''p'' begins with 9.

In this case we can write p = 9''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''9049''' ◁ ''p''. If 3 ◁ ''y'', then 349 ◁ ''p''. If 6 ◁ ''y'', then '''9649''' ◁ ''p''. If 9 ◁ ''y'', then '''9949''' ◁ ''p''. Hence we may assume ''y'' is empty.

If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' ∈ {6}, and thus ''p'' ∈ 94{6}9, and the smallest prime ''p'' ∈ 94{6}9 is 946669.

[[Category:Number theory]]</text>
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    <title>Motivation and emotion/Book/2026/Automaticity and goal pursuit</title>
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      <text bytes="11479" sha1="3lych99rogk9r4yrsbgapxbtrxem3b1" xml:space="preserve">{{title|Automaticity and goal pursuit:&lt;br&gt;How do habits and environmental cues drive unconscious goal pursuit?}}
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==Overview==
{{RoundBoxTop|theme=8}}
[[File:Driver, Driving the open top sports car, Rostov-on-Don, Russia.jpg|right|thumb|200px|'''Figure 1'''. Undercover officer in pursuit.]]

;Picture this...

You're undercover. The air is cold, the night is dark and worst of all... you're tired. You were about to make the arrest when the suspect gets jumpy and decides to book it. You waste no time going after them, lights flaring and sirens wailing as the tires of your unmarked police car squeal as you take off in pursuit. You spot your radio in the corner of your eye. You grab it and instantly cite the car make, colour, number plate, location and relevant call signs for support all without a second thought. As you drive corner to corner, street to street, you're gaining on the suspect but they're still out of reach. You watch their car lurch as they hit a catastrophic downshift, costing them seconds. You can smell the clutch. As they approach the highway, backup arrives blocking the top of the on-ramp. They give up, exiting the car with their hands held above their head and their eyes aimed at the ground. A successful arrest with no casualties.

As you think back on the night with a sense of pride you also find yourself in awe of your performance. You focused solely on maintaining visual of the suspect, but also managed to perform skilled operation of a vehicle, navigation and detailed but brief communication all resulting in incremental advantages lending themselves to the success of the arrest with barely any thought involved. Maybe it was your training? Maybe it was the adrenaline? Regardless of what's true you just can't shake the feeling that everything just felt... automatic. &quot;I'm a machine!&quot; you think to yourself, in a cool &quot;robocop&quot; kind of way. 

{{RoundBoxBottom}}

To be able to perform an action automatically frees up your brain for higher order thinking, allowing you to ascend your proficiency in goal areas. In fact, many behaviours we perform on a daily basis are automatic (see Figure 1). But it also has the very same capability to drag you down. Many people have behaviours they're unsatisfied with but do anyway. This is because they have formed habits and those habits execute themselves automatically in response to stimuli. Understanding how to leverage habit formation is a strong strategy when it comes to pursuing goals and making the behaviours responsible for achieving those goals sustainable. Psychological science can assist by specific frameworks to engineer the most effective cueing routine to increase the likelihood of taking action towards your goals, hopefully without even thinking about it.

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

# How do you develop automatic behaviours?
# What do environmental cues contribute? 
# How can we utilise automaticity in goal pursuit?

{{RoundBoxBottom}}

==Automatic behaviour formation==

Ever think your friend is weird for getting up at 5am in the morning? Or that undercover police officer is incredibly disciplined for going to the gym after work everyday? Well it turns out while those tasks might be foreign to some people, performing those actions is automatic to others. These are behaviours that were formed through repetition, and it is in this repetition where the behaviour eventually becomes automatic. The individual no longer questions &quot;should I go to the gym after work?&quot;, they just go. The famous [[wikipedia:Classical_conditioning|Pavlov's theory of classical conditioning]] explains this perfectly. Classical conditioning involves taking a neutral stimulus and transforming it within the individual to elicit a conditioned response (Sanvictores, et al. 2024).

* Neutral stimulus elicits no response (e.g. a bell).
* Unconditioned stimulus (e.g. food) elicits a direct response known as the unconditioned response (e.g. salivation).
* A conditioned response (e.g. salivating to the bell) happens when the Neutral stimulus creates the same response as the unconditioned stimulus (e.g. salivating) 

==Role of environmental cues==
Environmental cues function along a similar line to classical conditioning. Some common errors that arise from environmental cues are when you drive to the shops and accidentally start driving to work (Wood, et al. 2007). The environmental cue in that situation would be driving the same road you take to work. That behaviour is so routine it is programmed into your brain to be performed completely automatically. Wood et al. in 2007 claim {{ic|Grammar - use past tense here}} that habits are artifacts of previous goal pursuits and that the success of that particular method is ingrained within the body so it can recall it to repeat that success. Their model had two principles.

* The power of contexts to trigger habitual responding.
* The absense of goal mediation in context response associations.

Patterns arise in life intentional or otherwise. The first principle claims people store patterns as procedural memory, which once stored can be activated with the specific associated cues in that pattern. The second principle claims that goal orientated behaviours can stick around after the goal has been achieved or no longer relevent. This is great insight as it demonstrates that behaviours can be cognitively offloaded from a internal &quot;willpower&quot; system to a external system. However, it warns against and aims to explain the accidental occumulation of unhelpful behaviours and provide context to their ridgidity. 

==Pursuing goals with automaticity==
Goal pursuit is always envisioned with a strong conscious effort. Overcoming trials and adversity a steadfast courage and unbreakable will. So the idea that it could be an unconscious effort seems like it goes against everything pursuit would stand for. But cueing the desired behaviour removes decision-making which is arguably where most people get stuck. Pursuing goals through automaticity aims to remove decision-making around taking action.

In the overview the undercover police officer was presented multiple opportunities to freeze or question their actions. Due to training specific cues they activated lights and sirens, identified key information about the suspect and relayed the information with the appropriate callsign without hesitation. The lack of decision making freed up the mental capacity to give chase to the suspect and achieve the goal of a successful arrest.

Wood et al. (2016) state that habits interface with goal pursuit in three ways. '''Exposure''', '''activation or inhibition''' and '''inference'''.

# '''Exposure''' provides context cues. During training the officer would have practiced the same behaviours to the same stimulus again and again. Eventually the habits become linked to context cues ready for activation or inhibition.
# '''Activation and inhibition''' allows the cue to activate or inhibit a behaviour immediately. Suspect flees --&gt; Lights and sirens go up --&gt; Radio relevant information. Behavioural activation increases the likelihood of a particular behaviour occuring, often requiring conscious thought to intervene with the execution rather then thought preceeding execution. 
# '''Inference''' is observing your own behaviour and determining that performing it is inline with your goals. The police officer would be guided by their objective to apprehend the suspect in a safe manner. Lights and sirens increase safety, radioing important information increases chance of finding them if they escape, and calling for back up increases the odds of making an arrest. 

&lt;quiz display=simple&gt;
{Behaving in the best interest of your goal is ______:
|type=&quot;()&quot;}
+ Inference
- Activation
- Inhibition
- Exposure

{Activation and inhibition allow _________:
|type=&quot;()&quot;}
- You to turn a behaviour on or off at your own command.
+ Environmental cues to activate a learned behaviour.
- Priming of the brain to consider action
- Environmental cues to be maintained in the brain.
&lt;/quiz&gt;

==Conclusion==
* Being able to remove thinking from the goal pursuit process would be a milestone for anyone. Making choices is mentally demanding and the goal striving process is already its own mountain. 
* Through this page we discussed how automatic habits occur, what enviromental cues have to do in relation to it, and how important they actually are in a goal orientated process.
* Wood et al.'s (2016) model of exposure, activation and inhibition, and inference is a significant model that represents the ways in which habits interact with goal pursuit. These provide multiple avenues for individuals to try to prompt themselves to produce the best results they can when pursuing a goal.

==See also==
{{expand}}

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

APA style example:
{{Hanging indent|1=

Sanvictores, T., Mahabadi, N., &amp; Rehman, C. I. (2024). Classical conditioning. StatPearls Publishing. https://www.ncbi.nlm.nih.gov/books/NBK470326/

Wood, W., &amp; Neal, D. T. (2007). A New Look at Habits and the Habit-Goal Interface. Psychological Review, 114(4), 843–863. https://doi.org/10.1037/0033-295X.114.4.843

Wood, W., &amp; Rünger, D. (2016). Psychology of Habit. Annual Review of Psychology, 67(1), 289–314. https://doi.org/10.1146/annurev-psych-122414-033417


}}

{{tip|Suggestions for this section:
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
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* The most common mistakes include:
** Incorrect capitalisation
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** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

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

{{tip|Suggestions for this section:
* Link to the most relevant external resources about the topic
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}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Behaviour]]
[[Category:Motivation and emotion/Book/Goal striving]]
[[Category:Motivation and emotion/Book/Habit]]
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    <title>Motivation and emotion/Book/2026/Emotion regulation through exercise</title>
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==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[https://www.paulekman.com/universal-emotions/ Universal emotions] {{ic|Move external links to the External links section at the end}} were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what &lt;u&gt;can&lt;/u&gt; we do to keep our emotions from becoming too much?{{RoundBoxTop|theme=3}}'''Focus questions'''

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is Emotion Regulation? ==
The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==

=== Physiological Effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

Less cortisol and more dopamine mean emotional regulation is much easier. (reference)&lt;br /&gt;

=== Psychological Effects ===

=== Psychological Theories ===

== What exercise is best to help regulate emotions? ==
Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Resistance training has benefits on emotion regulation such as.......

[[Aerobic]] exercise is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important tp note is that there is immediate results on mood.

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}

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

;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

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

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

==Conclusion==
* In conclusion: 
* Draft clear take-home message(s), even at the topic development stage[[File:Old man exercise on the seashore.jpg|thumb|'''Figure 3.''' Move for your mind {{ic|Explain relevance to topic}}]]
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

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

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
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}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

&lt;noinclude&gt;
&lt;hr&gt;
__TOC__
[[Category:Motivation and emotion/Book]]</text>
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__TOC__

==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what &lt;u&gt;can&lt;/u&gt; we do to keep our emotions from becoming too much?{{RoundBoxTop|theme=3}}'''Focus questions'''

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is Emotion Regulation? ==
Universal emotions&lt;ref&gt;{{Cite web|url=https://www.paulekman.com/universal-emotions/|title=Universal Emotions|last=Ekman|first=Paul}}&lt;/ref&gt; were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==

=== Physiological Effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

Less cortisol and more dopamine mean emotional regulation is much easier. (reference)&lt;br /&gt;

=== Psychological Effects ===

=== Psychological Theories ===

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years|date=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

[[Aerobic]] exercise is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}

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

;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

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

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

==Conclusion==
* In conclusion: 
* Draft clear take-home message(s), even at the topic development stage[[File:Old man exercise on the seashore.jpg|thumb|'''Figure 3.''' Move for your mind {{ic|Explain relevance to topic}}]]
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

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

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

&lt;noinclude&gt;
&lt;hr&gt;
__TOC__
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__TOC__

==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what &lt;u&gt;can&lt;/u&gt; we do to keep our emotions from becoming too much?{{RoundBoxTop|theme=3}}'''Focus questions'''

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is Emotion Regulation? ==
Universal emotions&lt;ref&gt;{{Cite web|url=https://www.paulekman.com/universal-emotions/|title=Universal Emotions|last=Ekman|first=Paul}}&lt;/ref&gt; were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==

=== Physiological Effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

Less cortisol and more dopamine mean emotional regulation is much easier. (reference)&lt;br /&gt;

=== Psychological Effects ===

=== Psychological Theories ===

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

[[Aerobic]] exercise is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}

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

;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

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

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

==Conclusion==
* In conclusion: 
* Draft clear take-home message(s), even at the topic development stage[[File:Old man exercise on the seashore.jpg|thumb|'''Figure 3.''' Move for your mind {{ic|Explain relevance to topic}}]]
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

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

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

&lt;noinclude&gt;
&lt;hr&gt;
__TOC__
[[Category:Motivation and emotion/Book]]</text>
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__TOC__

==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what &lt;u&gt;can&lt;/u&gt; we do to keep our emotions from becoming too much?{{RoundBoxTop|theme=3}}'''Focus questions'''

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is Emotion Regulation? ==
Universal emotions&lt;ref&gt;{{Cite web|url=https://www.paulekman.com/universal-emotions/|title=Universal Emotions|last=Ekman|first=Paul}}&lt;/ref&gt; were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==

=== Physiological Effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

Less cortisol and more dopamine mean emotional regulation is much easier. (reference)&lt;br /&gt;

=== Psychological Effects ===

=== Psychological Theories ===

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

[[Aerobic]] exercise is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}

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

;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

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

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

==Conclusion==
* In conclusion: 
* Draft clear take-home message(s), even at the topic development stage[[File:Old man exercise on the seashore.jpg|thumb|'''Figure 3.''' Move for your mind {{ic|Explain relevance to topic}}]]
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

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

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

&lt;noinclude&gt;
&lt;hr&gt;
__TOC__
[[Category:Motivation and emotion/Book]]</text>
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__TOC__

==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what &lt;u&gt;can&lt;/u&gt; we do to keep our emotions from becoming too much?{{RoundBoxTop|theme=3}}'''Focus questions'''

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is Emotion Regulation? ==
Universal emotions&lt;ref&gt;{{Cite web|url=https://www.paulekman.com/universal-emotions/|title=Universal Emotions|last=Ekman|first=Paul}}&lt;/ref&gt; were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==

=== Physiological Effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

Less cortisol and more dopamine mean emotional regulation is much easier. (reference)&lt;br /&gt;

=== Psychological Effects ===

=== Psychological Theories ===

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

[[Aerobic]] exercise is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}

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

;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

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

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

==Conclusion==
In conclusion:

* One session of aerobic exercise can significantly boost positive mood and alleviate stress responses. It is recommended for use as an immediate mood regulation strategy.
* Any movement can be used such as walking, dancing or sport.

*
* Recommended length: 150 to 330 words

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

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

&lt;noinclude&gt;
&lt;hr&gt;
__TOC__
[[Category:Motivation and emotion/Book]]</text>
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    </revision>
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        <id>3105557</id>
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__TOC__

==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what &lt;u&gt;can&lt;/u&gt; we do to keep our emotions from becoming too much?{{RoundBoxTop|theme=3}}'''Focus questions'''

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is Emotion Regulation? ==
Universal emotions&lt;ref&gt;{{Cite web|url=https://www.paulekman.com/universal-emotions/|title=Universal Emotions|last=Ekman|first=Paul}}&lt;/ref&gt; were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==

=== Physiological Effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

Less cortisol and more dopamine mean emotional regulation is much easier. (reference)&lt;br /&gt;

=== Psychological Effects ===

=== Psychological Theories ===

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

Aerobic exercise&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/articles/7050-aerobic-exercise|title=Aerobic Exercise|last=Cleveland Clinic}}&lt;/ref&gt; is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}

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

;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

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

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

==Conclusion==
In conclusion:

* One session of aerobic exercise can significantly boost positive mood and alleviate stress responses. It is recommended for use as an immediate mood regulation strategy.
* Any movement can be used such as walking, dancing or sport.

*
* Recommended length: 150 to 330 words

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

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

&lt;noinclude&gt;
&lt;hr&gt;
__TOC__
[[Category:Motivation and emotion/Book]]</text>
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    </revision>
    <revision>
      <id>2831953</id>
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      <text bytes="12445" sha1="pkgb0n9c5jwjjp1hkr2im8wpqlqsoww" xml:space="preserve">{{title|Emotion regulation through exercise:&lt;br&gt;How do people use exercise to regulate their emotional states?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what &lt;u&gt;can&lt;/u&gt; we do to keep our emotions from becoming too much?{{RoundBoxTop|theme=3}}'''Focus questions'''

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is Emotion Regulation? ==
[https://www.paulekman.com/universal-emotions/ Universal emotions] were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==

=== Physiological Effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

Less cortisol and more dopamine mean emotional regulation is much easier. (reference)&lt;br /&gt;

=== Psychological Effects ===

=== Psychological Theories ===

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

Aerobic exercise&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/articles/7050-aerobic-exercise|title=Aerobic Exercise|last=Cleveland Clinic}}&lt;/ref&gt; is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}

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

;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

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

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

==Conclusion==
In conclusion:

* One session of aerobic exercise can significantly boost positive mood and alleviate stress responses. It is recommended for use as an immediate mood regulation strategy.
* Any movement can be used such as walking, dancing or sport.

*
* Recommended length: 150 to 330 words

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

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

&lt;noinclude&gt;
&lt;hr&gt;
__TOC__
[[Category:Motivation and emotion/Book]]</text>
      <sha1>pkgb0n9c5jwjjp1hkr2im8wpqlqsoww</sha1>
    </revision>
  </page>
  <page>
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      <text bytes="48646" sha1="gbkgri0c7sjwifwtipdb1l2136fsuub" xml:space="preserve">&lt;noinclude&gt;{{note|Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Topic|topic development]] exercise for [[motivation and emotion]].&lt;br&gt;&lt;br&gt;[[Help:Transclusion|Transclude]] on a chapter [[Help:Talk page|talk page]].}}
__NOTOC__&lt;/noinclude&gt;&lt;includeonly&gt;
==Topic development feedback==
{{RoundBoxTop|theme=8}}
The [[Motivation and emotion/Assessment/Topic|topic development]] has been reviewed according to the [[Motivation and emotion/Assessment/Topic#Marking criteria|marking criteria]]. Written feedback is provided below, plus see the [[Motivation and emotion/Assessment/Topic/Feedback|general feedback]] page. Also check the [[Special:History/{{PAGENAME}}|page history]] for changes made whilst reviewing the plan. If you don't understand the feedback or would like further information, [[Motivation and emotion/Staff|get in touch]] to discuss. Marks are available via {{Motivation and emotion/Canvas}}. Marks are based on the latest version before the due date.
{{RoundBoxBottom}}
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[[File:Autoroute icone.svg|right|85px]]
===1. [[Motivation and emotion/Assessment/Topic#Title|Title]]===
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===5. [[Motivation and emotion/Assessment/Topic#Figure|Figure]]===
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===6. [[Motivation and emotion/Assessment/Topic#Learning feature|Learning feature]]===
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===7. [[Motivation and emotion/Assessment/Topic#References|References]]===
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===8. [[Motivation and emotion/Assessment/Topic#Resources|Resources]]===
{{{8|No comment}}}
===9. [[Motivation and emotion/Assessment/Topic#User page|User page]]===
{{{9|No comment}}}
===10. [[Motivation and emotion/Assessment/Topic#Social contribution|Social contribution]]===
{{{10|No comment}}}
{{RoundBoxBottom}}&lt;/includeonly&gt;&lt;noinclude&gt;{{collapse top|Simple example}}
==Simple example==
See also [[#Detailed example|detailed example]]
&lt;pre&gt;
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~~~~
&lt;/pre&gt;
gives
&lt;!-- Official topic development feedback --&gt;
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-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:42, 17 August 2025 (UTC)
{{Collapse bottom}}
==Detailed example==
Example use of the template which includes commonly used feedback comments:
&lt;pre&gt;
&lt;!-- Official topic development feedback --&gt;
{{METF/2026
|1=
&lt;!-- Title --&gt;
# Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]]
# Title and/or subtitle not correctly worded and/or didn't use [[w:Letter case#Sentence casing|sentence casing]] (fixed)
# User name removed from the page; for authorship see [[Special:History/{{PAGENAME}}|the page's edit history]]
|2=
&lt;!-- Headings --&gt;
# See earlier comment about [[#heading casing|heading casing]]
&lt;!-- Heading structure --&gt;
&lt;!-- 2-level --&gt;
# Excellent – Well developed [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]]. Meaningful headings clearly relate directly to the core topic.
# Clear [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]]
# Promising [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]] – could benefit from further development and/or refinement
# Basic [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]] – could benefit from further development (expand)
&lt;!-- 1-level --&gt;
# Promising [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – could benefit from further development (e.g., consider using subheadings)
# Basic, [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – could benefit from further development, perhaps using a 2-level structure (i.e., use subheadings)
# Under-developed, [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – develop further, perhaps using a 2-level structure for larger section(s) (i.e., including subheadings)
&lt;!-- 3-level --&gt;
# Overly complicated[[Motivation and emotion/Assessment/Major project/Structure|3-level heading structure]] – consider simplifying
&lt;!-- Conceptual --&gt;
# Messy heading structure – needs work (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# The headings lack sufficient incision into, and exposition of, the topic
# Revise heading structure to place less emphasis on background concepts and more emphasis on the target topic (i.e., address the sub-title). The draft headings place too much emphasis on background concepts and too little on the relationship between the concepts.
&lt;!-- Other ---&gt;
# Aim for 3 to 6 top-level headings between the Overview and Conclusion, with 3 to 5 sub-headings for large sections
# The Overview and Conclusion should not use sub-headings
# Use default heading formatting (i.e., avoid additional formatting such as bold, italics, underline, changing the size etc.)
# Avoid having sections with only 1 sub-heading – use 0 or 2+ sub-headings
# &quot;Introduction&quot; heading isn't necessary – provide this information in Overview or move into subsequent sections
# Cover definition(s) in the Overview and/or subsequent sections with embedded inter-wiki link(s) to further information
# Case study doesn't need a separate heading; instead embed case study within relevant sections
# Quiz doesn't need a separate heading; instead embed quiz questions within relevant sections
# Check grammar (e.g,. missing question mark)
# Remove [[wikt:acronym#Noun|acronym]]s from headings
# Remove citations from headings
&lt;!-- Alignment with focus questions --&gt;
# Excellent alignment between sub-title, focus questions, and heading structure
# Very good alignment between sub-title, focus questions, and heading structure, but there may be room for improvement
# Good alignment between sub-title, focus questions, and heading structure, but there is room for improvement
# Reasonably good alignment between focus questions and heading structure, but aim for closer alignment
# Basic alignment between between sub-title, focus questions, and top-level headings. Aim to improve.
# Develop closer alignment between sub-title, focus questions, and top-level headings
# Insufficient alignment between sub-title, focus questions, and top-level headings
&lt;!-- GenAI ---&gt;
# Are the headings based on [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
|3=
&lt;!-- Overview--&gt;
# Excellent – Scenario, image, evocative description of the problem/topic, and focus questions
# Very good
# Good
# Basic
# Insufficient
# Hasn't been developed – Needs scenario, image, evocative description of the problem/topic, and focus questions
&lt;!-- GenAI ---&gt;
# Does this section include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, it needs to be acknowledged as such in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Scenario --&gt;
# A scenario or case study is presented in a feature box with an image at the start of this section
# A scenario or case study is presented in a feature box at the start of this section
# I moved an image into the feature box to help attract reader interest
# Add an image to the scenario to help attract reader interest
# Put the scenario or case study into a feature box at the start of this section (fixed)
# Make the scenario more practical or down-to-earth; it is currently too abstract
# Make the relevance of the scenario to the topic more clear. It should be obvious to a reader how the scenario illustrates the topic (i.e., the sub-title question). Revise the scenario to make this connection more explicit.
# Add a scenario or case study in a feature box (with an image) at the start of this section to help engage reader interest
&lt;!-- Description --&gt;
# A clear description of the problem/topic is planned or presented
# A promising description of the problem/topic is planned or presented
# A basic description of the problem/topic is planned or presented
# Introduce topic using plain English; most citations can be moved into subsequent setions
# Simplify/abbreviate the description of the problem/topic. Move detail into subsequent sections.
# Add a brief, evocative description of the problem/topic
&lt;!-- Style --&gt;
# Use present, rather than future, tense
# Use 3rd person point of view for main body text (except 1st/2nd person point of view can work within feature boxes for scenarios)
&lt;!-- Focus questions --&gt;
# Focus questions are aligned with sub-title and top-level headings
# Reasonably good alignment between focus questions and heading structure, but consider closer alignment
# Develop closer alignment between the sub-title, focus questions, and top-level headings
# Use open- rather then close-ended focus questions
# Use single- rather than double-barrelled focus questions
# Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# Present focus questions in a feature box at the end of this section
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Excellent – key points are well developed for each section
# Solid development
# Promising development
# Highlight the most relevant theories and synthesise the best research on the topic
# Focus on providing an integrative review of the most relevant theories and research on the topic
# Overly broad/comprehensive; not sufficiently focused/targetted on the topic; this often occurs when genAI content is used by a prompter with insufficient background reading and understanding of the topic and/or insufficient revising and rewriting of genAI content
# Basic development
# Partial development
# Insufficient development
# No development
# Provide more detailed edit summaries
&lt;!-- Scope --&gt;
# The scope is excellent (i.e., not too little/narrow or too big/broad)
# The scope is about right, but it may be that all planned aspects cannot be reasonably covered within the book chapter word count; in that case, be selective and concentrate on key aspects that address the question in the sub-title
# It may be that all planned aspects cannot be reasonably covered within the book chapter word count, so be selective and concentrate on key aspects that address the question in the sub-title
# It is unlikely that all planned aspects can be reasonably covered within the book chapter word count, so be selective and concentrate on the most important aspects which address the question in the sub-title
# All planned aspects cannot reasonably be covered within the book chapter word count, so be selective and concentrate on the most important aspects which address the question in the sub-title
&lt;!-- Writing style --&gt;
# The writing style is clear and easy to follow
# The writing style is generally clear but could be simplified or made more concise
# The writing style is difficult to follow (e.g., due to vagueness, complex wording, long sentences, long paragraphs, repetition, etc.)
&lt;!-- Theory and research --&gt;
# Good balance of theory and research
# Promising balance of theory and research
# Reasonably good coverage of theory; strive to balance the theoretical content with critical review of relevant research
# Balance theoretical content with critical synthesis of relevant research
# Too much theory. Not enough research. Strive for an integrated balance of the best psychological theory and research about this topic, with practical examples.
# Strive for an integrated balance of the best psychological theory and research about this topic, with practical examples.
# Select the best theories about this topic
# Select the best research about this topic
&lt;!-- Citations --&gt;
# Excellent use of citations
# Very good use of citations
# Good use of citations
# Promising use of citations
# Basic use of citations
# Insufficient use of citations
# Non-peer-reviewed sources should be moved to the &quot;External links&quot; section
# Tip: Rather than starting with an author name and citation, start with the more interesting part (i.e., the substance) and put the citation at the end or mid-way through the sentence
&lt;!-- Citation style --&gt;
# Use [https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles APA style 7th edition for citations] (e.g., do not include author initials)
# Use [https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles APA style 7th edition for citations] with three or more authors (i.e., FirstAuthor et al., year)
# [https://apastyle.apa.org/style-grammar-guidelines/punctuation/serial-comma APA style uses serial commas][[w:Serial comma|1]][https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should 2][https://www.youtube.com/watch?v=gBx8ooDupXY 3] (1 min)
&lt;!-- Other --&gt;
# For sections with sub-sections, provide key points for an overview paragraph prior to branching into the sub-headings
# ''Avoid providing too much background information''. Aim to briefly summarise general concepts and provide internal links to relevant book chapters and/or Wikipedia pages for further information. Focus most of the chapter on ''directly answering the core question(s)'' posed by the chapter sub-title.
# Direct quotes need page numbers (APA style) – even better, express the idea in your own words
# Use correct capitalisation ([https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style is a &quot;down&quot; style]) – [https://polishedpaper.com/blog/capitalization-apa-style more info]
# Use [https://www.aresearchguide.com/write-in-third-person.html 3rd person perspective], although a case study or feature box could use 1st or 2nd person perspective
# Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., analyze → analyse; behavior → behaviour)
# Move references into the References section. Keep citations in the main body.
# Consider using Studiosity Writing Feedback+ or a similar writing-support service (e.g., Grammarly) to improve the quality of written expression and check for grammatical and spelling errors in the book chapter draft.
&lt;!-- GenAI ---&gt;
# Well done on acknowledging genAI use in the edit summary. Also share link(s) to the conversation, as per the [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]].
# Do these key points include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Conclusion --&gt;
# Conclusion is well developed
# Conclusion is well underway
# Conclusion is underway
# Conclusion is underdeveloped
# Conclusion hasn't been developed
# What are the practical, take-home messages? (address the focus questions)
|5=
&lt;!-- Figure --&gt;
# Excellent - Relevant figure(s) presented, captioned, and cited
# Relevant figure(s) are presented and captioned
# Relevant figure(s) are presented
# The relevance of the figure to the topic is unclear
# A relevant figure is not presented and cited (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Caption --&gt;
# Figure caption(s) provide(s) a clear, appropriately detailed description that is meaningfully connected with the main text
# Figure caption(s) provide(s) a reasonably clear description that is connected with the main text
# Figure caption(s) provide(s) a somewhat clear description that is connected with the main text, but could be improved
# Figure caption(s) could better explain how the image connects to key points being made in the main text
# Figure caption(s) should include '''Figure X'''. ...
&lt;!-- Cite --&gt;
# Figure(s) are cited at least once in the main text
# Cite each figure at least once in the main text using APA style (e.g., see Figure 1)
&lt;!-- Size --&gt;
# Consider increasing image size(s) (especially if they have text) to make them easier to view
# Consider decreasing image size(s) to make them less dominant
&lt;!-- Creation --&gt;
# Well done on creating and uploading your own image! {{smile}}—this can also be listed on your user page as a social contribution
|6=
&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# Excellent in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]]
# Promising in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]]
# Two in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]]. Also embed links to [[Motivation and emotion/Book|book chapters]].
# One in-text [[m:Help:Interwiki linking|interwiki link]] for first mention of key term to [[w:|Wikipedia]]. Also embed links to [[Motivation and emotion/Book|book chapters]].
# Add in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]] (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Scenarios/examples/case studies --&gt;
# Excellent use of scenarios/examples/case studies
# Promising use of scenarios/examples/case studies
# Keep scenarios brief 
# Basic use of scenario/example/case study
# Placeholder use of scenarios/examples/case studies
# Make the relevance of the scenario to the topic more clear
# Consider incorporating additional scenarios, examples, or case studies to illustrate key concepts. These could build on the Overview scenario or introduce new real-world situations in the main body of the chapter to demonstrate how the concepts apply in practice.
&lt;!-- Quiz --&gt;
# Excellent use of quiz question(s)
# Promising use of quiz question(s)
# Place each quiz question in the most relevant section
# Focus the quiz question(s) on the take-home messages
# Placeholder use of quiz question(s)
# Consider including quiz question(s) about the take-home messages
&lt;!-- Tables --&gt;
# Excellent use of table(s)
# Promising use of table(s)
# Include acknowledgement (e.g., citation(s)) for sources of information presented in the table
# Use APA style for table captions
# Add table caption
# Cite each table at least once in the text
# Also consider using tables to summarise key information
|7=
&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Excellent
# Very good
# Good
# Basic
# Insufficient
# To be developed
&lt;!-- Systematic reviews --&gt;
# Well done on identifying relevant systematic reviews and/or meta-analyses
# At least one relevant systematic review and/or meta-analysis has been identified
# What are the most relevant systematic reviews/meta-analyses about this topic?
&lt;!-- Move --&gt;
# Move Wikipedia links to the &quot;See also&quot; section
# Move non-academic / non-peer reviewed sources to the &quot;External links&quot; section
&lt;!-- Citations --&gt;
# All references need in-text citation
# All citations need to be in the References
# Only include references which have been accessed and read
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## alphabetical order
## capitalisation
## [[Help:Wikitext quick reference|italicisation]]
## [https://apastyle.apa.org/instructional-aids/reference-guide.pdf doi formatting]
## make doi hyperlinks active (i.e., clickable)
## use dois where available instead of other links
## include hyperlinked dois
## page numbers should be separated by an en-dash (–) rather than a hyphen (-)
# A more thorough literature search is recommended. The goal is to identify and use the best academic theory and research about this topic
# Use APA style or wiki referencing style, but not both (currently, a mixture of referencing styles is used
# Don't cite AI-generated content because it is unreliable and not peer-reviewed. Instead, follow the [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] which include acknowledging and linking to genAI use in edit summaries, otherwise it is a violation of academic integrity.
|8=
&lt;!-- Resources --&gt;
&lt;!-- See also --&gt;
# See also
## Excellent
## Very good
## Good
## Basic
## One of two link types provided
### Also link to related [[Motivation and emotion/Book|motivation and emotion book chapters]]
### Also link to relevant [[w:|Wikipedia]] pages
## Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Use [[w:Letter case#Sentence casing|sentence casing]]
## Rename links so that they are more user friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Include source in brackets after link (e.g., (Wikipedia) or (Book chapter, year) for Wikiversity book chapters)
## Use alphabetical order
## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- External links --&gt;
# External links
## Excellent
## Very good
## Good
## Basic
## One of two required external links provided
## Move Wikipedia link(s) to the &quot;See also&quot; section
## Move academic sources into the &quot;References&quot; sections and provide in-text citation
## Only include links directly related to the sub-title
## Target an international audience; Australians only represent 0.33% of the world population
## Good choice of links, but poorly formatted (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Use [[w:Letter case#Sentence casing|sentence casing]]
## Rename links so that they are more user friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Include source in brackets after link
## Use alphabetical order
## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Link to the most relevant external resources about this topic
|9=
&lt;!-- User page --&gt;
# Excellent
# Used effectively
# Very good
# Good
# Basic but effective
# Not created – see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
&lt;!-- Description about self --&gt;
# Excellent description about self provided
# Description about self provided
# Brief description about self – consider expanding
# Very brief description about self – consider expanding
# Add description about self
&lt;!-- Links to profile(s) --&gt;
# Link(s) provided to professional profile(s)
# Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
# A link to the book chapter is provided
# Rename the link to the book chapter to make it more user-friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# Add link to book chapter
|10=
&lt;!-- Social contribution --&gt;
# Excellent – at least three different types of contributions with direct link(s) to evidence
# Good – two out of three types of contributions made with direct link(s) to evidence. The other type of contribution is making:
# One out of three types of contributions made with direct link(s) to evidence. The other types of contribution are making:
#* direct improvements to other [[Motivation and emotion/Book|chapters (past or current)]]
#* comments on the [[Help:Talk page|talk page]]s of other [[Motivation and emotion/Book|chapters (past or current)]]
#* posts about the unit or project on the {{Motivation and emotion/Canvas}} discussion forum
# To add direct links to evidence of Wikiversity edits or comments: view the page history, select the version of the page before and after your contributions, click &quot;compare selected revisions&quot;, and paste the comparison URL on your user page. For more info, see [[Motivation and emotion/Assessment/Chapter#Making and summarising social contributions|Making and summarising social contributions]]. This was demonstrated in [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]].
# Are these contributions based on AI-generated content? If so, please follow the [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]], otherwise it is a violation of academic integrity.
# Well done on creating and uploading your own image!
# Use a numbered list (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# Descriptions of contributions could be more precise/accurate/detailed
# Add a brief summary of each contribution
# Remember to sign comments on talk pages
# None summarised on user page with direct link(s) to evidence (see [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]]). Looking ahead to the book chapter, see [[Motivation and emotion/Assessment/Chapter#Socialcontribution|social contributions]].
}}
~~~~
&lt;/pre&gt;
gives
&lt;!-- Official topic development feedback --&gt;
{{METF/2026
|1=
&lt;!-- Title --&gt;
# Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]]
# Title and/or subtitle not correctly worded and/or didn't use [[w:Letter case#Sentence casing|sentence casing]] (fixed)
# User name removed from the page; for authorship see [[Special:History/{{PAGENAME}}|the page's edit history]]
|2=
&lt;!-- Headings --&gt;
# See earlier comment about [[#heading casing|heading casing]]
&lt;!-- Heading structure --&gt;
&lt;!-- 2-level --&gt;
# Excellent – Well developed [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]]. Meaningful headings clearly relate directly to the core topic.
# Clear [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]]
# Promising [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]] – could benefit from further development and/or refinement
# Basic [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]] – could benefit from further development (expand)
&lt;!-- 1-level --&gt;
# Promising [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – could benefit from further development (e.g., consider using subheadings)
# Basic, [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – could benefit from further development, perhaps using a 2-level structure (i.e., use subheadings)
# Under-developed, [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – develop further, perhaps using a 2-level structure for larger section(s) (i.e., including subheadings)
&lt;!-- 3-level --&gt;
# Overly complicated [[Motivation and emotion/Assessment/Major project/Structure|3-level heading structure]] – consider simplifying
&lt;!-- Conceptual --&gt;
# Messy heading structure – needs work (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# The headings lack sufficient incision into, and exposition of, the topic
# Revise heading structure to place less emphasis on background concepts and more emphasis on the target topic (i.e., address the sub-title). The draft headings place too much emphasis on background concepts and too little on the relationship between the concepts.
&lt;!-- Other ---&gt;
# Aim for 3 to 6 top-level headings between the Overview and Conclusion, with 3 to 5 sub-headings for large sections
# The Overview and Conclusion should not use sub-headings
# Use default heading formatting (i.e., avoid additional formatting such as bold, italics, underline, changing the size etc.)
# Avoid having sections with only 1 sub-heading – use 0 or 2+ sub-headings
# &quot;Introduction&quot; heading isn't necessary – provide this information in Overview or move into subsequent sections
# Cover definition(s) in the Overview and/or subsequent sections with embedded inter-wiki link(s) to further information
# Case study doesn't need a separate heading; instead embed case study within relevant sections
# Quiz doesn't need a separate heading; instead embed quiz questions within relevant sections
# Check grammar (e.g,. missing question mark)
# Remove [[wikt:acronym#Noun|acronym]]s from headings
# Remove citations from headings
&lt;!-- Alignment with focus questions --&gt;
# Excellent alignment between sub-title, focus questions, and heading structure
# Very good alignment between sub-title, focus questions, and heading structure, but there may be room for improvement
# Good alignment between sub-title, focus questions, and heading structure, but there is room for improvement
# Reasonably good alignment between focus questions and heading structure, but aim for closer alignment
# Basic alignment between between sub-title, focus questions, and top-level headings. Aim to improve.
# Develop closer alignment between sub-title, focus questions, and top-level headings
# Insufficient alignment between sub-title, focus questions, and top-level headings
&lt;!-- GenAI ---&gt;
# Are the headings based on [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
|3=
&lt;!-- Overview--&gt;
# Excellent – Scenario, image, evocative description of the problem/topic, and focus questions
# Very good
# Good
# Basic
# Insufficient
# Hasn't been developed – Needs scenario, image, evocative description of the problem/topic, and focus questions
&lt;!-- GenAI ---&gt;
# Does this section include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, it needs to be acknowledged as such in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Scenario --&gt;
# A scenario or case study is presented in a feature box with an image at the start of this section
# A scenario or case study is presented in a feature box at the start of this section
# I moved an image into the feature box to help attract reader interest
# Add an image to the scenario to help attract reader interest
# Put the scenario or case study into a feature box at the start of this section (fixed)
# Make the scenario more practical or down-to-earth; it is currently too abstract
# Make the relevance of the scenario to the topic more clear. It should be obvious to a reader how the scenario illustrates the topic (i.e., the sub-title question). Revise the scenario to make this connection more explicit.
# Add a scenario or case study in a feature box (with an image) at the start of this section to help engage reader interest
&lt;!-- Description --&gt;
# A clear description of the problem/topic is planned or presented
# A promising description of the problem/topic is planned or presented
# A basic description of the problem/topic is planned or presented
# Introduce topic using plain English; most citations can be moved into subsequent setions
# Simplify/abbreviate the description of the problem/topic. Move detail into subsequent sections.
# Add a brief, evocative description of the problem/topic
&lt;!-- Style --&gt;
# Use present, rather than future, tense
# Use 3rd person point of view for main body text (except 1st/2nd person point of view can work within feature boxes for scenarios)
&lt;!-- Focus questions --&gt;
# Focus questions are aligned with sub-title and top-level headings
# Reasonably good alignment between focus questions and heading structure, but consider closer alignment
# Develop closer alignment between the sub-title, focus questions, and top-level headings
# Use open- rather then close-ended focus questions
# Use single- rather than double-barrelled focus questions
# Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# Present focus questions in a feature box at the end of this section
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Excellent – key points are well developed for each section
# Solid development
# Promising development
# Highlight the most relevant theories and synthesise the best research on the topic
# Focus on providing an integrative review of the most relevant theories and research on the topic
# Overly broad/comprehensive; not sufficiently focused/targetted on the topic; this often occurs when genAI content is used by a prompter with insufficient background reading and understanding of the topic and/or insufficient revising and rewriting of genAI content
# Basic development
# Partial development
# Insufficient development
# No development
# Provide more detailed edit summaries
&lt;!-- Scope --&gt;
# The scope is excellent (i.e., not too little/narrow or too big/broad)
# The scope is about right, but it may be that all planned aspects cannot be reasonably covered within the book chapter word count; in that case, be selective and concentrate on key aspects that address the question in the sub-title
# It may be that all planned aspects cannot be reasonably covered within the book chapter word count, so be selective and concentrate on key aspects that address the question in the sub-title
# It is unlikely that all planned aspects can be reasonably covered within the book chapter word count, so be selective and concentrate on the most important aspects which address the question in the sub-title
# All planned aspects cannot reasonably be covered within the book chapter word count, so be selective and concentrate on the most important aspects which address the question in the sub-title
&lt;!-- Writing style --&gt;
# The writing style is clear and easy to follow
# The writing style is generally clear but could be simplified or made more concise
# The writing style is difficult to follow (e.g., due to vagueness, complex wording, long sentences, long paragraphs, repetition, etc.)
&lt;!-- Theory and research --&gt;
# Good balance of theory and research
# Promising balance of theory and research
# Reasonably good coverage of theory; strive to balance the theoretical content with critical review of relevant research
# Balance theoretical content with critical synthesis of relevant research
# Too much theory. Not enough research. Strive for an integrated balance of the best psychological theory and research about this topic, with practical examples. 
# Strive for an integrated balance of the best psychological theory and research about this topic, with practical examples. 
# Select the best theories about this topic
# Select the best research about this topic
&lt;!-- Citations --&gt;
# Excellent use of citations
# Very good use of citations
# Good use of citations
# Promising use of citations
# Basic use of citations
# Insufficient use of citations
# Non-peer-reviewed sources should be moved to the &quot;External links&quot; section
# Tip: Rather than starting with an author name and citation, start with the more interesting part (i.e., the substance) and put the citation at the end or mid-way through the sentence
&lt;!-- Citation style --&gt;
# Use [https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles APA style 7th edition for citations] (e.g., do not include author initials)
# Use [https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles APA style 7th edition for citations] with three or more authors (i.e., FirstAuthor et al., year)
# [https://apastyle.apa.org/style-grammar-guidelines/punctuation/serial-comma APA style uses serial commas][[w:Serial comma|1]][https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should 2][https://www.youtube.com/watch?v=gBx8ooDupXY 3] (1 min)
&lt;!-- Other --&gt;
# For sections with sub-sections, provide key points for an overview paragraph prior to branching into the sub-headings
# ''Avoid providing too much background information''. Aim to briefly summarise general concepts and provide internal links to relevant book chapters and/or Wikipedia pages for further information. Focus most of the chapter on ''directly answering the core question(s)'' posed by the chapter sub-title.
# Direct quotes need page numbers (APA style) – even better, express the idea in your own words
# Use correct capitalisation ([https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style is a &quot;down&quot; style]) – [https://polishedpaper.com/blog/capitalization-apa-style more info]
# Use [https://www.aresearchguide.com/write-in-third-person.html 3rd person perspective], although a case study or feature box could use 1st or 2nd person perspective
# Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., analyze → analyse; behavior → behaviour)
# Move references into the References section. Keep citations in the main body.
# Consider using Studiosity Writing Feedback+ or a similar writing-support service (e.g., Grammarly) to improve the quality of written expression and check for grammatical and spelling errors in the book chapter draft.
&lt;!-- GenAI ---&gt;
# Well done on acknowledging genAI use in the edit summary. Also share link(s) to the conversation, as per the [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]].
# Do these key points include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Conclusion --&gt;
# Conclusion is well developed
# Conclusion is well underway
# Conclusion is underway
# Conclusion is underdeveloped
# Conclusion hasn't been developed
# What are the practical, take-home messages? (address the focus questions)
|5=
&lt;!-- Figure --&gt;
# Excellent - Relevant figure(s) presented, captioned, and cited
# Relevant figure(s) are presented and captioned
# Relevant figure(s) are presented
# The relevance of the figure to the topic is unclear
# A relevant figure is not presented and cited (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Caption --&gt;
# Figure caption(s) provide(s) a clear, appropriately detailed description that is meaningfully connected with the main text
# Figure caption(s) provide(s) a reasonably clear description that is connected with the main text
# Figure caption(s) provide(s) a somewhat clear description that is connected with the main text, but could be improved
# Figure caption(s) could better explain how the image connects to key points being made in the main text
# Figure caption(s) should include '''Figure X'''. ...
&lt;!-- Cite --&gt;
# Figure(s) are cited at least once in the main text
# Cite each figure at least once in the main text using APA style (e.g., see Figure 1)
&lt;!-- Size --&gt;
# Consider increasing image size(s) (especially if they have text) to make them easier to view
# Consider decreasing image size(s) to make them less dominant
&lt;!-- Creation --&gt;
# Well done on creating and uploading your own image! {{smile}}—this can also be listed on your user page as a social contribution
|6=
&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# Excellent in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]]
# Promising in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]]
# Two in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]]. Also embed links to [[Motivation and emotion/Book|book chapters]].
# One in-text [[m:Help:Interwiki linking|interwiki link]] for first mention of key term to [[w:|Wikipedia]]. Also embed links to [[Motivation and emotion/Book|book chapters]].
# Add in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]] (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Scenarios/examples/case studies --&gt;
# Excellent use of scenarios/examples/case studies
# Promising use of scenarios/examples/case studies
# Keep scenarios brief 
# Basic use of scenario/example/case study
# Placeholder use of scenarios/examples/case studies
Consider incorporating additional scenarios, examples, or case studies to illustrate key concepts. These could build on the Overview scenario or introduce new real-world situations in the main body of the chapter to demonstrate how the concepts apply in practice.
&lt;!-- Quiz --&gt;
# Excellent use of quiz question(s)
# Promising use of quiz question(s)
# Place each quiz question in the most relevant section
# Focus the quiz question(s) on the take-home messages
# Placeholder use of quiz question(s)
# Consider including quiz question(s) about the take-home messages
&lt;!-- Tables --&gt;
# Excellent use of table(s)
# Promising use of table(s)
# Include acknowledgement (e.g., citation(s)) for sources of information presented in the table
# Use APA style for table captions
# Add table caption
# Cite each table at least once in the text
# Also consider using tables to summarise key information
|7=
&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Excellent
# Very good
# Good
# Basic
# Insufficient
# To be developed
&lt;!-- Systematic reviews --&gt;
# Well done on identifying relevant systematic reviews and/or meta-analyses
# At least one relevant systematic review and/or meta-analysis has been identified
# What are the most relevant systematic reviews/meta-analyses about this topic?
&lt;!-- Move --&gt;
# Move Wikipedia links to the &quot;See also&quot; section
# Move non-academic / non-peer reviewed sources to the &quot;External links&quot; section
&lt;!-- Citations --&gt;
# All references need in-text citation
# All citations need to be in the References
# Only include references which have been accessed and read
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## alphabetical order
## capitalisation
## [[Help:Wikitext quick reference|italicisation]]
## [https://apastyle.apa.org/instructional-aids/reference-guide.pdf doi formatting]
## make doi hyperlinks active (i.e., clickable)
## use dois where available instead of other links
## include hyperlinked dois
## page numbers should be separated by an en-dash (–) rather than a hyphen (-)
# A more thorough literature search is recommended. The goal is to identify and use the best academic theory and research about this topic
# Use APA style or wiki referencing style, but not both (currently, a mixture of referencing styles is used
# Don't cite AI-generated content because it is unreliable and not peer-reviewed. Instead, follow the [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] which include acknowledging and linking to genAI use in edit summaries, otherwise it is a violation of academic integrity.
|8=
&lt;!-- Resources --&gt;
&lt;!-- See also --&gt;
# See also
## Excellent
## Very good
## Good
## Basic
## One of two link types provided
### Also link to related [[Motivation and emotion/Book|motivation and emotion book chapters]]
### Also link to relevant [[w:|Wikipedia]] pages
## Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Use [[w:Letter case#Sentence casing|sentence casing]]
## Rename links so that they are more user friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Include source in brackets after link (e.g., (Wikipedia) or (Book chapter, year) for Wikiversity book chapters)
## Use alphabetical order
## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- External links --&gt;
# External links
## Excellent
## Very good
## Good
## Basic
## One of two required external links provided
## Move Wikipedia link(s) to the &quot;See also&quot; section
## Move academic sources into the &quot;References&quot; sections and provide in-text citation
## Only include links directly related to the sub-title
## Target an international audience; Australians only represent 0.33% of the world population
## Good choice of links, but poorly formatted (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Use [[w:Letter case#Sentence casing|sentence casing]]
## Rename links so that they are more user friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Include source in brackets after link
## Use alphabetical order
## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Link to the most relevant external resources about this topic
|9=
&lt;!-- User page --&gt;
# Excellent
# Used effectively
# Very good
# Good
# Basic but effective
# Not created – see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
&lt;!-- Description about self --&gt;
# Excellent description about self provided
# Description about self provided
# Brief description about self – consider expanding
# Very brief description about self – consider expanding
# Add description about self
&lt;!-- Links to profile(s) --&gt;
# Link(s) provided to professional profile(s)
# Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
# A link to the book chapter is provided
# Rename the link to the book chapter to make it more user-friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# Add link to book chapter
|10=
&lt;!-- Social contribution --&gt;
# Excellent – at least three different types of contributions with direct link(s) to evidence
# Good – two out of three types of contributions made with direct link(s) to evidence. The other type of contribution is making:
# One out of three types of contributions made with direct link(s) to evidence. The other types of contribution are making:
#* direct improvements to other [[Motivation and emotion/Book|chapters (past or current)]]
#* comments on the [[Help:Talk page|talk page]]s of other [[Motivation and emotion/Book|chapters (past or current)]]
#* posts about the unit or project on the {{Motivation and emotion/Canvas}} discussion forum
# To add direct links to evidence of Wikiversity edits or comments: view the page history, select the version of the page before and after your contributions, click &quot;compare selected revisions&quot;, and paste the comparison URL on your user page. For more info, see [[Motivation and emotion/Assessment/Chapter#Making and summarising social contributions|Making and summarising social contributions]]. This was demonstrated in [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]].
# Are these contributions based on AI-generated content? If so, please follow the [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]], otherwise it is a violation of academic integrity.
# Well done on creating and uploading your own image!
# Use a numbered list (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# Descriptions of contributions could be more precise/accurate/detailed
# Add a brief summary of each contribution
# Remember to sign comments on talk pages
# None summarised on user page with direct link(s) to evidence (see [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]]). Looking ahead to the book chapter, see [[Motivation and emotion/Assessment/Chapter#Socialcontribution|social contributions]].
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:58, 26 August 2026 (UTC)

==See also==
* [[Motivation and emotion/Assessment/Topic|Topic development guidelines]]
* [[Template:MEBF]]
* [[Template:MEMF]]

[[Category:Motivation and emotion/Admin/2026]]
[[Category:Motivation and emotion/Assessment/Topic]]
&lt;/noinclude&gt;</text>
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    <title>User talk:Sabbier</title>
    <ns>3</ns>
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      <contributor>
        <username>Lbeaumont</username>
        <id>278565</id>
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      <comment>/* I don't drink alcohol but I might go to a bar */ new section</comment>
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      <text bytes="1290" sha1="3r7fzbsa377m0en7uvpy877n2kdnp98" xml:space="preserve">== lovely!! ==

I was navigating on wikiversity courses and stumbled upon the Bartending one. Such a pleasant reading! so well-organized and simple, comprehensive. Love it! Can't wait to put some of my still-developing skills into practice!! [[User:Coltraneiaa|Coltraneiaa]] ([[User talk:Coltraneiaa|discuss]] • [[Special:Contributions/Coltraneiaa|contribs]]) 18:01, 31 August 2026 (UTC)

:Hey thanks !! I'm glad you found some use of it. If you find something you think would be better changed, feel free to make edits or let me know. You're probably among the first to read the course, so I'm happy to hear from you :) [[User:Sabbier|Sabbier]] ([[User talk:Sabbier|discuss]] • [[Special:Contributions/Sabbier|contribs]]) 00:27, 1 September 2026 (UTC)

== I don't drink alcohol but I might go to a bar ==

Thanks for your bartending course. I don't drink alcohol, but I sometimes go to a bar to be with friends. It will be helpful to add a section to the bartending course to address such patrons. It might include a suggested list of drinks (non-alcoholic beers, mocktails, ginger beer, etc.) and also etiquette that makes us feel welcome.   [[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 14:56, 6 September 2026 (UTC)</text>
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      <text bytes="1349" sha1="2iih1dy6yhj61xw59qwlswqpk3i7vj3" xml:space="preserve">== lovely!! ==

I was navigating on wikiversity courses and stumbled upon the Bartending one. Such a pleasant reading! so well-organized and simple, comprehensive. Love it! Can't wait to put some of my still-developing skills into practice!! [[User:Coltraneiaa|Coltraneiaa]] ([[User talk:Coltraneiaa|discuss]] • [[Special:Contributions/Coltraneiaa|contribs]]) 18:01, 31 August 2026 (UTC)

:Hey thanks !! I'm glad you found some use of it. If you find something you think would be better changed, feel free to make edits or let me know. You're probably among the first to read the course, so I'm happy to hear from you :) [[User:Sabbier|Sabbier]] ([[User talk:Sabbier|discuss]] • [[Special:Contributions/Sabbier|contribs]]) 00:27, 1 September 2026 (UTC)

== I don't drink alcohol but I might go to a bar ==

Thanks for your bartending course. I don't drink alcohol, but I sometimes go to a bar to be with friends. It will be helpful to add a section to the bartending course to address such patrons. It might include a suggested list of drinks (non-alcoholic beers, mocktails, ginger beer, etc.) and also etiquette that makes us feel welcome. 

Another idea is to add a section for bartending at home.
  [[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 14:56, 6 September 2026 (UTC)</text>
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      <comment>/* Recommended Materials */ Linked Boston shaker</comment>
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      <text bytes="3705" sha1="ffw60aqjyazqkco0bpkk8ops0vwsjyv" xml:space="preserve">=== Introduction ===
Mixing drinks, talking to people, and making money: that's bartending! If you find that definition to be less-than-enough, this course will guide you through the essential skills of a bartender. This course is intended for adults of legal drinking age where they live who want to start bartending in a professional establishment either as a side gig or a career. Adults wanting to learn about bartending in general or how to mix drinks at home can also benefit from this course. No prior experience is required. By the end of the course, you should know: how to mix common drinks ordered at different types of bars and how they are related to one another; the liquors, spirits, ales, wines and other drinks used at the bar; the tools of the trade; the basics of safety as a bartender; and how to create a hospitable environment for bar patrons

This course makes use of the [[wikipedia:Wikimedia_Foundation#Projects_and_initiatives|Wikimedia ecosystem]] of projects. Throughout the course, there will be links to Wikipedia pages, Wiktionary entries, and images from Wikimedia Commons. When a link is casually included in a lesson, I encourage you to browse its contents. Occasionally, clicking a link and digesting its contents will be formally assigned as part of the course.
[[File:Bartender at Sylvarum cocktail bar, Alicante.jpg|thumb|451x451px|This could be you!]]

=== Structure of the Course ===
This course is composed of lessons which each focus on a component of bartending. It is recommended to complete them in order, as each lesson will build on the previous. The lessons can be found below:

# [[Bartending/Bartending Basics|Bartending Basics]]
# [[Bartending/Mixing Drinks|Mixing Drinks]]
# [[Bartending/Hospitality|Hospitality]]

=== Course Objectives ===
By the end of the course, you should be able to:

* Share information about and identify the different types of alcohol
* Identify and use the tools of a bartender to complete common techniques
* Mix 20 essential cocktails
* Serve bar patrons safely and hospitably

=== Recommended Materials ===
Bartending is a physical practice, and theory alone is not enough to prepare yourself. There will be activities that you complete at home as part of the course. The materials required to complete these activities are:

# [[w:Cocktail_shaker#Varieties|Boston shaker]] (Preferably not a Cobbler shaker or a Parisian shaker, though they may be easier to find.)
# Hawthorn Strainer
# Bar Spoon
# Jigger
# A glass for mixing, and a glass to pour drinks into (Don't worry about the style of glass, it just needs to be large enough to hold ice and 10 oz of liquid.)

[[File:Bartender_Photo.jpg|left|thumb|Bartender with Boston Shaker]]
[[File:Cocktail-strainer.jpg|thumb|Hawthorne Strainer]]
[[File:Jigger.jpg|center|thumb|160x160px|Jigger]]


Many of these materials can bought online or found at secondhand or thrift shops depending on your area. There may also be a specialty store near you catering to restaurants and bars. Having these materials at home are an invaluable way to practice mixing drinks, with the added benefit of allowing you to entertain guests at home! If you cannot acquire these materials, the course is still able to be completed in theory, but you will miss out on the practical aspects of the course. No materials are needed for lesson one.

In addition to these materials, you will also need the ingredients to the recipes we'll prepare. This will be discussed when we talk about mixing drinks.

Start here with [[Bartending/Bartending Basics|Lesson One: Bartending Basics]].

[[Category:Professional and vocational studies]]
[[Category:Professions]]
[[Category:Drinks]]
[[Category:Courses]]</text>
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      <comment>Aerobic</comment>
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      <text bytes="2552" sha1="nevw9knynsss5wnvvpjbtfdebqn2511" xml:space="preserve">==Welcome==
{{Robelbox|theme=9|title='''[[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]],  KB3250298!'''|width=100%}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or get in touch with [[User talk:Jtneill|me personally]] if you would like some [[Help:Contents|help]].

Remember to [[Wikiversity:Signature#How to add your signature|sign]] your comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. Using the signature icon [[File:OOjs UI icon signature-ltr.svg]] makes it simple.

We invite you to [[Wikiversity:Be bold|be bold]] and [[Wikiversity|assume good faith]]. Please abide by our [[Wikiversity:Civility|civility]], [[Wikiversity:Privacy policy|privacy]], and [[Foundation:Terms of Use|terms of use]] policies.

To find your way around, check out:
&lt;!-- The Left column --&gt;
&lt;div style=&quot;width:50.0%; float:left&quot;&gt;
* [[Wikiversity:Introduction|Introduction to Wikiversity]]
* [[Help:Guides|Take a guided tour]] and learn [[Help:Editing|how to edit]]
* [[Wikiversity:Browse|Browse]] or visit an educational level portal:&lt;br&gt;[[Portal:Pre-school Education|pre-school]] | [[Portal:Primary Education|primary]] | [[Portal:Secondary Education|secondary]] | [[Portal:Tertiary Education|tertiary]] | [[Portal:Non-formal Education|non-formal]]
* [[Wikiversity:Introduction explore|Explore]] links in left-hand navigation menu
&lt;/div&gt;
&lt;!-- The Right column --&gt;
&lt;div style=&quot;width:50.0%; float:left&quot;&gt;

* Read an [[Wikiversity:Wikiversity teachers|introduction for teachers]]
* Learn [[Help:How to write an educational resource|how to write an educational resource]]
* Find out about [[Wikiversity:Research|research]] activities
* Give [[Wikiversity:Feedback|feedback]] about your observations
* Discuss issues or ask questions at the [[Wikiversity:Colloquium|colloquium]]
&lt;/div&gt;
&lt;br clear=&quot;both&quot;/&gt;

To get started, experiment in the [[wikiversity:sandbox|sandbox]] or on [[special:mypage|your userpage]].

See you around Wikiversity! ---- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:01, 6 August 2026 (UTC)&lt;/div&gt;
&lt;!-- Template:Welcome --&gt;
{{Robelbox/close}}

==Aerobic==
To link to a definition, try Wiktionary e.g., [[wikt:aerobic|aerobic]].

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:40, 7 September 2026 (UTC)</text>
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    <title>User talk:Amirrorslens</title>
    <ns>3</ns>
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      <contributor>
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      <comment>/* Book Chapter Formatting */ new section</comment>
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      <text bytes="2681" sha1="gj75sfk5a0yz6chwjh7mjoi9o3hzjau" xml:space="preserve">==Welcome==
{{Robelbox|theme=9|title='''[[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]],  Amirrorslens!'''|width=100%}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
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== Book Chapter Formatting ==

wondering if there's a better way to format the flow and wording of the book chapter section? Since it's a title with a subtitle that's a question within a sentence. [[User:Amirrorslens|Amirrorslens]] ([[User talk:Amirrorslens|discuss]] • [[Special:Contributions/Amirrorslens|contribs]]) 22:00, 6 September 2026 (UTC)</text>
      <sha1>gj75sfk5a0yz6chwjh7mjoi9o3hzjau</sha1>
    </revision>
  </page>
  <page>
    <title>Motivation and emotion/Book/2026/Impulsivity versus sensation-seeking</title>
    <ns>0</ns>
    <id>331004</id>
    <revision>
      <id>2832002</id>
      <parentid>2831445</parentid>
      <timestamp>2026-09-07T11:04:53Z</timestamp>
      <contributor>
        <username>~2026-48491-08</username>
        <id>3110705</id>
      </contributor>
      <comment>/* Understanding impulsivity */</comment>
      <origin>2832002</origin>
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      <text bytes="33007" sha1="5wrwr8bwm9f5ne76ie8q443q4nlrd1v" xml:space="preserve">{{title|Impulsivity versus sensation-seeking:&lt;br&gt;What is the distinction between impulsivity and sensation-seeking and how does this affect behaviour?}}
&lt;div align=center&gt;Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].&lt;br&gt;[[Motivation and emotion/About/Staff|Seek approval]] for any changes.&lt;br&gt;Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).&lt;/div&gt;
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[[File: Beer Cantus.jpg|right|thumb|250px|'''Figure 1.''' Social drinking can involve similar observable behaviours despite differences in the psychological processes underlying an individual's decision to participate.]]

'''Imagine this:'''

At a university party, two students are offered an unfamiliar alcoholic beverage. The first accepts immediately, without hesitation, considering the possible consequences. The second pauses but deliberately chooses to try it because the experience is new and exciting. From the outside, their behaviour looks almost identical: both accept the drink. Psychologically, however, the processes motivating their decisions may be quite different.
{{RoundBoxBottom}}

Impulsivity and sensation seeking are related but distinct psychological constructs that can help explain why people engage in seemingly similar behaviours for different reasons. Impulsivity is multidimensional and includes tendencies such as acting without sufficient forethought, whereas sensation seeking reflects the pursuit of novel, exciting, or stimulating experiences (Goh et al., 2020; Ravert &amp; Donnellan, 2021). Consequently, risk taking behaviour does not necessarily indicate that an individual is simply &quot;impulsive&quot;. Understanding the motivation and psychological processes behind the behaviour can provide a more complete explanation of why it occurs.

Distinguishing impulsivity from sensation seeking is particularly essential when considering risk taking behaviour. Different dimensions of impulsivity and sensation seeking are associated with different patterns of health risk behaviour, suggesting that similar actions may arise through varied psychological pathways (Rogers et al., 2021). In the opening scenario, for instance, immediately accepting the drink without considering its consequences may reflect a lack of premeditation, whereas deliberately accepting it for novelty and excitement may more closely reflect sensation seeking. The behavioural outcome is similar, but the motivation is not.

Alcohol use provides a useful real world example of why this distinction matters. Research with university students suggests that sensation seeking and impulsivity can relate to alcohol involvement through different pathways, with sensation seeking more strongly associated with alcohol consumption and impulsivity more closely associated with alcohol related problems (Magid et al., 2007). Identifying these differences can therefore improve understanding of not only whether someone engages in risky behaviour, but also the psychological processes that may contribute to that behaviour and its consequences.

This chapter examines the theoretical and empirical distinction between impulsivity and sensation seeking and evaluates how each may influence behaviour. By examining their conceptual overlap, underlying psychological processes, relationships with risk taking, and associations with alcohol use, the chapter demonstrates why understanding ''why'' a person behaves in a particular way can be as important as observing ''what'' they do.

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'''Focus questions'''

# What is impulsivity and what are its key characteristics?
# What is sensation seeking and how does it differ from impulsivity?
# What psychological processes distinguish impulsivity from sensation seeking?
# How do impulsivity and sensation seeking differentially influence risk-taking behaviour?
# How can these differences help explain alcohol use and related consequences?
{{RoundBoxBottom}}

== Understanding impulsivity ==

Impulsivity is commonly understood as acting without thinking, but psychological research suggests that it is not a single characteristic. Behaviours described as impulsive can result from varied psychological processes, such as acting impetuously during intense emotions, failing to consider future consequences, or struggling to persist with difficult tasks. Research supports this multidimensional understanding, finding that measures labelled as impulsivity assess several related but distinguishable characteristics rather than one unified trait (Berg et al., 2015; Sharma et al., 2014). Thus, understanding why an individual acts impulsively may provide more information than simply labelling the behaviour as impulsive.

=== The UPPS-P model ===

One influential framework for understanding these differences is the '''UPPS-P model of impulsive personality'''. The original UPPS model proposed four dimensions: '''negative urgency''', or acting rashly during negative emotion; '''lack of premeditation''', or acting without adequately considering consequences, '''lack of perseverance''', involving difficulty remaining focused on demanding or boring tasks and '''sensation seeking''', involving preference for exciting and novel experiences (Whiteside &amp; Lynam, 2001). The framework was later expanded to distinguish '''positive urgency''', referring to hastely actions during intense positive emotion, from negative urgency (Cyders &amp; Smith, 2008). Consequently, two apparently impulsive decisions may originate from quite different combinations of emotion, planning, persistence and reward seeking.

Experts agree that these components should be measured individually. Network analysis of the UPPS-P found meaningful relationships between its components while also indicating that the dimensions are not interchangeable (Goh et al., 2020). Other research has continued to examine and refine multidimensional measures of impulsivity, demonstrating both the usefulness and continuing complexity of defining the construct (Samiefard et al., 2023; Türkmen et al., 2023). This is an important limitation of the broad term impulsivity: although multidimensional models provide greater precision, disagreement about exactly how impulsivity should be organised and measured remains.

=== Emotion and urgency ===

The distinction between positive and negative urgency further demonstrates why motivation matters. Urgency theory proposes that intense emotional states can increase the likelihood of reckless action, with positive urgency occurring during strongly positive emotion and negative urgency during strongly negative emotion (Cyders &amp; Smith, 2008). This differs from lack of premeditation because a person may ordinarily consider consequences effectively but behave differently when experiencing intense emotion.

The opening party scenario illustrates this distinction. Immediately accepting the unfamiliar drink without adequately considering its consequences may indicate lack of premeditation. If the decision instead occurred during intense excitement at the party, positive urgency might provide another explanation. The observable action alone therefore cannot identify which dimension was responsible.

== Understanding sensation seeking ==

Sensation seeking is strongly correlated to impulsivity but places greater emphasis on the motivation to experience novelty, intensity and stimulation. The construct has traditionally been understood as an individual difference in preference for varied, novel, complex and intense experiences, sometimes accompanied by willingness to accept risk to obtain those experiences (Roberti, 2004; Zuckerman &amp; Kuhlman, 2000). Ultimately indicating that risk itself does not always have to be the person's goal. Instead, risk may be accepted because it accompanies an experience considered sufficiently interesting or rewarding.

=== A motivational perspective ===

This provides an important distinction from other impulsivity dimensions. Someone displaying lack of premeditation may act before adequately considering the consequences, whereas a sensation seeker may recognise the consequences and deliberately decide that the potential stimulation is worthwhile. In the opening scenario, the second student hesitates before accepting the unfamiliar drink but chooses it because the experience is new and exciting. The decision may therefore involve forethought while still being associated with risk.

Sensation seeking should consequently not be treated as inherently dysfunctional. Ravert and Donnellan (2021) found different associations between impulsivity, sensation seeking and psychological well being, supporting the idea that the constructs should not simply be combined into a general tendency towards problematic behaviour. Sensation seeking may encourage exploration and engagement as well as potentially hazardous behaviour, meaning that its consequences depend partly on how and where the need for stimulation is expressed.

=== A theoretical complication ===

An important theoretical complication is that sensation seeking is simultaneously treated as a distinct construct and included as a dimension within the UPPS-P model of impulsivity (Whiteside &amp; Lynam, 2001). The inclusion of sensation seeking within the UPPS-P model does not mean that it is the same as other forms of impulsivity; rather, it is considered one distinct pathway that may contribute to impulsive behaviour. Contrastingly, it demonstrates that the boundaries surrounding the broader concept of impulsivity remain debated and depend partly on how researchers define and measure it. If all sensation seeking were simply impulsivity, there would be little reason to expect the two to show different relationships with behaviour. Evidence that they predict different outcomes can therefore help determine whether distinguishing them is psychologically meaningful.

== Distinguishing impulsivity from sensation seeking ==

Impulsivity and sensation seeking overlap because both can contribute to behaviours involving uncertainty or risk. The key distinction concerns the process motivating the action. Dimensions such as urgency and lack of premeditation emphasise rash action or insufficient regulation, whereas sensation seeking emphasises approach towards novelty, excitement and stimulation (Cyders &amp; Smith, 2008; Zuckerman &amp; Kuhlman, 2000). Similar behaviour can therefore emerge through different psychological pathways.

Research comparing the constructs provides support for this distinction. Magid et al. (2007), found that sensation seeking and impulsivity showed different relationships with alcohol involvement, suggesting that combining them could overlook meaningful differences. Similarly, a meta-analysis found that sensation seeking and impulsivity were both associated with greater risk taking, but sensation seeking showed a somewhat stronger relationship with risky behaviour than impulsivity (Lauriola et al., 2014). These findings support distinguishing the constructs while also demonstrating that neither provides a complete explanation of risky behaviour.

'''Table 1'''

''Comparison of impulsivity and sensation seeking''

{| class=&quot;wikitable&quot;
|-
! Characteristic
! Impulsivity
! Sensation seeking
|-
| '''Central process'''
| Rash action, insufficient forethought or regulation
| Pursuit of novelty, excitement and stimulation
|-
| '''Role of consequences'''
| May be insufficiently considered
| May be recognised but accepted
|-
| '''Role of emotion'''
| Urgency can produce rash action during intense emotion
| Excitement/stimulation can motivate approach
|-
| '''Relationship with risk'''
| Risk can result from poor planning or regulation
| Risk may be tolerated to obtain stimulation
|-
| '''Example'''
| Immediately accepting a drink without considering consequences
| Choosing the drink because trying something unfamiliar is exciting
|}

=== Development and the dual systems model ===

The dual systems model provides another theoretical perspective for understanding this distinction. The model proposes that heightened reward sensitivity develops differently from capacities associated with cognitive control, potentially contributing to increased risk taking during adolescence (Steinberg, 2010). From this perspective, attraction towards rewarding or stimulating experiences and the ability to regulate behaviour are related but separable processes.

Conversely, the model has also been critically reconsidered. Shulman et al. (2016) concluded that evidence broadly supports different developmental trajectories for reward-related and cognitive control systems while also highlighting complexities that cannot be captured by a simple imbalance between two systems. Risk taking varies substantially across people and situations, so developmental models should not be interpreted as suggesting that risky behaviour is inevitable or caused by one neural mechanism. The theory is useful for explaining why reward seeking and behavioural control can be distinguished, but it should complement rather than replace personality and contextual explanations.

== Impulsivity, sensation seeking, and risk taking behaviour ==

The theoretical distinction becomes particularly useful when considering risk taking behaviour. If impulsivity and sensation seeking represented the same underlying characteristic, they would be expected to show broadly equivalent relationships with risky outcomes. Instead, evidence indicates that different dimensions can be associated with different behaviours and consequences.

Lauriola et al. (2014) examined this issue meta-analytically using the Balloon Analogue Risk Task and found that both sensation seeking and impulsivity were positively but modestly associated with behavioural risk taking. Research across other contexts similarly associates sensation seeking or impulsivity related traits with health-risk behaviours (Rogers et al., 2021), adolescent risk taking (Siraj et al., 2021), and speeding behaviour (Sârbescu &amp; Rusu, 2021). More recently, Grubbs et al. (2024) demonstrated further specificity within sports wagering: sensation seeking was associated with having engaged in sports wagering, while urgency related dimensions showed different associations with wagering involvement and gambling related problems.

These findings provide evidence for the theoretical distinction, whilst also requiring cautious interpretation. Personality traits generally explain only part of the variation in complex behaviours, and correlations cannot establish that a trait directly causes an individual to take a particular risk. Social influences, opportunity, emotional state, perceived rewards and the specific type of risk may interact with personality characteristics. Therefore, describing someone simply as a &quot;risk taker&quot; may obscure both the psychological pathway and the context contributing to their behaviour.

== Alcohol use and related consequences ==

Alcohol use provides an especially useful real-world example because drinking and experiencing alcohol related problems are not the same outcome. Sensation seeking may motivate approach towards stimulating social or drinking experiences, whereas other impulsivity dimensions may be more relevant to rash decisions and harmful consequences. This distinction directly reflects the opening scenario: both students accept the same drink, however their reasons for doing so differ.

Magid et al. (2007) found that sensation seeking and impulsivity related differently to alcohol use and alcohol related problems among university students. Broader research evidence supports this outcome specific approach; for instance across 96 studies, Coskunpinar et al. (2013) found that different UPPS dimensions showed different relationships with alcohol outcomes, with urgency dimensions particularly relevant to alcohol related problems. Evidence from individuals entering residential alcohol detoxification also demonstrates clinically relevant relationships between UPPS-P dimensions and substance related characteristics (Kempeneers et al., 2023).

These findings illustrate why psychological explanations should expand beyond asking whether someone is simply &quot;impulsive&quot;. Identifying whether behaviour is motivated primarily by stimulation, emotional urgency, insufficient forethought or another process may provide a more precise understanding of the behaviour. Simultaniously, much of this evidence is correlational and relies on self report measures, so personality should not be interpreted as determining whether an individual will drink or experience alcohol related harm.

=== From explanation to application ===

Understanding different pathways may also have practical implications. Individuals motivated primarily by sensation seeking may benefit from finding safer ways to obtain novelty and stimulation, whereas behaviour associated with urgency may require greater attention to managing intense emotional states before acting. Lack of premeditation is particularly relevant, strategies that introduce time for considering consequences may be more appropriate.

These possibilities illustrate why distinguishing psychological processes can contribute to improving everyday behaviour rather than merely attaching personality labels to people. However, individualised strategies should not be inferred solely from personality scores, and the available evidence does not demonstrate that matching interventions to UPPS-P dimensions will necessarily produce better outcomes. Instead, the distinction provides a framework for understanding why the same behaviour may require different explanations and potentially different approaches to change.

== Conclusion ==

Impulsivity and sensation seeking are related psychological constructs, however should not automatically be treated as interchangeable. Multidimensional models such as the UPPS-P demonstrate that behaviour commonly labelled &quot;impulsive&quot; can arise through different pathways involving emotion, forethought, persistence and attraction towards stimulation. Sensation seeking is particularly important because it overlaps conceptually with impulsivity while emphasising the motivation to pursue novel and exciting experiences.

Research supports the practical value of distinguishing these processes. Sensation seeking and different dimensions of impulsivity show different patterns of association with risk taking, alcohol involvement and other potentially harmful behaviours, although these relationships are generally probabilistic rather than deterministic. Consequently, observable behaviour alone cannot reveal why an individual acted as they did.

The opening scenario illustrates the practical significance of distinguishing between these psychological processes. Accepting an unfamiliar drink may result from acting without considering consequences, seeking an exciting new experience, responding rashly to intense emotion, or a combination of these processes. Understanding why behaviour occurs, rather than simply labelling what occurred, can provide a more useful foundation for understanding and potentially improving everyday decision making.

== Understanding sensation seeking ==
'''Understanding sensation seeking key points''':
*Sensation seeking reflects a tendency to pursue novel, varied, exciting, or stimulating experiences and can be distinguished from impulsivity characterised by poor inhibition or forethought (Ravert &amp; Donnellan, 2021).
*Sensation seeking is represented as a distinct dimension within multidimensional models such as the UPPS-P, supporting the view that it should not be treated as synonymous with other impulsivity related traits (Goh et al., 2020; Samiefard et al., 2023).
*Higher sensation seeking is associated with greater risk taking behaviour, although the pursuit of stimulation rather than risk itself may underlie this association (Siraj et al., 2021).
== Distinguishing impulsivity from sensation seeking ==
'''Distinguishing impulsivity from sensation seeking key points''':
*Whilst impulsivity and sensation seeking can both contribute to risky behaviour, they represent distinguishable psychological tendencies rather than interchangeable explanations for behaviour (Magid et al., 2007; Ravert &amp; Donnellan, 2021).
*A central distinction concerns the processes underlying behaviour; sensation seeking involves the pursuit of stimulation and novel experiences, whereas other dimensions of impulsivity involve tendencies such as acting without adequate forethought or under strong emotional states (Goh et al., 2020; Samiefard et al., 2023).
*Consequently, similar observable behaviours may arise through different psychological pathways, meaning that identifying what a person does does not necessarily explain why they do it (Magid et al., 2007).
== Impulsivity, sensation seeking, and risk taking behaviour ==
'''Impulsivity, sensation seeking, and risk taking behaviour key points''':
*Different profiles of impulsivity are associated with different patterns of health risk behaviour, including substance use and risky sexual behaviour, suggesting that individual impulsivity dimensions may have different behavioural consequences (Rogers et al., 2021).
*Sensation seeking is positively associated with risk taking, while social factors such as peer influence can also independently contribute to risky behaviour (Siraj et al., 2021).
*Different impulsivity related traits show differing associations to specific forms of risk taking; for example, recent research found sensation seeking associated with having tried sports wagering, while positive urgency was associated with greater frequency and variety of wagering and urgency with gambling disorder symptoms (Grubbs et al., 2024).

== Alcohol use and related consequences ==
'''Alcohol use and related consequences key points''':
*Sensation seeking and impulsivity can contribute to alcohol involvement through different pathways, supporting their treatment as distinct constructs rather than interchangeable predictors of drinking behaviour (Magid et al., 2007).
*Sensation seeking may be particularly relevant to alcohol consumption and the rewarding or stimulating aspects of drinking, whereas impulsivity can contribute differently to alcohol related problems and consequences (Magid et al., 2007).
*Multidimensional assessment is also relevant in clinical substance use contexts: UPPS-P dimensions can be separately assessed among individuals undergoing residential detoxification, reinforcing the value of considering distinct impulsivity related traits in understanding substance related behaviour (Kempeneers et al., 2023).

==Figures==
[[File:Sensation seeking Vs Impulsivity.png|thumb|387x387px|'''Figure 2'''. Comparison of the UPPS-P dimensions of impulsive behaviour and Zuckerman’s dimensions of sensation seeking, highlighting areas of conceptual overlap and distinction (Goh et al., 2020; Magid et al., 2007; Samiefard et al., 2023). (image created independently using Canva software).|center]]

==Learning features==
'''Table 1''' 

'''Table – Comparing impulsivity and sensation''' '''seeking''' 

The comparison table summarises the major conceptual differences and similarities between impulsivity and sensation seeking, including their defining characteristics, underlying processes, and relationships with risk taking behaviour.
{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! Feature !! Impulsivity !! Sensation seeking
|-
| '''Core characteristic''' || Tendency toward rash or insufficiently considered action across multiple dimensions || Tendency to seek novel, varied, exciting or stimulating experiences
|-
| '''Key Process''' || Can involve reduced forethought, urgency or behavioural regulation || Motivation toward novelty, excitement and stimulation
|-
|'''Risk Taking'''
|Risk may result from insufficient consideration of consequences or other impulsive tendencies
|Risk may be accepted in pursuit of rewarding or stimulating experiences
|-
|'''UPPS-P'''
|Multidimensional model including positive urgency, negative urgency, lack of premeditation, lack of perseverance and sensation seeking
|Sensation seeking is one distinct dimension within the UPPS-P model
|-
|'''Example'''
|Immediately accepting an unfamiliar drink without considering consequences
|Deliberately trying the drink because the experience is novel and exciting
|-
|'''Behavioural Outcome'''
|Can contribute to health-risk, gambling and substance related behaviours
|Can contribute to risk taking, alcohol use and novelty oriented behaviour
|}
Whilst impulsivity and sensation seeking can contribute to similar observable behaviours, their underlying characteristics and psychological processes differ (see Table 1; Goh et al., 2020; Magid et al., 2007).

'''Quiz: Impulsivity or sensation seeking?'''
&lt;quiz display=&quot;simple&quot;&gt;
{A student is offered an unfamiliar alcoholic drink at a party and immediately accepts without considering the possible consequences. Which characteristic best explains this behaviour?
|type=&quot;()&quot;}

+ Lack of premeditation
- Thrill and adventure seeking
- Experience seeking
- Boredom susceptibility

{A student deliberately chooses to try an unfamiliar activity because they enjoy novelty, excitement, and stimulation. Which construct best explains this motivation?
|type=&quot;()&quot;}

- Lack of perseverance
+ Sensation seeking
- Negative urgency
- Lack of premeditation

{Which statement best describes the distinction between impulsivity and sensation seeking?
|type=&quot;()&quot;}

- Impulsivity and sensation seeking are interchangeable terms for the same psychological construct.
- Sensation seeking always involves acting without considering consequences.
+ Similar observable behaviours can arise from different underlying motivations and psychological processes.
- Only impulsivity is associated with risk taking behaviour.
&lt;/quiz&gt;

== [[Conclusion]] ==
'''Conclusion key points''':
*Impulsivity and sensation seeking are related but psychologically distinguishable constructs, and similar behaviours should not automatically be assumed to reflect the same underlying process (see Figure 2; Magid et al., 2007; Ravert &amp; Donnellan, 2021).
*Impulsivity and sensation seeking behavioural effects vary across contexts, with different dimensions showing different associations with health risk behaviour, risk taking, gambling, and substance related outcomes (Rogers et al., 2021; Grubbs et al., 2024).
*Distinguishing why an individual engages in behaviour such as seeking stimulation versus acting with insufficient forethought provides a more nuanced psychological explanation of risk taking and its consequences (Magid et al., 2007).

== See also ==
* [[Motivation and emotion/Book/2011/Sensation seeking|Sensation seeking]] (Book chapter, 2011)
* [[w:Sensation Seeking Scale|Sensation Seeking Scale]] (Wikipedia)

== References ==

{{Hanging indent|Berg, J. M., Latzman, R. D., Bliwise, N. G., &amp; Lilienfeld, S. O. (2015). Parsing the heterogeneity of impulsivity: A meta-analytic review of the behavioral implications of the UPPS for psychopathology. ''Psychological Assessment, 27''(4), 1129–1146. https://doi.org/10.1037/pas0000111}}

{{Hanging indent|Coskunpinar, A., Dir, A. L., &amp; Cyders, M. A. (2013). Multidimensionality in impulsivity and alcohol use: A meta-analysis using the UPPS model of impulsivity. ''Alcoholism: Clinical and Experimental Research, 37''(9), 1441–1450. https://doi.org/10.1111/acer.12131}}

{{Hanging indent|Cyders, M. A., &amp; Smith, G. T. (2008). Emotion-based dispositions to rash action: Positive and negative urgency. ''Psychological Bulletin, 134''(6), 807–828. https://doi.org/10.1037/a0013341}}

{{Hanging indent|Goh, P. K., Lee, C. A., Martel, M. M., Fillmore, M. T., Derefinko, K. J., &amp; Lynam, D. R. (2020). Conceptualizing the UPPS-P model of impulsive personality through network analysis: Key dimensions and general robustness across young adulthood. ''Journal of Personality, 88''(6), 1302–1314. https://doi.org/10.1111/jopy.12572}}

{{Hanging indent|Grubbs, J. B., Connolly, A. J., Floyd, C. G., Kim, H. S., &amp; Kraus, S. W. (2024). Impulsivity and diverse forms of sports wagering in the U.S.: An examination of the UPPS-P model. ''Addictive Behaviors, 156'', 108058. https://doi.org/10.1016/j.addbeh.2024.108058}}

{{Hanging indent|Kempeneers, P., Mreyen, K., Pallincourt, R., Remacle, F., Wildemeersch, G., &amp; Simon, J. (2023). Validation of the UPPS-P Impulsive Behavior Scale and clinical correlates of its scores in French-speaking patients starting a residential detoxification program. ''Indian Journal of Psychological Medicine, 45''(5), 503–510. https://doi.org/10.1177/02537176231157411}}

{{Hanging indent|Lauriola, M., Panno, A., Levin, I. P., &amp; Lejuez, C. W. (2014). Individual differences in risky decision making: A meta-analysis of sensation seeking and impulsivity with the Balloon Analogue Risk Task. ''Journal of Behavioral Decision Making, 27''(1), 20–36. https://doi.org/10.1002/bdm.1784}}

{{Hanging indent|Magid, V., MacLean, M. G., &amp; Colder, C. R. (2007). Differentiating between sensation seeking and impulsivity through their mediated relations with alcohol use and problems. ''Addictive Behaviors, 32''(10), 2046–2061. https://doi.org/10.1016/j.addbeh.2007.01.015}}

{{Hanging indent|Ravert, R. D., &amp; Donnellan, M. B. (2021). Impulsivity and sensation seeking: Differing associations with psychological well-being. ''Applied Research in Quality of Life, 16''(4), 1503–1515. https://doi.org/10.1007/s11482-020-09829-y}}

{{Hanging indent|Roberti, J. W. (2004). A review of behavioral and biological correlates of sensation seeking. ''Journal of Research in Personality, 38''(3), 256–279. https://doi.org/10.1016/S0092-6566(03)00067-9}}

{{Hanging indent|Rogers, M. M., Kelley, K., &amp; McKinney, C. (2021). Trait impulsivity and health risk behaviors: A latent profile analysis. ''Personality and Individual Differences, 171'', 110511. https://doi.org/10.1016/j.paid.2020.110511}}

{{Hanging indent|Samiefard, M., Salehi Fadardi, J., Kareshki, H., &amp; Stacy, A. W. (2023). Validity and reliability of a revised S-UPPS-P Impulsive Behavior Scale: The interplay between impulsivity and working memory. ''Journal of Personality Assessment, 105''(2), 174–186. https://doi.org/10.1080/00223891.2022.2081922}}

{{Hanging indent|Sârbescu, P., &amp; Rusu, A. (2021). Personality predictors of speeding: Anger-aggression and impulsive-sensation seeking. A systematic review and meta-analysis. ''Journal of Safety Research, 77'', 86–98. https://doi.org/10.1016/j.jsr.2021.02.004}}

{{Hanging indent|Sharma, L., Markon, K. E., &amp; Clark, L. A. (2014). Toward a theory of distinct types of “impulsive” behaviors: A meta-analysis of self-report and behavioral measures. ''Psychological Bulletin, 140''(2), 374–408. https://doi.org/10.1037/a0034418}}

{{Hanging indent|Shulman, E. P., Smith, A. R., Silva, K., Icenogle, G., Duell, N., Chein, J., &amp; Steinberg, L. (2016). The dual systems model: Review, reappraisal, and reaffirmation. ''Developmental Cognitive Neuroscience, 17'', 103–117. https://doi.org/10.1016/j.dcn.2015.12.010}}

{{Hanging indent|Siraj, R., Najam, B., &amp; Ghazal, S. (2021). Sensation seeking, peer influence, and risk-taking behavior in adolescents. ''Education Research International, 2021'', 8403024. https://doi.org/10.1155/2021/8403024}}

{{Hanging indent|Steinberg, L. (2010). A dual systems model of adolescent risk-taking. ''Developmental Psychobiology, 52''(3), 216–224. https://doi.org/10.1002/dev.20445}}

{{Hanging indent|Türkmen, İ., Rodoplu, N., Üner, B. S., Esmer, Ş. C., Altan-Atalay, A., &amp; Ece, B. (2023). When the UPPS-P model of impulsivity meets a revised approach: The development and validation of the TRUE Multidimensional Impulsivity Scale. ''Journal of Personality Assessment, 105''(3), 355–370. https://doi.org/10.1080/00223891.2022.2093730}}

{{Hanging indent|Whiteside, S. P., &amp; Lynam, D. R. (2001). The five factor model and impulsivity: Using a structural model of personality to understand impulsivity. ''Personality and Individual Differences, 30''(4), 669–689. https://doi.org/10.1016/S0191-8869(00)00064-7}}

{{Hanging indent|Zuckerman, M., &amp; Kuhlman, D. M. (2000). Personality and risk-taking: Common biosocial factors. ''Journal of Personality, 68''(6), 999–1029. https://doi.org/10.1111/1467-6494.00124}}

==External links==
* [https://dictionary.apa.org/sensation-seeking-scale APA Dictionary of Psychology – Sensation-Seeking Scale]
* [https://onlinelibrary.wiley.com/doi/full/10.1002/9781405186407.wbiecs029 Sensation Seeking – Zuckerman] {{ic|Move academic sources to citations/references}}
* [https://www.impulsivity.org/measurement/upps_p/ UPPS-P Impulsive Behavior Scale]

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Impulsivity]]
[[Category:Motivation and emotion/Book/Sensation-seeking]]</text>
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        <username>Reillyu3280706</username>
        <id>3106308</id>
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      <text bytes="29595" sha1="3fq93albiqzr8pervwpuo9w4dxwhvi6" xml:space="preserve">{{title|Impulsivity versus sensation-seeking:&lt;br&gt;What is the distinction between impulsivity and sensation-seeking and how does this affect behaviour?}}
&lt;div align=center&gt;Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].&lt;br&gt;[[Motivation and emotion/About/Staff|Seek approval]] for any changes.&lt;br&gt;Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).&lt;/div&gt;
__TOC__

{{RoundBoxTop|theme=2}}
[[File: Beer Cantus.jpg|right|thumb|250px|'''Figure 1.''' Social drinking can involve similar observable behaviours despite differences in the psychological processes underlying an individual's decision to participate.]]

'''Imagine this:'''

At a university party, two students are offered an unfamiliar alcoholic beverage. The first accepts immediately, without hesitation, considering the possible consequences. The second pauses but deliberately chooses to try it because the experience is new and exciting. From the outside, their behaviour looks almost identical: both accept the drink. Psychologically, however, the processes motivating their decisions may be quite different.
{{RoundBoxBottom}}

Impulsivity and sensation seeking are related but distinct psychological constructs that can help explain why people engage in seemingly similar behaviours for different reasons. Impulsivity is multidimensional and includes tendencies such as acting without sufficient forethought, whereas sensation seeking reflects the pursuit of novel, exciting, or stimulating experiences (Goh et al., 2020; Ravert &amp; Donnellan, 2021). Consequently, risk taking behaviour does not necessarily indicate that an individual is simply &quot;impulsive&quot;. Understanding the motivation and psychological processes behind the behaviour can provide a more complete explanation of why it occurs.

Distinguishing impulsivity from sensation seeking is particularly essential when considering risk taking behaviour. Different dimensions of impulsivity and sensation seeking are associated with different patterns of health risk behaviour, suggesting that similar actions may arise through varied psychological pathways (Rogers et al., 2021). In the opening scenario, for instance, immediately accepting the drink without considering its consequences may reflect a lack of premeditation, whereas deliberately accepting it for novelty and excitement may more closely reflect sensation seeking. The behavioural outcome is similar, but the motivation is not.

Alcohol use provides a useful real world example of why this distinction matters. Research with university students suggests that sensation seeking and impulsivity can relate to alcohol involvement through different pathways, with sensation seeking more strongly associated with alcohol consumption and impulsivity more closely associated with alcohol related problems (Magid et al., 2007). Identifying these differences can therefore improve understanding of not only whether someone engages in risky behaviour, but also the psychological processes that may contribute to that behaviour and its consequences.

This chapter examines the theoretical and empirical distinction between impulsivity and sensation seeking and evaluates how each may influence behaviour. By examining their conceptual overlap, underlying psychological processes, relationships with risk taking, and associations with alcohol use, the chapter demonstrates why understanding ''why'' a person behaves in a particular way can be as important as observing ''what'' they do.

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

# What is impulsivity and what are its key characteristics?
# What is sensation seeking and how does it differ from impulsivity?
# What psychological processes distinguish impulsivity from sensation seeking?
# How do impulsivity and sensation seeking differentially influence risk-taking behaviour?
# How can these differences help explain alcohol use and related consequences?
{{RoundBoxBottom}}

== Understanding impulsivity ==

Impulsivity is commonly understood as acting without thinking, but psychological research suggests that it is not a single characteristic. Behaviours described as impulsive can result from varied psychological processes, such as acting impetuously during intense emotions, failing to consider future consequences, or struggling to persist with difficult tasks. Research supports this multidimensional understanding, finding that measures labelled as impulsivity assess several related but distinguishable characteristics rather than one unified trait (Berg et al., 2015; Sharma et al., 2014). Thus, understanding why an individual acts impulsively may provide more information than simply labelling the behaviour as impulsive.

=== The UPPS-P model ===

One influential framework for understanding these differences is the UPPS-P model of impulsive personality. The original UPPS model proposed four dimensions: negative urgency, or acting rashly during negative emotion; lack of premeditation, or acting without adequately considering consequences, lack of perseverance, involving difficulty remaining focused on demanding or boring tasks and sensation seeking, involving preference for exciting and novel experiences (Whiteside &amp; Lynam, 2001). The framework was later expanded to distinguish positive urgency, referring to hastely actions during intense positive emotion, from negative urgency (Cyders &amp; Smith, 2008). Consequently, two apparently impulsive decisions may originate from quite different combinations of emotion, planning, persistence and reward seeking.

Experts agree that these components should be measured individually. Network analysis of the UPPS-P found meaningful relationships between its components while also indicating that the dimensions are not interchangeable (Goh et al., 2020). Other research has continued to examine and refine multidimensional measures of impulsivity, demonstrating both the usefulness and continuing complexity of defining the construct (Samiefard et al., 2023; Türkmen et al., 2023). This is an important limitation of the broad term impulsivity: although multidimensional models provide greater precision, disagreement about exactly how impulsivity should be organised and measured remains.

=== Emotion and urgency ===

The distinction between positive and negative urgency further demonstrates why motivation matters. Urgency theory proposes that intense emotional states can increase the likelihood of reckless action, with positive urgency occurring during strongly positive emotion and negative urgency during strongly negative emotion (Cyders &amp; Smith, 2008). This differs from lack of premeditation because a person may ordinarily consider consequences effectively but behave differently when experiencing intense emotion.

The opening party scenario illustrates this distinction. Immediately accepting the unfamiliar drink without adequately considering its consequences may indicate lack of premeditation. If the decision instead occurred during intense excitement at the party, positive urgency might provide another explanation. The observable action alone therefore cannot identify which dimension was responsible.

== Understanding sensation seeking ==

Sensation seeking is strongly correlated to impulsivity but places greater emphasis on the motivation to experience novelty, intensity and stimulation. The construct has traditionally been understood as an individual difference in preference for varied, novel, complex and intense experiences, sometimes accompanied by willingness to accept risk to obtain those experiences (Roberti, 2004; Zuckerman &amp; Kuhlman, 2000). Ultimately indicating that risk itself does not always have to be the person's goal. Instead, risk may be accepted because it accompanies an experience considered sufficiently interesting or rewarding.

=== A motivational perspective ===

This provides an important distinction from other impulsivity dimensions. Someone displaying lack of premeditation may act before adequately considering the consequences, whereas a sensation seeker may recognise the consequences and deliberately decide that the potential stimulation is worthwhile. In the opening scenario, the second student hesitates before accepting the unfamiliar drink but chooses it because the experience is new and exciting. The decision may therefore involve forethought while still being associated with risk.

Sensation seeking should consequently not be treated as inherently dysfunctional. Ravert and Donnellan (2021) found different associations between impulsivity, sensation seeking and psychological well being, supporting the idea that the constructs should not simply be combined into a general tendency towards problematic behaviour. Sensation seeking may encourage exploration and engagement as well as potentially hazardous behaviour, meaning that its consequences depend partly on how and where the need for stimulation is expressed.

=== A theoretical complication ===

An important theoretical complication is that sensation seeking is simultaneously treated as a distinct construct and included as a dimension within the UPPS-P model of impulsivity (Whiteside &amp; Lynam, 2001). The inclusion of sensation seeking within the UPPS-P model does not mean that it is the same as other forms of impulsivity; rather, it is considered one distinct pathway that may contribute to impulsive behaviour. Contrastingly, it demonstrates that the boundaries surrounding the broader concept of impulsivity remain debated and depend partly on how researchers define and measure it. If all sensation seeking were simply impulsivity, there would be little reason to expect the two to show different relationships with behaviour. Evidence that they predict different outcomes can therefore help determine whether distinguishing them is psychologically meaningful.

== Distinguishing impulsivity from sensation seeking ==

Impulsivity and sensation seeking overlap because both can contribute to behaviours involving uncertainty or risk. The key distinction concerns the process motivating the action. Dimensions such as urgency and lack of premeditation emphasise rash action or insufficient regulation, whereas sensation seeking emphasises approach towards novelty, excitement and stimulation (Cyders &amp; Smith, 2008; Zuckerman &amp; Kuhlman, 2000). Similar behaviour can therefore emerge through different psychological pathways.

Research comparing the constructs provides support for this distinction. Magid et al. (2007), found that sensation seeking and impulsivity showed different relationships with alcohol involvement, suggesting that combining them could overlook meaningful differences. Similarly, a meta-analysis found that sensation seeking and impulsivity were both associated with greater risk taking, but sensation seeking showed a somewhat stronger relationship with risky behaviour than impulsivity (Lauriola et al., 2014). These findings support distinguishing the constructs while also demonstrating that neither provides a complete explanation of risky behaviour.

'''Table 1'''

''Comparison of impulsivity and sensation seeking''

{| class=&quot;wikitable&quot;
|-
! Characteristic
! Impulsivity
! Sensation seeking
|-
| '''Central process'''
| Rash action, insufficient forethought or regulation
| Pursuit of novelty, excitement and stimulation
|-
| '''Role of consequences'''
| May be insufficiently considered
| May be recognised but accepted
|-
| '''Role of emotion'''
| Urgency can produce rash action during intense emotion
| Excitement/stimulation can motivate approach
|-
| '''Relationship with risk'''
| Risk can result from poor planning or regulation
| Risk may be tolerated to obtain stimulation
|-
| '''Example'''
| Immediately accepting a drink without considering consequences
| Choosing the drink because trying something unfamiliar is exciting
|}

=== Development and the dual systems model ===

The dual systems model provides another theoretical perspective for understanding this distinction. The model proposes that heightened reward sensitivity develops differently from capacities associated with cognitive control, potentially contributing to increased risk taking during adolescence (Steinberg, 2010). From this perspective, attraction towards rewarding or stimulating experiences and the ability to regulate behaviour are related but separable processes.

Conversely, the model has also been critically reconsidered. Shulman et al. (2016) concluded that evidence broadly supports different developmental trajectories for reward related and cognitive control systems while also highlighting complexities that cannot be captured by a simple imbalance between two systems. Risk taking varies substantially across people and situations, so developmental models should not be interpreted as suggesting that risky behaviour is inevitable or caused by one neural mechanism. The theory is useful for explaining why reward seeking and behavioural control can be distinguished, but it should complement rather than replace personality and contextual explanations.

== Impulsivity, sensation seeking, and risk taking behaviour ==

The theoretical distinction becomes particularly useful when considering risk taking behaviour. If impulsivity and sensation seeking represented the same underlying characteristic, they would be expected to show broadly equivalent relationships with risky outcomes. Instead, evidence indicates that different dimensions can be associated with different behaviours and consequences.

Research examining risk taking has found that both sensation seeking and impulsivity are associated with a greater tendency to engage in risky behaviour, although these relationships are relatively modest (Lauriola et al., 2014). This pattern extends across varied types of behaviour, with sensation seeking and impulsivity related traits associated with health risk behaviours (Rogers et al., 2021), adolescent risk taking (Siraj et al., 2021), and speeding behaviour (Sârbescu &amp; Rusu, 2021). More recently, Grubbs et al. (2024) demonstrated that the specific psychological trait involved may also relate to different aspects of risky behaviour. Sensation seeking was associated with whether individuals had engaged in sports wagering, while urgency related dimensions were associated with different patterns of wagering involvement and gambling related problems. 

These findings provide evidence for the theoretical distinction, whilst also requiring cautious interpretation. Personality traits generally explain only part of the variation in complex behaviours, and correlations cannot establish that a trait directly causes an individual to take a particular risk. Social influences, opportunity, emotional state, perceived rewards and the specific type of risk may interact with personality characteristics. Therefore, describing someone simply as a &quot;risk taker&quot; may obscure both the psychological pathway and the context contributing to their behaviour.

== Alcohol use and related consequences ==

Alcohol use provides an especially useful real-world example because drinking and experiencing alcohol related problems are not the same outcome. Sensation seeking may motivate approach towards stimulating social or drinking experiences, whereas other impulsivity dimensions may be more relevant to rash decisions and harmful consequences. This distinction directly reflects the opening scenario: both students accept the same drink, however their reasons for doing so differ.

Magid et al. (2007) found that sensation seeking and impulsivity related differently to alcohol use and alcohol related problems among university students. Broader research evidence supports this outcome specific approach; for instance across 96 studies, Coskunpinar et al. (2013) found that different UPPS dimensions showed different relationships with alcohol outcomes, with urgency dimensions particularly relevant to alcohol related problems. Evidence from individuals entering residential alcohol detoxification also demonstrates clinically relevant relationships between UPPS-P dimensions and substance related characteristics (Kempeneers et al., 2023).

These findings illustrate why psychological explanations should expand beyond asking whether someone is simply &quot;impulsive&quot;. Identifying whether behaviour is motivated primarily by stimulation, emotional urgency, insufficient forethought or another process may provide a more precise understanding of the behaviour. Simultaniously, much of this evidence is correlational and relies on self report measures, so personality should not be interpreted as determining whether an individual will drink or experience alcohol related harm.

=== From explanation to application ===

Understanding different pathways may also have practical implications. Individuals motivated primarily by sensation seeking may benefit from finding safer ways to obtain novelty and stimulation, whereas behaviour associated with urgency may require greater attention to managing intense emotional states before acting. Lack of premeditation is particularly relevant, strategies that introduce time for considering consequences may be more appropriate.

These possibilities illustrate why distinguishing psychological processes can contribute to improving everyday behaviour rather than merely attaching personality labels to people. However, individualised strategies should not be inferred solely from personality scores, and the available evidence does not demonstrate that matching interventions to UPPS-P dimensions will necessarily produce better outcomes. Instead, the distinction provides a framework for understanding why the same behaviour may require different explanations and potentially different approaches to change.

== Conclusion ==

Impulsivity and sensation seeking are related psychological constructs, however should not automatically be treated as interchangeable. Multidimensional models such as the UPPS-P demonstrate that behaviour commonly labelled &quot;impulsive&quot; can arise through different pathways involving emotion, forethought, persistence and attraction towards stimulation. Sensation seeking is particularly important because it overlaps conceptually with impulsivity while emphasising the motivation to pursue novel and exciting experiences.

Research supports the practical value of distinguishing these processes. Sensation seeking and different dimensions of impulsivity show different patterns of association with risk taking, alcohol involvement and other potentially harmful behaviours, although these relationships are generally probabilistic rather than deterministic. Consequently, observable behaviour alone cannot reveal why an individual acted as they did.

The opening scenario illustrates the practical significance of distinguishing between these psychological processes. Accepting an unfamiliar drink may result from acting without considering consequences, seeking an exciting new experience, responding rashly to intense emotion, or a combination of these processes. Understanding why behaviour occurs, rather than simply labelling what occurred, can provide a more useful foundation for understanding and potentially improving everyday decision making.

==Figures==
[[File:Sensation seeking Vs Impulsivity.png|thumb|387x387px|'''Figure 2'''. Comparison of the UPPS-P dimensions of impulsive behaviour and Zuckerman’s dimensions of sensation seeking, highlighting areas of conceptual overlap and distinction (Goh et al., 2020; Magid et al., 2007; Samiefard et al., 2023). (image created independently using Canva software).|center]]

==Learning features==
'''Table 1''' 

'''Table – Comparing impulsivity and sensation''' '''seeking''' 

The comparison table summarises the major conceptual differences and similarities between impulsivity and sensation seeking, including their defining characteristics, underlying processes, and relationships with risk taking behaviour.
{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! Feature !! Impulsivity !! Sensation seeking
|-
| '''Core characteristic''' || Tendency toward rash or insufficiently considered action across multiple dimensions || Tendency to seek novel, varied, exciting or stimulating experiences
|-
| '''Key Process''' || Can involve reduced forethought, urgency or behavioural regulation || Motivation toward novelty, excitement and stimulation
|-
|'''Risk Taking'''
|Risk may result from insufficient consideration of consequences or other impulsive tendencies
|Risk may be accepted in pursuit of rewarding or stimulating experiences
|-
|'''UPPS-P'''
|Multidimensional model including positive urgency, negative urgency, lack of premeditation, lack of perseverance and sensation seeking
|Sensation seeking is one distinct dimension within the UPPS-P model
|-
|'''Example'''
|Immediately accepting an unfamiliar drink without considering consequences
|Deliberately trying the drink because the experience is novel and exciting
|-
|'''Behavioural Outcome'''
|Can contribute to health-risk, gambling and substance related behaviours
|Can contribute to risk taking, alcohol use and novelty oriented behaviour
|}
Whilst impulsivity and sensation seeking can contribute to similar observable behaviours, their underlying characteristics and psychological processes differ (see Table 1; Goh et al., 2020; Magid et al., 2007).

'''Quiz: Impulsivity or sensation seeking?'''
&lt;quiz display=&quot;simple&quot;&gt;
{A student is offered an unfamiliar alcoholic drink at a party and immediately accepts without considering the possible consequences. Which characteristic best explains this behaviour?
|type=&quot;()&quot;}

+ Lack of premeditation
- Thrill and adventure seeking
- Experience seeking
- Boredom susceptibility

{A student deliberately chooses to try an unfamiliar activity because they enjoy novelty, excitement, and stimulation. Which construct best explains this motivation?
|type=&quot;()&quot;}

- Lack of perseverance
+ Sensation seeking
- Negative urgency
- Lack of premeditation

{Which statement best describes the distinction between impulsivity and sensation seeking?
|type=&quot;()&quot;}

- Impulsivity and sensation seeking are interchangeable terms for the same psychological construct.
- Sensation seeking always involves acting without considering consequences.
+ Similar observable behaviours can arise from different underlying motivations and psychological processes.
- Only impulsivity is associated with risk taking behaviour.
&lt;/quiz&gt;

== [[Conclusion]] ==
'''Conclusion key points''':
*Impulsivity and sensation seeking are related but psychologically distinguishable constructs, and similar behaviours should not automatically be assumed to reflect the same underlying process (see Figure 2; Magid et al., 2007; Ravert &amp; Donnellan, 2021).
*Impulsivity and sensation seeking behavioural effects vary across contexts, with different dimensions showing different associations with health risk behaviour, risk taking, gambling, and substance related outcomes (Rogers et al., 2021; Grubbs et al., 2024).
*Distinguishing why an individual engages in behaviour such as seeking stimulation versus acting with insufficient forethought provides a more nuanced psychological explanation of risk taking and its consequences (Magid et al., 2007).

== See also ==
* [[Motivation and emotion/Book/2011/Sensation seeking|Sensation seeking]] (Book chapter, 2011)
* [[w:Sensation Seeking Scale|Sensation Seeking Scale]] (Wikipedia)

== References ==

{{Hanging indent|Berg, J. M., Latzman, R. D., Bliwise, N. G., &amp; Lilienfeld, S. O. (2015). Parsing the heterogeneity of impulsivity: A meta-analytic review of the behavioral implications of the UPPS for psychopathology. ''Psychological Assessment, 27''(4), 1129–1146. https://doi.org/10.1037/pas0000111}}

{{Hanging indent|Coskunpinar, A., Dir, A. L., &amp; Cyders, M. A. (2013). Multidimensionality in impulsivity and alcohol use: A meta-analysis using the UPPS model of impulsivity. ''Alcoholism: Clinical and Experimental Research, 37''(9), 1441–1450. https://doi.org/10.1111/acer.12131}}

{{Hanging indent|Cyders, M. A., &amp; Smith, G. T. (2008). Emotion-based dispositions to rash action: Positive and negative urgency. ''Psychological Bulletin, 134''(6), 807–828. https://doi.org/10.1037/a0013341}}

{{Hanging indent|Goh, P. K., Lee, C. A., Martel, M. M., Fillmore, M. T., Derefinko, K. J., &amp; Lynam, D. R. (2020). Conceptualizing the UPPS-P model of impulsive personality through network analysis: Key dimensions and general robustness across young adulthood. ''Journal of Personality, 88''(6), 1302–1314. https://doi.org/10.1111/jopy.12572}}

{{Hanging indent|Grubbs, J. B., Connolly, A. J., Floyd, C. G., Kim, H. S., &amp; Kraus, S. W. (2024). Impulsivity and diverse forms of sports wagering in the U.S.: An examination of the UPPS-P model. ''Addictive Behaviors, 156'', 108058. https://doi.org/10.1016/j.addbeh.2024.108058}}

{{Hanging indent|Kempeneers, P., Mreyen, K., Pallincourt, R., Remacle, F., Wildemeersch, G., &amp; Simon, J. (2023). Validation of the UPPS-P Impulsive Behavior Scale and clinical correlates of its scores in French-speaking patients starting a residential detoxification program. ''Indian Journal of Psychological Medicine, 45''(5), 503–510. https://doi.org/10.1177/02537176231157411}}

{{Hanging indent|Lauriola, M., Panno, A., Levin, I. P., &amp; Lejuez, C. W. (2014). Individual differences in risky decision making: A meta-analysis of sensation seeking and impulsivity with the Balloon Analogue Risk Task. ''Journal of Behavioral Decision Making, 27''(1), 20–36. https://doi.org/10.1002/bdm.1784}}

{{Hanging indent|Magid, V., MacLean, M. G., &amp; Colder, C. R. (2007). Differentiating between sensation seeking and impulsivity through their mediated relations with alcohol use and problems. ''Addictive Behaviors, 32''(10), 2046–2061. https://doi.org/10.1016/j.addbeh.2007.01.015}}

{{Hanging indent|Ravert, R. D., &amp; Donnellan, M. B. (2021). Impulsivity and sensation seeking: Differing associations with psychological well-being. ''Applied Research in Quality of Life, 16''(4), 1503–1515. https://doi.org/10.1007/s11482-020-09829-y}}

{{Hanging indent|Roberti, J. W. (2004). A review of behavioral and biological correlates of sensation seeking. ''Journal of Research in Personality, 38''(3), 256–279. https://doi.org/10.1016/S0092-6566(03)00067-9}}

{{Hanging indent|Rogers, M. M., Kelley, K., &amp; McKinney, C. (2021). Trait impulsivity and health risk behaviors: A latent profile analysis. ''Personality and Individual Differences, 171'', 110511. https://doi.org/10.1016/j.paid.2020.110511}}

{{Hanging indent|Samiefard, M., Salehi Fadardi, J., Kareshki, H., &amp; Stacy, A. W. (2023). Validity and reliability of a revised S-UPPS-P Impulsive Behavior Scale: The interplay between impulsivity and working memory. ''Journal of Personality Assessment, 105''(2), 174–186. https://doi.org/10.1080/00223891.2022.2081922}}

{{Hanging indent|Sârbescu, P., &amp; Rusu, A. (2021). Personality predictors of speeding: Anger-aggression and impulsive-sensation seeking. A systematic review and meta-analysis. ''Journal of Safety Research, 77'', 86–98. https://doi.org/10.1016/j.jsr.2021.02.004}}

{{Hanging indent|Sharma, L., Markon, K. E., &amp; Clark, L. A. (2014). Toward a theory of distinct types of “impulsive” behaviors: A meta-analysis of self-report and behavioral measures. ''Psychological Bulletin, 140''(2), 374–408. https://doi.org/10.1037/a0034418}}

{{Hanging indent|Shulman, E. P., Smith, A. R., Silva, K., Icenogle, G., Duell, N., Chein, J., &amp; Steinberg, L. (2016). The dual systems model: Review, reappraisal, and reaffirmation. ''Developmental Cognitive Neuroscience, 17'', 103–117. https://doi.org/10.1016/j.dcn.2015.12.010}}

{{Hanging indent|Siraj, R., Najam, B., &amp; Ghazal, S. (2021). Sensation seeking, peer influence, and risk-taking behavior in adolescents. ''Education Research International, 2021'', 8403024. https://doi.org/10.1155/2021/8403024}}

{{Hanging indent|Steinberg, L. (2010). A dual systems model of adolescent risk-taking. ''Developmental Psychobiology, 52''(3), 216–224. https://doi.org/10.1002/dev.20445}}

{{Hanging indent|Türkmen, İ., Rodoplu, N., Üner, B. S., Esmer, Ş. C., Altan-Atalay, A., &amp; Ece, B. (2023). When the UPPS-P model of impulsivity meets a revised approach: The development and validation of the TRUE Multidimensional Impulsivity Scale. ''Journal of Personality Assessment, 105''(3), 355–370. https://doi.org/10.1080/00223891.2022.2093730}}

{{Hanging indent|Whiteside, S. P., &amp; Lynam, D. R. (2001). The five factor model and impulsivity: Using a structural model of personality to understand impulsivity. ''Personality and Individual Differences, 30''(4), 669–689. https://doi.org/10.1016/S0191-8869(00)00064-7}}

{{Hanging indent|Zuckerman, M., &amp; Kuhlman, D. M. (2000). Personality and risk-taking: Common biosocial factors. ''Journal of Personality, 68''(6), 999–1029. https://doi.org/10.1111/1467-6494.00124}}

==External links==
* [https://dictionary.apa.org/sensation-seeking-scale APA Dictionary of Psychology – Sensation-Seeking Scale]
* [https://onlinelibrary.wiley.com/doi/full/10.1002/9781405186407.wbiecs029 Sensation Seeking – Zuckerman] {{ic|Move academic sources to citations/references}}
* [https://www.impulsivity.org/measurement/upps_p/ UPPS-P Impulsive Behavior Scale]

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Impulsivity]]
[[Category:Motivation and emotion/Book/Sensation-seeking]]</text>
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      <contributor>
        <username>Reillyu3280706</username>
        <id>3106308</id>
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      <text bytes="28797" sha1="g8tg2thj2u5brq9w7h1e5wdu1iqu1qd" xml:space="preserve">{{title|Impulsivity versus sensation-seeking:&lt;br&gt;What is the distinction between impulsivity and sensation-seeking and how does this affect behaviour?}}
&lt;div align=center&gt;Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].&lt;br&gt;[[Motivation and emotion/About/Staff|Seek approval]] for any changes.&lt;br&gt;Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).&lt;/div&gt;
__TOC__

{{RoundBoxTop|theme=2}}
[[File: Beer Cantus.jpg|right|thumb|250px|'''Figure 1.''' Social drinking can involve similar observable behaviours despite differences in the psychological processes underlying an individual's decision to participate.]]

'''Imagine this:'''

At a university party, two students are offered an unfamiliar alcoholic beverage. The first accepts immediately, without hesitation, considering the possible consequences. The second pauses but deliberately chooses to try it because the experience is new and exciting. From the outside, their behaviour looks almost identical: both accept the drink. Psychologically, however, the processes motivating their decisions may be quite different.
{{RoundBoxBottom}}

Impulsivity and sensation seeking are related but distinct psychological constructs that can help explain why people engage in seemingly similar behaviours for different reasons. Impulsivity is multidimensional and includes tendencies such as acting without sufficient forethought, whereas sensation seeking reflects the pursuit of novel, exciting, or stimulating experiences (Goh et al., 2020; Ravert &amp; Donnellan, 2021). Consequently, risk taking behaviour does not necessarily indicate that an individual is simply &quot;impulsive&quot;. Understanding the motivation and psychological processes behind the behaviour can provide a more complete explanation of why it occurs.

Distinguishing impulsivity from sensation seeking is particularly essential when considering risk taking behaviour. Different dimensions of impulsivity and sensation seeking are associated with different patterns of health risk behaviour, suggesting that similar actions may arise through varied psychological pathways (Rogers et al., 2021). In the opening scenario, for instance, immediately accepting the drink without considering its consequences may reflect a lack of premeditation, whereas deliberately accepting it for novelty and excitement may more closely reflect sensation seeking. The behavioural outcome is similar, but the motivation is not.

Alcohol use provides a useful real world example of why this distinction matters. Research with university students suggests that sensation seeking and impulsivity can relate to alcohol involvement through different pathways, with sensation seeking more strongly associated with alcohol consumption and impulsivity more closely associated with alcohol related problems (Magid et al., 2007). Identifying these differences can therefore improve understanding of not only whether someone engages in risky behaviour, but also the psychological processes that may contribute to that behaviour and its consequences.

This chapter examines the theoretical and empirical distinction between impulsivity and sensation seeking and evaluates how each may influence behaviour. By examining their conceptual overlap, underlying psychological processes, relationships with risk taking, and associations with alcohol use, the chapter demonstrates why understanding ''why'' a person behaves in a particular way can be as important as observing ''what'' they do.

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

# What is impulsivity and what are its key characteristics?
# What is sensation seeking and how does it differ from impulsivity?
# What psychological processes distinguish impulsivity from sensation seeking?
# How do impulsivity and sensation seeking differentially influence risk-taking behaviour?
# How can these differences help explain alcohol use and related consequences?
{{RoundBoxBottom}}

== Understanding impulsivity ==

Impulsivity is commonly understood as acting without thinking, but psychological research suggests that it is not a single characteristic. Behaviours described as impulsive can result from varied psychological processes, such as acting impetuously during intense emotions, failing to consider future consequences, or struggling to persist with difficult tasks. Research supports this multidimensional understanding, finding that measures labelled as impulsivity assess several related but distinguishable characteristics rather than one unified trait (Berg et al., 2015; Sharma et al., 2014). Thus, understanding why an individual acts impulsively may provide more information than simply labelling the behaviour as impulsive.

=== The UPPS-P model ===

One influential framework for understanding these differences is the UPPS-P model of impulsive personality. The original UPPS model proposed four dimensions: negative urgency, or acting rashly during negative emotion; lack of premeditation, or acting without adequately considering consequences, lack of perseverance, involving difficulty remaining focused on demanding or boring tasks and sensation seeking, involving preference for exciting and novel experiences (Whiteside &amp; Lynam, 2001). The framework was later expanded to distinguish positive urgency, referring to hastely actions during intense positive emotion, from negative urgency (Cyders &amp; Smith, 2008). Consequently, two apparently impulsive decisions may originate from quite different combinations of emotion, planning, persistence and reward seeking.

Experts agree that these components should be measured individually. Network analysis of the UPPS-P found meaningful relationships between its components while also indicating that the dimensions are not interchangeable (Goh et al., 2020). Other research has continued to examine and refine multidimensional measures of impulsivity, demonstrating both the usefulness and continuing complexity of defining the construct (Samiefard et al., 2023; Türkmen et al., 2023). This is an important limitation of the broad term impulsivity: although multidimensional models provide greater precision, disagreement about exactly how impulsivity should be organised and measured remains.

=== Emotion and urgency ===

The distinction between positive and negative urgency further demonstrates why motivation matters. Urgency theory proposes that intense emotional states can increase the likelihood of reckless action, with positive urgency occurring during strongly positive emotion and negative urgency during strongly negative emotion (Cyders &amp; Smith, 2008). This differs from lack of premeditation because a person may ordinarily consider consequences effectively but behave differently when experiencing intense emotion.

The opening party scenario illustrates this distinction. Immediately accepting the unfamiliar drink without adequately considering its consequences may indicate lack of premeditation. If the decision instead occurred during intense excitement at the party, positive urgency might provide another explanation. The observable action alone therefore cannot identify which dimension was responsible.

== Understanding sensation seeking ==

Sensation seeking is strongly correlated to impulsivity but places greater emphasis on the motivation to experience novelty, intensity and stimulation. The construct has traditionally been understood as an individual difference in preference for varied, novel, complex and intense experiences, sometimes accompanied by willingness to accept risk to obtain those experiences (Roberti, 2004; Zuckerman &amp; Kuhlman, 2000). Ultimately indicating that risk itself does not always have to be the person's goal. Instead, risk may be accepted because it accompanies an experience considered sufficiently interesting or rewarding.

=== A motivational perspective ===

This provides an important distinction from other impulsivity dimensions. Someone displaying lack of premeditation may act before adequately considering the consequences, whereas a sensation seeker may recognise the consequences and deliberately decide that the potential stimulation is worthwhile. In the opening scenario, the second student hesitates before accepting the unfamiliar drink but chooses it because the experience is new and exciting. The decision may therefore involve forethought while still being associated with risk.

Sensation seeking should consequently not be treated as inherently dysfunctional. Ravert and Donnellan (2021) found different associations between impulsivity, sensation seeking and psychological well being, supporting the idea that the constructs should not simply be combined into a general tendency towards problematic behaviour. Sensation seeking may encourage exploration and engagement as well as potentially hazardous behaviour, meaning that its consequences depend partly on how and where the need for stimulation is expressed.

=== A theoretical complication ===

An important theoretical complication is that sensation seeking is simultaneously treated as a distinct construct and included as a dimension within the UPPS-P model of impulsivity (Whiteside &amp; Lynam, 2001). The inclusion of sensation seeking within the UPPS-P model does not mean that it is the same as other forms of impulsivity; rather, it is considered one distinct pathway that may contribute to impulsive behaviour. Contrastingly, it demonstrates that the boundaries surrounding the broader concept of impulsivity remain debated and depend partly on how researchers define and measure it. If all sensation seeking were simply impulsivity, there would be little reason to expect the two to show different relationships with behaviour. Evidence that they predict different outcomes can therefore help determine whether distinguishing them is psychologically meaningful.

== Distinguishing impulsivity from sensation seeking ==

Impulsivity and sensation seeking overlap because both can contribute to behaviours involving uncertainty or risk. The key distinction concerns the process motivating the action. Dimensions such as urgency and lack of premeditation emphasise rash action or insufficient regulation, whereas sensation seeking emphasises approach towards novelty, excitement and stimulation (Cyders &amp; Smith, 2008; Zuckerman &amp; Kuhlman, 2000). Similar behaviour can therefore emerge through different psychological pathways.

Research comparing the constructs provides support for this distinction. Magid et al. (2007), found that sensation seeking and impulsivity showed different relationships with alcohol involvement, suggesting that combining them could overlook meaningful differences. Similarly, a meta-analysis found that sensation seeking and impulsivity were both associated with greater risk taking, but sensation seeking showed a somewhat stronger relationship with risky behaviour than impulsivity (Lauriola et al., 2014). These findings support distinguishing the constructs while also demonstrating that neither provides a complete explanation of risky behaviour.

'''Table 1'''

''Comparison of impulsivity and sensation seeking''

{| class=&quot;wikitable&quot;
|-
! Characteristic
! Impulsivity
! Sensation seeking
|-
| '''Central process'''
| Rash action, insufficient forethought or regulation
| Pursuit of novelty, excitement and stimulation
|-
| '''Role of consequences'''
| May be insufficiently considered
| May be recognised but accepted
|-
| '''Role of emotion'''
| Urgency can produce rash action during intense emotion
| Excitement/stimulation can motivate approach
|-
| '''Relationship with risk'''
| Risk can result from poor planning or regulation
| Risk may be tolerated to obtain stimulation
|-
| '''Example'''
| Immediately accepting a drink without considering consequences
| Choosing the drink because trying something unfamiliar is exciting
|}

=== Development and the dual systems model ===

The dual systems model provides another theoretical perspective for understanding this distinction. The model proposes that heightened reward sensitivity develops differently from capacities associated with cognitive control, potentially contributing to increased risk taking during adolescence (Steinberg, 2010). From this perspective, attraction towards rewarding or stimulating experiences and the ability to regulate behaviour are related but separable processes.

Conversely, the model has also been critically reconsidered. Shulman et al. (2016) concluded that evidence broadly supports different developmental trajectories for reward related and cognitive control systems while also highlighting complexities that cannot be captured by a simple imbalance between two systems. Risk taking varies substantially across people and situations, so developmental models should not be interpreted as suggesting that risky behaviour is inevitable or caused by one neural mechanism. The theory is useful for explaining why reward seeking and behavioural control can be distinguished, but it should complement rather than replace personality and contextual explanations.

== Impulsivity, sensation seeking, and risk taking behaviour ==

The theoretical distinction becomes particularly useful when considering risk taking behaviour. If impulsivity and sensation seeking represented the same underlying characteristic, they would be expected to show broadly equivalent relationships with risky outcomes. Instead, evidence indicates that different dimensions can be associated with different behaviours and consequences.

Research examining risk taking has found that both sensation seeking and impulsivity are associated with a greater tendency to engage in risky behaviour, although these relationships are relatively modest (Lauriola et al., 2014). This pattern extends across varied types of behaviour, with sensation seeking and impulsivity related traits associated with health risk behaviours (Rogers et al., 2021), adolescent risk taking (Siraj et al., 2021), and speeding behaviour (Sârbescu &amp; Rusu, 2021). More recently, Grubbs et al. (2024) demonstrated that the specific psychological trait involved may also relate to different aspects of risky behaviour. Sensation seeking was associated with whether individuals had engaged in sports wagering, while urgency related dimensions were associated with different patterns of wagering involvement and gambling related problems. 

These findings provide evidence for the theoretical distinction, whilst also requiring cautious interpretation. Personality traits generally explain only part of the variation in complex behaviours, and correlations cannot establish that a trait directly causes an individual to take a particular risk. Social influences, opportunity, emotional state, perceived rewards and the specific type of risk may interact with personality characteristics. Therefore, describing someone simply as a &quot;risk taker&quot; may obscure both the psychological pathway and the context contributing to their behaviour.

== Alcohol use and related consequences ==

Alcohol use provides an especially useful real-world example because drinking and experiencing alcohol related problems are not the same outcome. Sensation seeking may motivate approach towards stimulating social or drinking experiences, whereas other impulsivity dimensions may be more relevant to rash decisions and harmful consequences. This distinction directly reflects the opening scenario: both students accept the same drink, however their reasons for doing so differ.

Magid et al. (2007) found that sensation seeking and impulsivity related differently to alcohol use and alcohol related problems among university students. Broader research evidence supports this outcome specific approach; for instance across 96 studies, Coskunpinar et al. (2013) found that different UPPS dimensions showed different relationships with alcohol outcomes, with urgency dimensions particularly relevant to alcohol related problems. Evidence from individuals entering residential alcohol detoxification also demonstrates clinically relevant relationships between UPPS-P dimensions and substance related characteristics (Kempeneers et al., 2023).

These findings illustrate why psychological explanations should expand beyond asking whether someone is simply &quot;impulsive&quot;. Identifying whether behaviour is motivated primarily by stimulation, emotional urgency, insufficient forethought or another process may provide a more precise understanding of the behaviour. Simultaniously, much of this evidence is correlational and relies on self report measures, so personality should not be interpreted as determining whether an individual will drink or experience alcohol related harm.

=== From explanation to application ===

Understanding different pathways may also have practical implications. Individuals motivated primarily by sensation seeking may benefit from finding safer ways to obtain novelty and stimulation, whereas behaviour associated with urgency may require greater attention to managing intense emotional states before acting. Lack of premeditation is particularly relevant, strategies that introduce time for considering consequences may be more appropriate.

These possibilities illustrate why distinguishing psychological processes can contribute to improving everyday behaviour rather than merely attaching personality labels to people. However, individualised strategies should not be inferred solely from personality scores, and the available evidence does not demonstrate that matching interventions to UPPS-P dimensions will necessarily produce better outcomes. Instead, the distinction provides a framework for understanding why the same behaviour may require different explanations and potentially different approaches to change.

==Figures==
[[File:Sensation seeking Vs Impulsivity.png|thumb|387x387px|'''Figure 2'''. Comparison of the UPPS-P dimensions of impulsive behaviour and Zuckerman’s dimensions of sensation seeking, highlighting areas of conceptual overlap and distinction (Goh et al., 2020; Magid et al., 2007; Samiefard et al., 2023). (image created independently using Canva software).|center]]

==Learning features==
'''Table 1''' 

'''Table – Comparing impulsivity and sensation''' '''seeking''' 

The comparison table summarises the major conceptual differences and similarities between impulsivity and sensation seeking, including their defining characteristics, underlying processes, and relationships with risk taking behaviour.
{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! Feature !! Impulsivity !! Sensation seeking
|-
| '''Core characteristic''' || Tendency toward rash or insufficiently considered action across multiple dimensions || Tendency to seek novel, varied, exciting or stimulating experiences
|-
| '''Key Process''' || Can involve reduced forethought, urgency or behavioural regulation || Motivation toward novelty, excitement and stimulation
|-
|'''Risk Taking'''
|Risk may result from insufficient consideration of consequences or other impulsive tendencies
|Risk may be accepted in pursuit of rewarding or stimulating experiences
|-
|'''UPPS-P'''
|Multidimensional model including positive urgency, negative urgency, lack of premeditation, lack of perseverance and sensation seeking
|Sensation seeking is one distinct dimension within the UPPS-P model
|-
|'''Example'''
|Immediately accepting an unfamiliar drink without considering consequences
|Deliberately trying the drink because the experience is novel and exciting
|-
|'''Behavioural Outcome'''
|Can contribute to health-risk, gambling and substance related behaviours
|Can contribute to risk taking, alcohol use and novelty oriented behaviour
|}
Whilst impulsivity and sensation seeking can contribute to similar observable behaviours, their underlying characteristics and psychological processes differ (see Table 1; Goh et al., 2020; Magid et al., 2007).

'''Quiz: Impulsivity or sensation seeking?'''
&lt;quiz display=&quot;simple&quot;&gt;
{A student is offered an unfamiliar alcoholic drink at a party and immediately accepts without considering the possible consequences. Which characteristic best explains this behaviour?
|type=&quot;()&quot;}

+ Lack of premeditation
- Thrill and adventure seeking
- Experience seeking
- Boredom susceptibility

{A student deliberately chooses to try an unfamiliar activity because they enjoy novelty, excitement, and stimulation. Which construct best explains this motivation?
|type=&quot;()&quot;}

- Lack of perseverance
+ Sensation seeking
- Negative urgency
- Lack of premeditation

{Which statement best describes the distinction between impulsivity and sensation seeking?
|type=&quot;()&quot;}

- Impulsivity and sensation seeking are interchangeable terms for the same psychological construct.
- Sensation seeking always involves acting without considering consequences.
+ Similar observable behaviours can arise from different underlying motivations and psychological processes.
- Only impulsivity is associated with risk taking behaviour.
&lt;/quiz&gt;

== [[Conclusion]] ==
Impulsivity and sensation seeking are related psychological constructs, however should not automatically be treated as interchangeable. Multidimensional models such as the UPPS-P demonstrate that behaviour commonly labelled &quot;impulsive&quot; can arise through different pathways involving emotion, forethought, persistence and attraction towards stimulation. Sensation seeking is particularly important because it overlaps conceptually with impulsivity while emphasising the motivation to pursue novel and exciting experiences.

Research supports the practical value of distinguishing these processes. Sensation seeking and different dimensions of impulsivity show different patterns of association with risk taking, alcohol involvement and other potentially harmful behaviours, although these relationships are generally probabilistic rather than deterministic. Consequently, observable behaviour alone cannot reveal why an individual acted as they did.

The opening scenario illustrates the practical significance of distinguishing between these psychological processes. Accepting an unfamiliar drink may result from acting without considering consequences, seeking an exciting new experience, responding rashly to intense emotion, or a combination of these processes. Understanding why behaviour occurs, rather than simply labelling what occurred, can provide a more useful foundation for understanding and potentially improving everyday decision making.

== See also ==
* [[Motivation and emotion/Book/2011/Sensation seeking|Sensation seeking]] (Book chapter, 2011)
* [[w:Sensation Seeking Scale|Sensation Seeking Scale]] (Wikipedia)

== References ==

{{Hanging indent|Berg, J. M., Latzman, R. D., Bliwise, N. G., &amp; Lilienfeld, S. O. (2015). Parsing the heterogeneity of impulsivity: A meta-analytic review of the behavioral implications of the UPPS for psychopathology. ''Psychological Assessment, 27''(4), 1129–1146. https://doi.org/10.1037/pas0000111}}

{{Hanging indent|Coskunpinar, A., Dir, A. L., &amp; Cyders, M. A. (2013). Multidimensionality in impulsivity and alcohol use: A meta-analysis using the UPPS model of impulsivity. ''Alcoholism: Clinical and Experimental Research, 37''(9), 1441–1450. https://doi.org/10.1111/acer.12131}}

{{Hanging indent|Cyders, M. A., &amp; Smith, G. T. (2008). Emotion-based dispositions to rash action: Positive and negative urgency. ''Psychological Bulletin, 134''(6), 807–828. https://doi.org/10.1037/a0013341}}

{{Hanging indent|Goh, P. K., Lee, C. A., Martel, M. M., Fillmore, M. T., Derefinko, K. J., &amp; Lynam, D. R. (2020). Conceptualizing the UPPS-P model of impulsive personality through network analysis: Key dimensions and general robustness across young adulthood. ''Journal of Personality, 88''(6), 1302–1314. https://doi.org/10.1111/jopy.12572}}

{{Hanging indent|Grubbs, J. B., Connolly, A. J., Floyd, C. G., Kim, H. S., &amp; Kraus, S. W. (2024). Impulsivity and diverse forms of sports wagering in the U.S.: An examination of the UPPS-P model. ''Addictive Behaviors, 156'', 108058. https://doi.org/10.1016/j.addbeh.2024.108058}}

{{Hanging indent|Kempeneers, P., Mreyen, K., Pallincourt, R., Remacle, F., Wildemeersch, G., &amp; Simon, J. (2023). Validation of the UPPS-P Impulsive Behavior Scale and clinical correlates of its scores in French-speaking patients starting a residential detoxification program. ''Indian Journal of Psychological Medicine, 45''(5), 503–510. https://doi.org/10.1177/02537176231157411}}

{{Hanging indent|Lauriola, M., Panno, A., Levin, I. P., &amp; Lejuez, C. W. (2014). Individual differences in risky decision making: A meta-analysis of sensation seeking and impulsivity with the Balloon Analogue Risk Task. ''Journal of Behavioral Decision Making, 27''(1), 20–36. https://doi.org/10.1002/bdm.1784}}

{{Hanging indent|Magid, V., MacLean, M. G., &amp; Colder, C. R. (2007). Differentiating between sensation seeking and impulsivity through their mediated relations with alcohol use and problems. ''Addictive Behaviors, 32''(10), 2046–2061. https://doi.org/10.1016/j.addbeh.2007.01.015}}

{{Hanging indent|Ravert, R. D., &amp; Donnellan, M. B. (2021). Impulsivity and sensation seeking: Differing associations with psychological well-being. ''Applied Research in Quality of Life, 16''(4), 1503–1515. https://doi.org/10.1007/s11482-020-09829-y}}

{{Hanging indent|Roberti, J. W. (2004). A review of behavioral and biological correlates of sensation seeking. ''Journal of Research in Personality, 38''(3), 256–279. https://doi.org/10.1016/S0092-6566(03)00067-9}}

{{Hanging indent|Rogers, M. M., Kelley, K., &amp; McKinney, C. (2021). Trait impulsivity and health risk behaviors: A latent profile analysis. ''Personality and Individual Differences, 171'', 110511. https://doi.org/10.1016/j.paid.2020.110511}}

{{Hanging indent|Samiefard, M., Salehi Fadardi, J., Kareshki, H., &amp; Stacy, A. W. (2023). Validity and reliability of a revised S-UPPS-P Impulsive Behavior Scale: The interplay between impulsivity and working memory. ''Journal of Personality Assessment, 105''(2), 174–186. https://doi.org/10.1080/00223891.2022.2081922}}

{{Hanging indent|Sârbescu, P., &amp; Rusu, A. (2021). Personality predictors of speeding: Anger-aggression and impulsive-sensation seeking. A systematic review and meta-analysis. ''Journal of Safety Research, 77'', 86–98. https://doi.org/10.1016/j.jsr.2021.02.004}}

{{Hanging indent|Sharma, L., Markon, K. E., &amp; Clark, L. A. (2014). Toward a theory of distinct types of “impulsive” behaviors: A meta-analysis of self-report and behavioral measures. ''Psychological Bulletin, 140''(2), 374–408. https://doi.org/10.1037/a0034418}}

{{Hanging indent|Shulman, E. P., Smith, A. R., Silva, K., Icenogle, G., Duell, N., Chein, J., &amp; Steinberg, L. (2016). The dual systems model: Review, reappraisal, and reaffirmation. ''Developmental Cognitive Neuroscience, 17'', 103–117. https://doi.org/10.1016/j.dcn.2015.12.010}}

{{Hanging indent|Siraj, R., Najam, B., &amp; Ghazal, S. (2021). Sensation seeking, peer influence, and risk-taking behavior in adolescents. ''Education Research International, 2021'', 8403024. https://doi.org/10.1155/2021/8403024}}

{{Hanging indent|Steinberg, L. (2010). A dual systems model of adolescent risk-taking. ''Developmental Psychobiology, 52''(3), 216–224. https://doi.org/10.1002/dev.20445}}

{{Hanging indent|Türkmen, İ., Rodoplu, N., Üner, B. S., Esmer, Ş. C., Altan-Atalay, A., &amp; Ece, B. (2023). When the UPPS-P model of impulsivity meets a revised approach: The development and validation of the TRUE Multidimensional Impulsivity Scale. ''Journal of Personality Assessment, 105''(3), 355–370. https://doi.org/10.1080/00223891.2022.2093730}}

{{Hanging indent|Whiteside, S. P., &amp; Lynam, D. R. (2001). The five factor model and impulsivity: Using a structural model of personality to understand impulsivity. ''Personality and Individual Differences, 30''(4), 669–689. https://doi.org/10.1016/S0191-8869(00)00064-7}}

{{Hanging indent|Zuckerman, M., &amp; Kuhlman, D. M. (2000). Personality and risk-taking: Common biosocial factors. ''Journal of Personality, 68''(6), 999–1029. https://doi.org/10.1111/1467-6494.00124}}

==External links==
* [https://dictionary.apa.org/sensation-seeking-scale APA Dictionary of Psychology – Sensation-Seeking Scale]
* [https://onlinelibrary.wiley.com/doi/full/10.1002/9781405186407.wbiecs029 Sensation Seeking – Zuckerman] {{ic|Move academic sources to citations/references}}
* [https://www.impulsivity.org/measurement/upps_p/ UPPS-P Impulsive Behavior Scale]

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__TOC__

{{RoundBoxTop|theme=2}}
[[File: Beer Cantus.jpg|right|thumb|250px|'''Figure 1.''' Social drinking can involve similar observable behaviours despite differences in the psychological processes underlying an individual's decision to participate.]]

'''Imagine this:'''

At a university party, two students are offered an unfamiliar alcoholic beverage. The first accepts immediately, without hesitation, considering the possible consequences. The second pauses but deliberately chooses to try it because the experience is new and exciting. From the outside, their behaviour looks almost identical: both accept the drink. Psychologically, however, the processes motivating their decisions may be quite different.
{{RoundBoxBottom}}

Impulsivity and sensation seeking are related but distinct psychological constructs that can help explain why people engage in seemingly similar behaviours for different reasons. Impulsivity is multidimensional and includes tendencies such as acting without sufficient forethought, whereas sensation seeking reflects the pursuit of novel, exciting, or stimulating experiences (Goh et al., 2020; Ravert &amp; Donnellan, 2021). Consequently, risk taking behaviour does not necessarily indicate that an individual is simply &quot;impulsive&quot;. Understanding the motivation and psychological processes behind the behaviour can provide a more complete explanation of why it occurs.

Distinguishing impulsivity from sensation seeking is particularly essential when considering risk taking behaviour. Different dimensions of impulsivity and sensation seeking are associated with different patterns of health risk behaviour, suggesting that similar actions may arise through varied psychological pathways (Rogers et al., 2021). In the opening scenario, for instance, immediately accepting the drink without considering its consequences may reflect a lack of premeditation, whereas deliberately accepting it for novelty and excitement may more closely reflect sensation seeking. The behavioural outcome is similar, but the motivation is not.

Alcohol use provides a useful real world example of why this distinction matters. Research with university students suggests that sensation seeking and impulsivity can relate to alcohol involvement through different pathways, with sensation seeking more strongly associated with alcohol consumption and impulsivity more closely associated with alcohol related problems (Magid et al., 2007). Identifying these differences can therefore improve understanding of not only whether someone engages in risky behaviour, but also the psychological processes that may contribute to that behaviour and its consequences.

This chapter examines the theoretical and empirical distinction between impulsivity and sensation seeking and evaluates how each may influence behaviour. By examining their conceptual overlap, underlying psychological processes, relationships with risk taking, and associations with alcohol use, the chapter demonstrates why understanding ''why'' a person behaves in a particular way can be as important as observing ''what'' they do.

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

# What is impulsivity and what are its key characteristics?
# What is sensation seeking and how does it differ from impulsivity?
# What psychological processes distinguish impulsivity from sensation seeking?
# How do impulsivity and sensation seeking differentially influence risk-taking behaviour?
# How can these differences help explain alcohol use and related consequences?
{{RoundBoxBottom}}

== Understanding impulsivity ==

Impulsivity is commonly understood as acting without thinking, but psychological research suggests that it is not a single characteristic. Behaviours described as impulsive can result from varied psychological processes, such as acting impetuously during intense emotions, failing to consider future consequences, or struggling to persist with difficult tasks. Research supports this multidimensional understanding, finding that measures labelled as impulsivity assess several related but distinguishable characteristics rather than one unified trait (Berg et al., 2015; Sharma et al., 2014). Thus, understanding why an individual acts impulsively may provide more information than simply labelling the behaviour as impulsive.

=== The UPPS-P model ===

One influential framework for understanding these differences is the UPPS-P model of impulsive personality. The original UPPS model proposed four dimensions: negative urgency, or acting rashly during negative emotion; lack of premeditation, or acting without adequately considering consequences, lack of perseverance, involving difficulty remaining focused on demanding or boring tasks and sensation seeking, involving preference for exciting and novel experiences (Whiteside &amp; Lynam, 2001). The framework was later expanded to distinguish positive urgency, referring to hastely actions during intense positive emotion, from negative urgency (Cyders &amp; Smith, 2008). Consequently, two apparently impulsive decisions may originate from quite different combinations of emotion, planning, persistence and reward seeking.

Experts agree that these components should be measured individually. Network analysis of the UPPS-P found meaningful relationships between its components while also indicating that the dimensions are not interchangeable (Goh et al., 2020). Other research has continued to examine and refine multidimensional measures of impulsivity, demonstrating both the usefulness and continuing complexity of defining the construct (Samiefard et al., 2023; Türkmen et al., 2023). This is an important limitation of the broad term impulsivity: although multidimensional models provide greater precision, disagreement about exactly how impulsivity should be organised and measured remains.

=== Emotion and urgency ===

The distinction between positive and negative urgency further demonstrates why motivation matters. Urgency theory proposes that intense emotional states can increase the likelihood of reckless action, with positive urgency occurring during strongly positive emotion and negative urgency during strongly negative emotion (Cyders &amp; Smith, 2008). This differs from lack of premeditation because a person may ordinarily consider consequences effectively but behave differently when experiencing intense emotion.

The opening party scenario illustrates this distinction. Immediately accepting the unfamiliar drink without adequately considering its consequences may indicate lack of premeditation. If the decision instead occurred during intense excitement at the party, positive urgency might provide another explanation. The observable action alone therefore cannot identify which dimension was responsible.

== Understanding sensation seeking ==

Sensation seeking is strongly correlated to impulsivity but places greater emphasis on the motivation to experience novelty, intensity and stimulation. The construct has traditionally been understood as an individual difference in preference for varied, novel, complex and intense experiences, sometimes accompanied by willingness to accept risk to obtain those experiences (Roberti, 2004; Zuckerman &amp; Kuhlman, 2000). Ultimately indicating that risk itself does not always have to be the person's goal. Instead, risk may be accepted because it accompanies an experience considered sufficiently interesting or rewarding.

=== A motivational perspective ===

This provides an important distinction from other impulsivity dimensions. Someone displaying lack of premeditation may act before adequately considering the consequences, whereas a sensation seeker may recognise the consequences and deliberately decide that the potential stimulation is worthwhile. In the opening scenario, the second student hesitates before accepting the unfamiliar drink but chooses it because the experience is new and exciting. The decision may therefore involve forethought while still being associated with risk.

Sensation seeking should consequently not be treated as inherently dysfunctional. Ravert and Donnellan (2021) found different associations between impulsivity, sensation seeking and psychological well being, supporting the idea that the constructs should not simply be combined into a general tendency towards problematic behaviour. Sensation seeking may encourage exploration and engagement as well as potentially hazardous behaviour, meaning that its consequences depend partly on how and where the need for stimulation is expressed.

=== A theoretical complication ===

An important theoretical complication is that sensation seeking is simultaneously treated as a distinct construct and included as a dimension within the UPPS-P model of impulsivity (Whiteside &amp; Lynam, 2001). The inclusion of sensation seeking within the UPPS-P model does not mean that it is the same as other forms of impulsivity; rather, it is considered one distinct pathway that may contribute to impulsive behaviour. Contrastingly, it demonstrates that the boundaries surrounding the broader concept of impulsivity remain debated and depend partly on how researchers define and measure it. If all sensation seeking were simply impulsivity, there would be little reason to expect the two to show different relationships with behaviour. Evidence that they predict different outcomes can therefore help determine whether distinguishing them is psychologically meaningful.

== Distinguishing impulsivity from sensation seeking ==

[[File:Sensation seeking Vs Impulsivity.png|right|thumb|387px|'''Figure 2'''. Comparison of the UPPS-P dimensions of impulsive behaviour and Zuckerman’s dimensions of sensation seeking, highlighting areas of conceptual overlap and distinction (Goh et al., 2020; Magid et al., 2007; Samiefard et al., 2023). (image created independently using Canva software).]]

Impulsivity and sensation seeking overlap because both can contribute to behaviours involving uncertainty or risk. The key distinction concerns the process motivating the action. Dimensions such as urgency and lack of premeditation emphasise rash action or insufficient regulation, whereas sensation seeking emphasises approach towards novelty, excitement and stimulation (Cyders &amp; Smith, 2008; Zuckerman &amp; Kuhlman, 2000). Similar behaviour can therefore emerge through different psychological pathways.

Research comparing the constructs provides support for this distinction. Magid et al. (2007), found that sensation seeking and impulsivity showed different relationships with alcohol involvement, suggesting that combining them could overlook meaningful differences. Similarly, a meta-analysis found that sensation seeking and impulsivity were both associated with greater risk taking, but sensation seeking showed a somewhat stronger relationship with risky behaviour than impulsivity (Lauriola et al., 2014). These findings support distinguishing the constructs while also demonstrating that neither provides a complete explanation of risky behaviour.

'''Table 1'''

''Comparison of impulsivity and sensation seeking''

{| class=&quot;wikitable&quot;
|-
! Characteristic
! Impulsivity
! Sensation seeking
|-
| '''Central process'''
| Rash action, insufficient forethought or regulation
| Pursuit of novelty, excitement and stimulation
|-
| '''Role of consequences'''
| May be insufficiently considered
| May be recognised but accepted
|-
| '''Role of emotion'''
| Urgency can produce rash action during intense emotion
| Excitement/stimulation can motivate approach
|-
| '''Relationship with risk'''
| Risk can result from poor planning or regulation
| Risk may be tolerated to obtain stimulation
|-
| '''Example'''
| Immediately accepting a drink without considering consequences
| Choosing the drink because trying something unfamiliar is exciting
|}

=== Development and the dual systems model ===

The dual systems model provides another theoretical perspective for understanding this distinction. The model proposes that heightened reward sensitivity develops differently from capacities associated with cognitive control, potentially contributing to increased risk taking during adolescence (Steinberg, 2010). From this perspective, attraction towards rewarding or stimulating experiences and the ability to regulate behaviour are related but separable processes.

Conversely, the model has also been critically reconsidered. Shulman et al. (2016) concluded that evidence broadly supports different developmental trajectories for reward related and cognitive control systems while also highlighting complexities that cannot be captured by a simple imbalance between two systems. Risk taking varies substantially across people and situations, so developmental models should not be interpreted as suggesting that risky behaviour is inevitable or caused by one neural mechanism. The theory is useful for explaining why reward seeking and behavioural control can be distinguished, but it should complement rather than replace personality and contextual explanations.

== Impulsivity, sensation seeking, and risk taking behaviour ==

The theoretical distinction becomes particularly useful when considering risk taking behaviour. If impulsivity and sensation seeking represented the same underlying characteristic, they would be expected to show broadly equivalent relationships with risky outcomes. Instead, evidence indicates that different dimensions can be associated with different behaviours and consequences.

Research examining risk taking has found that both sensation seeking and impulsivity are associated with a greater tendency to engage in risky behaviour, although these relationships are relatively modest (Lauriola et al., 2014). This pattern extends across varied types of behaviour, with sensation seeking and impulsivity related traits associated with health risk behaviours (Rogers et al., 2021), adolescent risk taking (Siraj et al., 2021), and speeding behaviour (Sârbescu &amp; Rusu, 2021). More recently, Grubbs et al. (2024) demonstrated that the specific psychological trait involved may also relate to different aspects of risky behaviour. Sensation seeking was associated with whether individuals had engaged in sports wagering, while urgency related dimensions were associated with different patterns of wagering involvement and gambling related problems. 

These findings provide evidence for the theoretical distinction, whilst also requiring cautious interpretation. Personality traits generally explain only part of the variation in complex behaviours, and correlations cannot establish that a trait directly causes an individual to take a particular risk. Social influences, opportunity, emotional state, perceived rewards and the specific type of risk may interact with personality characteristics. Therefore, describing someone simply as a &quot;risk taker&quot; may obscure both the psychological pathway and the context contributing to their behaviour.

== Alcohol use and related consequences ==

Alcohol use provides an especially useful real-world example because drinking and experiencing alcohol related problems are not the same outcome. Sensation seeking may motivate approach towards stimulating social or drinking experiences, whereas other impulsivity dimensions may be more relevant to rash decisions and harmful consequences. This distinction directly reflects the opening scenario: both students accept the same drink, however their reasons for doing so differ.

Magid et al. (2007) found that sensation seeking and impulsivity related differently to alcohol use and alcohol related problems among university students. Broader research evidence supports this outcome specific approach; for instance across 96 studies, Coskunpinar et al. (2013) found that different UPPS dimensions showed different relationships with alcohol outcomes, with urgency dimensions particularly relevant to alcohol related problems. Evidence from individuals entering residential alcohol detoxification also demonstrates clinically relevant relationships between UPPS-P dimensions and substance related characteristics (Kempeneers et al., 2023).

These findings illustrate why psychological explanations should expand beyond asking whether someone is simply &quot;impulsive&quot;. Identifying whether behaviour is motivated primarily by stimulation, emotional urgency, insufficient forethought or another process may provide a more precise understanding of the behaviour. Simultaniously, much of this evidence is correlational and relies on self report measures, so personality should not be interpreted as determining whether an individual will drink or experience alcohol related harm.

=== From explanation to application ===

Understanding different pathways may also have practical implications. Individuals motivated primarily by sensation seeking may benefit from finding safer ways to obtain novelty and stimulation, whereas behaviour associated with urgency may require greater attention to managing intense emotional states before acting. Lack of premeditation is particularly relevant, strategies that introduce time for considering consequences may be more appropriate.

These possibilities illustrate why distinguishing psychological processes can contribute to improving everyday behaviour rather than merely attaching personality labels to people. However, individualised strategies should not be inferred solely from personality scores, and the available evidence does not demonstrate that matching interventions to UPPS-P dimensions will necessarily produce better outcomes. Instead, the distinction provides a framework for understanding why the same behaviour may require different explanations and potentially different approaches to change.

==Figures==
[[File:Sensation seeking Vs Impulsivity.png|thumb|387x387px|'''Figure 2'''. Comparison of the UPPS-P dimensions of impulsive behaviour and Zuckerman’s dimensions of sensation seeking, highlighting areas of conceptual overlap and distinction (Goh et al., 2020; Magid et al., 2007; Samiefard et al., 2023). (image created independently using Canva software).|center]]

==Learning features==
'''Table 1''' 

'''Table – Comparing impulsivity and sensation''' '''seeking''' 

The comparison table summarises the major conceptual differences and similarities between impulsivity and sensation seeking, including their defining characteristics, underlying processes, and relationships with risk taking behaviour.
{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! Feature !! Impulsivity !! Sensation seeking
|-
| '''Core characteristic''' || Tendency toward rash or insufficiently considered action across multiple dimensions || Tendency to seek novel, varied, exciting or stimulating experiences
|-
| '''Key Process''' || Can involve reduced forethought, urgency or behavioural regulation || Motivation toward novelty, excitement and stimulation
|-
|'''Risk Taking'''
|Risk may result from insufficient consideration of consequences or other impulsive tendencies
|Risk may be accepted in pursuit of rewarding or stimulating experiences
|-
|'''UPPS-P'''
|Multidimensional model including positive urgency, negative urgency, lack of premeditation, lack of perseverance and sensation seeking
|Sensation seeking is one distinct dimension within the UPPS-P model
|-
|'''Example'''
|Immediately accepting an unfamiliar drink without considering consequences
|Deliberately trying the drink because the experience is novel and exciting
|-
|'''Behavioural Outcome'''
|Can contribute to health-risk, gambling and substance related behaviours
|Can contribute to risk taking, alcohol use and novelty oriented behaviour
|}
Whilst impulsivity and sensation seeking can contribute to similar observable behaviours, their underlying characteristics and psychological processes differ (see Table 1; Goh et al., 2020; Magid et al., 2007).

'''Quiz: Impulsivity or sensation seeking?'''
&lt;quiz display=&quot;simple&quot;&gt;
{A student is offered an unfamiliar alcoholic drink at a party and immediately accepts without considering the possible consequences. Which characteristic best explains this behaviour?
|type=&quot;()&quot;}

+ Lack of premeditation
- Thrill and adventure seeking
- Experience seeking
- Boredom susceptibility

{A student deliberately chooses to try an unfamiliar activity because they enjoy novelty, excitement, and stimulation. Which construct best explains this motivation?
|type=&quot;()&quot;}

- Lack of perseverance
+ Sensation seeking
- Negative urgency
- Lack of premeditation

{Which statement best describes the distinction between impulsivity and sensation seeking?
|type=&quot;()&quot;}

- Impulsivity and sensation seeking are interchangeable terms for the same psychological construct.
- Sensation seeking always involves acting without considering consequences.
+ Similar observable behaviours can arise from different underlying motivations and psychological processes.
- Only impulsivity is associated with risk taking behaviour.
&lt;/quiz&gt;

== [[Conclusion]] ==
Impulsivity and sensation seeking are related psychological constructs, however should not automatically be treated as interchangeable. Multidimensional models such as the UPPS-P demonstrate that behaviour commonly labelled &quot;impulsive&quot; can arise through different pathways involving emotion, forethought, persistence and attraction towards stimulation. Sensation seeking is particularly important because it overlaps conceptually with impulsivity while emphasising the motivation to pursue novel and exciting experiences.

Research supports the practical value of distinguishing these processes. Sensation seeking and different dimensions of impulsivity show different patterns of association with risk taking, alcohol involvement and other potentially harmful behaviours, although these relationships are generally probabilistic rather than deterministic. Consequently, observable behaviour alone cannot reveal why an individual acted as they did.

The opening scenario illustrates the practical significance of distinguishing between these psychological processes. Accepting an unfamiliar drink may result from acting without considering consequences, seeking an exciting new experience, responding rashly to intense emotion, or a combination of these processes. Understanding why behaviour occurs, rather than simply labelling what occurred, can provide a more useful foundation for understanding and potentially improving everyday decision making.

== See also ==
* [[Motivation and emotion/Book/2011/Sensation seeking|Sensation seeking]] (Book chapter, 2011)
* [[w:Sensation Seeking Scale|Sensation Seeking Scale]] (Wikipedia)

== References ==

{{Hanging indent|Berg, J. M., Latzman, R. D., Bliwise, N. G., &amp; Lilienfeld, S. O. (2015). Parsing the heterogeneity of impulsivity: A meta-analytic review of the behavioral implications of the UPPS for psychopathology. ''Psychological Assessment, 27''(4), 1129–1146. https://doi.org/10.1037/pas0000111}}

{{Hanging indent|Coskunpinar, A., Dir, A. L., &amp; Cyders, M. A. (2013). Multidimensionality in impulsivity and alcohol use: A meta-analysis using the UPPS model of impulsivity. ''Alcoholism: Clinical and Experimental Research, 37''(9), 1441–1450. https://doi.org/10.1111/acer.12131}}

{{Hanging indent|Cyders, M. A., &amp; Smith, G. T. (2008). Emotion-based dispositions to rash action: Positive and negative urgency. ''Psychological Bulletin, 134''(6), 807–828. https://doi.org/10.1037/a0013341}}

{{Hanging indent|Goh, P. K., Lee, C. A., Martel, M. M., Fillmore, M. T., Derefinko, K. J., &amp; Lynam, D. R. (2020). Conceptualizing the UPPS-P model of impulsive personality through network analysis: Key dimensions and general robustness across young adulthood. ''Journal of Personality, 88''(6), 1302–1314. https://doi.org/10.1111/jopy.12572}}

{{Hanging indent|Grubbs, J. B., Connolly, A. J., Floyd, C. G., Kim, H. S., &amp; Kraus, S. W. (2024). Impulsivity and diverse forms of sports wagering in the U.S.: An examination of the UPPS-P model. ''Addictive Behaviors, 156'', 108058. https://doi.org/10.1016/j.addbeh.2024.108058}}

{{Hanging indent|Kempeneers, P., Mreyen, K., Pallincourt, R., Remacle, F., Wildemeersch, G., &amp; Simon, J. (2023). Validation of the UPPS-P Impulsive Behavior Scale and clinical correlates of its scores in French-speaking patients starting a residential detoxification program. ''Indian Journal of Psychological Medicine, 45''(5), 503–510. https://doi.org/10.1177/02537176231157411}}

{{Hanging indent|Lauriola, M., Panno, A., Levin, I. P., &amp; Lejuez, C. W. (2014). Individual differences in risky decision making: A meta-analysis of sensation seeking and impulsivity with the Balloon Analogue Risk Task. ''Journal of Behavioral Decision Making, 27''(1), 20–36. https://doi.org/10.1002/bdm.1784}}

{{Hanging indent|Magid, V., MacLean, M. G., &amp; Colder, C. R. (2007). Differentiating between sensation seeking and impulsivity through their mediated relations with alcohol use and problems. ''Addictive Behaviors, 32''(10), 2046–2061. https://doi.org/10.1016/j.addbeh.2007.01.015}}

{{Hanging indent|Ravert, R. D., &amp; Donnellan, M. B. (2021). Impulsivity and sensation seeking: Differing associations with psychological well-being. ''Applied Research in Quality of Life, 16''(4), 1503–1515. https://doi.org/10.1007/s11482-020-09829-y}}

{{Hanging indent|Roberti, J. W. (2004). A review of behavioral and biological correlates of sensation seeking. ''Journal of Research in Personality, 38''(3), 256–279. https://doi.org/10.1016/S0092-6566(03)00067-9}}

{{Hanging indent|Rogers, M. M., Kelley, K., &amp; McKinney, C. (2021). Trait impulsivity and health risk behaviors: A latent profile analysis. ''Personality and Individual Differences, 171'', 110511. https://doi.org/10.1016/j.paid.2020.110511}}

{{Hanging indent|Samiefard, M., Salehi Fadardi, J., Kareshki, H., &amp; Stacy, A. W. (2023). Validity and reliability of a revised S-UPPS-P Impulsive Behavior Scale: The interplay between impulsivity and working memory. ''Journal of Personality Assessment, 105''(2), 174–186. https://doi.org/10.1080/00223891.2022.2081922}}

{{Hanging indent|Sârbescu, P., &amp; Rusu, A. (2021). Personality predictors of speeding: Anger-aggression and impulsive-sensation seeking. A systematic review and meta-analysis. ''Journal of Safety Research, 77'', 86–98. https://doi.org/10.1016/j.jsr.2021.02.004}}

{{Hanging indent|Sharma, L., Markon, K. E., &amp; Clark, L. A. (2014). Toward a theory of distinct types of “impulsive” behaviors: A meta-analysis of self-report and behavioral measures. ''Psychological Bulletin, 140''(2), 374–408. https://doi.org/10.1037/a0034418}}

{{Hanging indent|Shulman, E. P., Smith, A. R., Silva, K., Icenogle, G., Duell, N., Chein, J., &amp; Steinberg, L. (2016). The dual systems model: Review, reappraisal, and reaffirmation. ''Developmental Cognitive Neuroscience, 17'', 103–117. https://doi.org/10.1016/j.dcn.2015.12.010}}

{{Hanging indent|Siraj, R., Najam, B., &amp; Ghazal, S. (2021). Sensation seeking, peer influence, and risk-taking behavior in adolescents. ''Education Research International, 2021'', 8403024. https://doi.org/10.1155/2021/8403024}}

{{Hanging indent|Steinberg, L. (2010). A dual systems model of adolescent risk-taking. ''Developmental Psychobiology, 52''(3), 216–224. https://doi.org/10.1002/dev.20445}}

{{Hanging indent|Türkmen, İ., Rodoplu, N., Üner, B. S., Esmer, Ş. C., Altan-Atalay, A., &amp; Ece, B. (2023). When the UPPS-P model of impulsivity meets a revised approach: The development and validation of the TRUE Multidimensional Impulsivity Scale. ''Journal of Personality Assessment, 105''(3), 355–370. https://doi.org/10.1080/00223891.2022.2093730}}

{{Hanging indent|Whiteside, S. P., &amp; Lynam, D. R. (2001). The five factor model and impulsivity: Using a structural model of personality to understand impulsivity. ''Personality and Individual Differences, 30''(4), 669–689. https://doi.org/10.1016/S0191-8869(00)00064-7}}

{{Hanging indent|Zuckerman, M., &amp; Kuhlman, D. M. (2000). Personality and risk-taking: Common biosocial factors. ''Journal of Personality, 68''(6), 999–1029. https://doi.org/10.1111/1467-6494.00124}}

==External links==
* [https://dictionary.apa.org/sensation-seeking-scale APA Dictionary of Psychology – Sensation-Seeking Scale]
* [https://onlinelibrary.wiley.com/doi/full/10.1002/9781405186407.wbiecs029 Sensation Seeking – Zuckerman] {{ic|Move academic sources to citations/references}}
* [https://www.impulsivity.org/measurement/upps_p/ UPPS-P Impulsive Behavior Scale]

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&lt;div align=center&gt;Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].&lt;br&gt;[[Motivation and emotion/About/Staff|Seek approval]] for any changes.&lt;br&gt;Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).&lt;/div&gt;
__TOC__

{{RoundBoxTop|theme=2}}
[[File: Beer Cantus.jpg|right|thumb|250px|'''Figure 1.''' Social drinking can involve similar observable behaviours despite differences in the psychological processes underlying an individual's decision to participate.]]

'''Imagine this:'''

At a university party, two students are offered an unfamiliar alcoholic beverage. The first accepts immediately, without hesitation, considering the possible consequences. The second pauses but deliberately chooses to try it because the experience is new and exciting. From the outside, their behaviour looks almost identical: both accept the drink. Psychologically, however, the processes motivating their decisions may be quite different.
{{RoundBoxBottom}}

Impulsivity and sensation seeking are related but distinct psychological constructs that can help explain why people engage in seemingly similar behaviours for different reasons. Impulsivity is multidimensional and includes tendencies such as acting without sufficient forethought, whereas sensation seeking reflects the pursuit of novel, exciting, or stimulating experiences (Goh et al., 2020; Ravert &amp; Donnellan, 2021). Consequently, risk taking behaviour does not necessarily indicate that an individual is simply &quot;impulsive&quot;. Understanding the motivation and psychological processes behind the behaviour can provide a more complete explanation of why it occurs.

Distinguishing impulsivity from sensation seeking is particularly essential when considering risk taking behaviour. Different dimensions of impulsivity and sensation seeking are associated with different patterns of health risk behaviour, suggesting that similar actions may arise through varied psychological pathways (Rogers et al., 2021). In the opening scenario, for instance, immediately accepting the drink without considering its consequences may reflect a lack of premeditation, whereas deliberately accepting it for novelty and excitement may more closely reflect sensation seeking. The behavioural outcome is similar, but the motivation is not.

Alcohol use provides a useful real world example of why this distinction matters. Research with university students suggests that sensation seeking and impulsivity can relate to alcohol involvement through different pathways, with sensation seeking more strongly associated with alcohol consumption and impulsivity more closely associated with alcohol related problems (Magid et al., 2007). Identifying these differences can therefore improve understanding of not only whether someone engages in risky behaviour, but also the psychological processes that may contribute to that behaviour and its consequences.

This chapter examines the theoretical and empirical distinction between impulsivity and sensation seeking and evaluates how each may influence behaviour. By examining their conceptual overlap, underlying psychological processes, relationships with risk taking, and associations with alcohol use, the chapter demonstrates why understanding ''why'' a person behaves in a particular way can be as important as observing ''what'' they do.

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

# What is impulsivity and what are its key characteristics?
# What is sensation seeking and how does it differ from impulsivity?
# What psychological processes distinguish impulsivity from sensation seeking?
# How do impulsivity and sensation seeking differentially influence risk-taking behaviour?
# How can these differences help explain alcohol use and related consequences?
{{RoundBoxBottom}}

== Understanding impulsivity ==

Impulsivity is commonly understood as acting without thinking, but psychological research suggests that it is not a single characteristic. Behaviours described as impulsive can result from varied psychological processes, such as acting impetuously during intense emotions, failing to consider future consequences, or struggling to persist with difficult tasks. Research supports this multidimensional understanding, finding that measures labelled as impulsivity assess several related but distinguishable characteristics rather than one unified trait (Berg et al., 2015; Sharma et al., 2014). Thus, understanding why an individual acts impulsively may provide more information than simply labelling the behaviour as impulsive.

=== The UPPS-P model ===

One influential framework for understanding these differences is the UPPS-P model of impulsive personality. The original UPPS model proposed four dimensions: negative urgency, or acting rashly during negative emotion; lack of premeditation, or acting without adequately considering consequences, lack of perseverance, involving difficulty remaining focused on demanding or boring tasks and sensation seeking, involving preference for exciting and novel experiences (Whiteside &amp; Lynam, 2001). The framework was later expanded to distinguish positive urgency, referring to hastely actions during intense positive emotion, from negative urgency (Cyders &amp; Smith, 2008). Consequently, two apparently impulsive decisions may originate from quite different combinations of emotion, planning, persistence and reward seeking.

Experts agree that these components should be measured individually. Network analysis of the UPPS-P found meaningful relationships between its components while also indicating that the dimensions are not interchangeable (Goh et al., 2020). Other research has continued to examine and refine multidimensional measures of impulsivity, demonstrating both the usefulness and continuing complexity of defining the construct (Samiefard et al., 2023; Türkmen et al., 2023). This is an important limitation of the broad term impulsivity: although multidimensional models provide greater precision, disagreement about exactly how impulsivity should be organised and measured remains.

=== Emotion and urgency ===

The distinction between positive and negative urgency further demonstrates why motivation matters. Urgency theory proposes that intense emotional states can increase the likelihood of reckless action, with positive urgency occurring during strongly positive emotion and negative urgency during strongly negative emotion (Cyders &amp; Smith, 2008). This differs from lack of premeditation because a person may ordinarily consider consequences effectively but behave differently when experiencing intense emotion.

The opening party scenario illustrates this distinction. Immediately accepting the unfamiliar drink without adequately considering its consequences may indicate lack of premeditation. If the decision instead occurred during intense excitement at the party, positive urgency might provide another explanation. The observable action alone therefore cannot identify which dimension was responsible.

== Understanding sensation seeking ==

Sensation seeking is strongly correlated to impulsivity but places greater emphasis on the motivation to experience novelty, intensity and stimulation. The construct has traditionally been understood as an individual difference in preference for varied, novel, complex and intense experiences, sometimes accompanied by willingness to accept risk to obtain those experiences (Roberti, 2004; Zuckerman &amp; Kuhlman, 2000). Ultimately indicating that risk itself does not always have to be the person's goal. Instead, risk may be accepted because it accompanies an experience considered sufficiently interesting or rewarding.

=== A motivational perspective ===

This provides an important distinction from other impulsivity dimensions. Someone displaying lack of premeditation may act before adequately considering the consequences, whereas a sensation seeker may recognise the consequences and deliberately decide that the potential stimulation is worthwhile. In the opening scenario, the second student hesitates before accepting the unfamiliar drink but chooses it because the experience is new and exciting. The decision may therefore involve forethought while still being associated with risk.

Sensation seeking should consequently not be treated as inherently dysfunctional. Ravert and Donnellan (2021) found different associations between impulsivity, sensation seeking and psychological well being, supporting the idea that the constructs should not simply be combined into a general tendency towards problematic behaviour. Sensation seeking may encourage exploration and engagement as well as potentially hazardous behaviour, meaning that its consequences depend partly on how and where the need for stimulation is expressed.

=== A theoretical complication ===

An important theoretical complication is that sensation seeking is simultaneously treated as a distinct construct and included as a dimension within the UPPS-P model of impulsivity (Whiteside &amp; Lynam, 2001). The inclusion of sensation seeking within the UPPS-P model does not mean that it is the same as other forms of impulsivity; rather, it is considered one distinct pathway that may contribute to impulsive behaviour. Contrastingly, it demonstrates that the boundaries surrounding the broader concept of impulsivity remain debated and depend partly on how researchers define and measure it. If all sensation seeking were simply impulsivity, there would be little reason to expect the two to show different relationships with behaviour. Evidence that they predict different outcomes can therefore help determine whether distinguishing them is psychologically meaningful.

== Distinguishing impulsivity from sensation seeking ==

[[File:Sensation seeking Vs Impulsivity.png|right|thumb|387px|'''Figure 2'''. Comparison of the UPPS-P dimensions of impulsive behaviour and Zuckerman’s dimensions of sensation seeking, highlighting areas of conceptual overlap and distinction (Goh et al., 2020; Magid et al., 2007; Samiefard et al., 2023). (image created independently using Canva software).]]

Impulsivity and sensation seeking overlap because both can contribute to behaviours involving uncertainty or risk. The key distinction concerns the process motivating the action. Dimensions such as urgency and lack of premeditation emphasise rash action or insufficient regulation, whereas sensation seeking emphasises approach towards novelty, excitement and stimulation (Cyders &amp; Smith, 2008; Zuckerman &amp; Kuhlman, 2000). Similar behaviour can therefore emerge through different psychological pathways.

Research comparing the constructs provides support for this distinction. Magid et al. (2007), found that sensation seeking and impulsivity showed different relationships with alcohol involvement, suggesting that combining them could overlook meaningful differences. Similarly, a meta-analysis found that sensation seeking and impulsivity were both associated with greater risk taking, but sensation seeking showed a somewhat stronger relationship with risky behaviour than impulsivity (Lauriola et al., 2014). These findings support distinguishing the constructs while also demonstrating that neither provides a complete explanation of risky behaviour.

'''Table 1''' 

'''Table – Comparing impulsivity and sensation''' '''seeking''' 

The comparison table summarises the major conceptual differences and similarities between impulsivity and sensation seeking, including their defining characteristics, underlying processes, and relationships with risk taking behaviour.
{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! Feature !! Impulsivity !! Sensation seeking
|-
| '''Core characteristic''' || Tendency toward rash or insufficiently considered action across multiple dimensions || Tendency to seek novel, varied, exciting or stimulating experiences
|-
| '''Key Process''' || Can involve reduced forethought, urgency or behavioural regulation || Motivation toward novelty, excitement and stimulation
|-
|'''Risk Taking'''
|Risk may result from insufficient consideration of consequences or other impulsive tendencies
|Risk may be accepted in pursuit of rewarding or stimulating experiences
|-
|'''UPPS-P'''
|Multidimensional model including positive urgency, negative urgency, lack of premeditation, lack of perseverance and sensation seeking
|Sensation seeking is one distinct dimension within the UPPS-P model
|-
|'''Example'''
|Immediately accepting an unfamiliar drink without considering consequences
|Deliberately trying the drink because the experience is novel and exciting
|-
|'''Behavioural Outcome'''
|Can contribute to health risk, gambling and substance related behaviours
|Can contribute to risk taking, alcohol use and novelty oriented behaviour
|}
Whilst impulsivity and sensation seeking can contribute to similar observable behaviours, their underlying characteristics and psychological processes differ (see Table 1; Goh et al., 2020; Magid et al., 2007).

=== Development and the dual systems model ===

The dual systems model provides another theoretical perspective for understanding this distinction. The model proposes that heightened reward sensitivity develops differently from capacities associated with cognitive control, potentially contributing to increased risk taking during adolescence (Steinberg, 2010). From this perspective, attraction towards rewarding or stimulating experiences and the ability to regulate behaviour are related but separable processes.

Conversely, the model has also been critically reconsidered. Shulman et al. (2016) concluded that evidence broadly supports different developmental trajectories for reward related and cognitive control systems while also highlighting complexities that cannot be captured by a simple imbalance between two systems. Risk taking varies substantially across people and situations, so developmental models should not be interpreted as suggesting that risky behaviour is inevitable or caused by one neural mechanism. The theory is useful for explaining why reward seeking and behavioural control can be distinguished, but it should complement rather than replace personality and contextual explanations.

== Impulsivity, sensation seeking, and risk taking behaviour ==

The theoretical distinction becomes particularly useful when considering risk taking behaviour. If impulsivity and sensation seeking represented the same underlying characteristic, they would be expected to show broadly equivalent relationships with risky outcomes. Instead, evidence indicates that different dimensions can be associated with different behaviours and consequences.

Research examining risk taking has found that both sensation seeking and impulsivity are associated with a greater tendency to engage in risky behaviour, although these relationships are relatively modest (Lauriola et al., 2014). This pattern extends across varied types of behaviour, with sensation seeking and impulsivity related traits associated with health risk behaviours (Rogers et al., 2021), adolescent risk taking (Siraj et al., 2021), and speeding behaviour (Sârbescu &amp; Rusu, 2021). More recently, Grubbs et al. (2024) demonstrated that the specific psychological trait involved may also relate to different aspects of risky behaviour. Sensation seeking was associated with whether individuals had engaged in sports wagering, while urgency related dimensions were associated with different patterns of wagering involvement and gambling related problems. 

These findings provide evidence for the theoretical distinction, whilst also requiring cautious interpretation. Personality traits generally explain only part of the variation in complex behaviours, and correlations cannot establish that a trait directly causes an individual to take a particular risk. Social influences, opportunity, emotional state, perceived rewards and the specific type of risk may interact with personality characteristics. Therefore, describing someone simply as a &quot;risk taker&quot; may obscure both the psychological pathway and the context contributing to their behaviour.

== Alcohol use and related consequences ==

Alcohol use provides an especially useful real-world example because drinking and experiencing alcohol related problems are not the same outcome. Sensation seeking may motivate approach towards stimulating social or drinking experiences, whereas other impulsivity dimensions may be more relevant to rash decisions and harmful consequences. This distinction directly reflects the opening scenario: both students accept the same drink, however their reasons for doing so differ.

Magid et al. (2007) found that sensation seeking and impulsivity related differently to alcohol use and alcohol related problems among university students. Broader research evidence supports this outcome specific approach; for instance across 96 studies, Coskunpinar et al. (2013) found that different UPPS dimensions showed different relationships with alcohol outcomes, with urgency dimensions particularly relevant to alcohol related problems. Evidence from individuals entering residential alcohol detoxification also demonstrates clinically relevant relationships between UPPS-P dimensions and substance related characteristics (Kempeneers et al., 2023).

These findings illustrate why psychological explanations should expand beyond asking whether someone is simply &quot;impulsive&quot;. Identifying whether behaviour is motivated primarily by stimulation, emotional urgency, insufficient forethought or another process may provide a more precise understanding of the behaviour. Simultaniously, much of this evidence is correlational and relies on self report measures, so personality should not be interpreted as determining whether an individual will drink or experience alcohol related harm.

=== From explanation to application ===

Understanding different pathways may also have practical implications. Individuals motivated primarily by sensation seeking may benefit from finding safer ways to obtain novelty and stimulation, whereas behaviour associated with urgency may require greater attention to managing intense emotional states before acting. Lack of premeditation is particularly relevant, strategies that introduce time for considering consequences may be more appropriate.

These possibilities illustrate why distinguishing psychological processes can contribute to improving everyday behaviour rather than merely attaching personality labels to people. However, individualised strategies should not be inferred solely from personality scores, and the available evidence does not demonstrate that matching interventions to UPPS-P dimensions will necessarily produce better outcomes. Instead, the distinction provides a framework for understanding why the same behaviour may require different explanations and potentially different approaches to change.

==Figures==
[[File:Sensation seeking Vs Impulsivity.png|thumb|387x387px|'''Figure 2'''. Comparison of the UPPS-P dimensions of impulsive behaviour and Zuckerman’s dimensions of sensation seeking, highlighting areas of conceptual overlap and distinction (Goh et al., 2020; Magid et al., 2007; Samiefard et al., 2023). (image created independently using Canva software).|center]]

==Learning features==
'''Table 1''' 

'''Table – Comparing impulsivity and sensation''' '''seeking''' 

The comparison table summarises the major conceptual differences and similarities between impulsivity and sensation seeking, including their defining characteristics, underlying processes, and relationships with risk taking behaviour.
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
|-
! Feature !! Impulsivity !! Sensation seeking
|-
| '''Core characteristic''' || Tendency toward rash or insufficiently considered action across multiple dimensions || Tendency to seek novel, varied, exciting or stimulating experiences
|-
| '''Key Process''' || Can involve reduced forethought, urgency or behavioural regulation || Motivation toward novelty, excitement and stimulation
|-
|'''Risk Taking'''
|Risk may result from insufficient consideration of consequences or other impulsive tendencies
|Risk may be accepted in pursuit of rewarding or stimulating experiences
|-
|'''UPPS-P'''
|Multidimensional model including positive urgency, negative urgency, lack of premeditation, lack of perseverance and sensation seeking
|Sensation seeking is one distinct dimension within the UPPS-P model
|-
|'''Example'''
|Immediately accepting an unfamiliar drink without considering consequences
|Deliberately trying the drink because the experience is novel and exciting
|-
|'''Behavioural Outcome'''
|Can contribute to health-risk, gambling and substance related behaviours
|Can contribute to risk taking, alcohol use and novelty oriented behaviour
|}
Whilst impulsivity and sensation seeking can contribute to similar observable behaviours, their underlying characteristics and psychological processes differ (see Table 1; Goh et al., 2020; Magid et al., 2007).

'''Quiz: Impulsivity or sensation seeking?'''
&lt;quiz display=&quot;simple&quot;&gt;
{A student is offered an unfamiliar alcoholic drink at a party and immediately accepts without considering the possible consequences. Which characteristic best explains this behaviour?
|type=&quot;()&quot;}

+ Lack of premeditation
- Thrill and adventure seeking
- Experience seeking
- Boredom susceptibility

{A student deliberately chooses to try an unfamiliar activity because they enjoy novelty, excitement, and stimulation. Which construct best explains this motivation?
|type=&quot;()&quot;}

- Lack of perseverance
+ Sensation seeking
- Negative urgency
- Lack of premeditation

{Which statement best describes the distinction between impulsivity and sensation seeking?
|type=&quot;()&quot;}

- Impulsivity and sensation seeking are interchangeable terms for the same psychological construct.
- Sensation seeking always involves acting without considering consequences.
+ Similar observable behaviours can arise from different underlying motivations and psychological processes.
- Only impulsivity is associated with risk taking behaviour.
&lt;/quiz&gt;

== [[Conclusion]] ==
Impulsivity and sensation seeking are related psychological constructs, however should not automatically be treated as interchangeable. Multidimensional models such as the UPPS-P demonstrate that behaviour commonly labelled &quot;impulsive&quot; can arise through different pathways involving emotion, forethought, persistence and attraction towards stimulation. Sensation seeking is particularly important because it overlaps conceptually with impulsivity while emphasising the motivation to pursue novel and exciting experiences.

Research supports the practical value of distinguishing these processes. Sensation seeking and different dimensions of impulsivity show different patterns of association with risk taking, alcohol involvement and other potentially harmful behaviours, although these relationships are generally probabilistic rather than deterministic. Consequently, observable behaviour alone cannot reveal why an individual acted as they did.

The opening scenario illustrates the practical significance of distinguishing between these psychological processes. Accepting an unfamiliar drink may result from acting without considering consequences, seeking an exciting new experience, responding rashly to intense emotion, or a combination of these processes. Understanding why behaviour occurs, rather than simply labelling what occurred, can provide a more useful foundation for understanding and potentially improving everyday decision making.

== See also ==
* [[Motivation and emotion/Book/2011/Sensation seeking|Sensation seeking]] (Book chapter, 2011)
* [[w:Sensation Seeking Scale|Sensation Seeking Scale]] (Wikipedia)

== References ==

{{Hanging indent|Berg, J. M., Latzman, R. D., Bliwise, N. G., &amp; Lilienfeld, S. O. (2015). Parsing the heterogeneity of impulsivity: A meta-analytic review of the behavioral implications of the UPPS for psychopathology. ''Psychological Assessment, 27''(4), 1129–1146. https://doi.org/10.1037/pas0000111}}

{{Hanging indent|Coskunpinar, A., Dir, A. L., &amp; Cyders, M. A. (2013). Multidimensionality in impulsivity and alcohol use: A meta-analysis using the UPPS model of impulsivity. ''Alcoholism: Clinical and Experimental Research, 37''(9), 1441–1450. https://doi.org/10.1111/acer.12131}}

{{Hanging indent|Cyders, M. A., &amp; Smith, G. T. (2008). Emotion-based dispositions to rash action: Positive and negative urgency. ''Psychological Bulletin, 134''(6), 807–828. https://doi.org/10.1037/a0013341}}

{{Hanging indent|Goh, P. K., Lee, C. A., Martel, M. M., Fillmore, M. T., Derefinko, K. J., &amp; Lynam, D. R. (2020). Conceptualizing the UPPS-P model of impulsive personality through network analysis: Key dimensions and general robustness across young adulthood. ''Journal of Personality, 88''(6), 1302–1314. https://doi.org/10.1111/jopy.12572}}

{{Hanging indent|Grubbs, J. B., Connolly, A. J., Floyd, C. G., Kim, H. S., &amp; Kraus, S. W. (2024). Impulsivity and diverse forms of sports wagering in the U.S.: An examination of the UPPS-P model. ''Addictive Behaviors, 156'', 108058. https://doi.org/10.1016/j.addbeh.2024.108058}}

{{Hanging indent|Kempeneers, P., Mreyen, K., Pallincourt, R., Remacle, F., Wildemeersch, G., &amp; Simon, J. (2023). Validation of the UPPS-P Impulsive Behavior Scale and clinical correlates of its scores in French-speaking patients starting a residential detoxification program. ''Indian Journal of Psychological Medicine, 45''(5), 503–510. https://doi.org/10.1177/02537176231157411}}

{{Hanging indent|Lauriola, M., Panno, A., Levin, I. P., &amp; Lejuez, C. W. (2014). Individual differences in risky decision making: A meta-analysis of sensation seeking and impulsivity with the Balloon Analogue Risk Task. ''Journal of Behavioral Decision Making, 27''(1), 20–36. https://doi.org/10.1002/bdm.1784}}

{{Hanging indent|Magid, V., MacLean, M. G., &amp; Colder, C. R. (2007). Differentiating between sensation seeking and impulsivity through their mediated relations with alcohol use and problems. ''Addictive Behaviors, 32''(10), 2046–2061. https://doi.org/10.1016/j.addbeh.2007.01.015}}

{{Hanging indent|Ravert, R. D., &amp; Donnellan, M. B. (2021). Impulsivity and sensation seeking: Differing associations with psychological well-being. ''Applied Research in Quality of Life, 16''(4), 1503–1515. https://doi.org/10.1007/s11482-020-09829-y}}

{{Hanging indent|Roberti, J. W. (2004). A review of behavioral and biological correlates of sensation seeking. ''Journal of Research in Personality, 38''(3), 256–279. https://doi.org/10.1016/S0092-6566(03)00067-9}}

{{Hanging indent|Rogers, M. M., Kelley, K., &amp; McKinney, C. (2021). Trait impulsivity and health risk behaviors: A latent profile analysis. ''Personality and Individual Differences, 171'', 110511. https://doi.org/10.1016/j.paid.2020.110511}}

{{Hanging indent|Samiefard, M., Salehi Fadardi, J., Kareshki, H., &amp; Stacy, A. W. (2023). Validity and reliability of a revised S-UPPS-P Impulsive Behavior Scale: The interplay between impulsivity and working memory. ''Journal of Personality Assessment, 105''(2), 174–186. https://doi.org/10.1080/00223891.2022.2081922}}

{{Hanging indent|Sârbescu, P., &amp; Rusu, A. (2021). Personality predictors of speeding: Anger-aggression and impulsive-sensation seeking. A systematic review and meta-analysis. ''Journal of Safety Research, 77'', 86–98. https://doi.org/10.1016/j.jsr.2021.02.004}}

{{Hanging indent|Sharma, L., Markon, K. E., &amp; Clark, L. A. (2014). Toward a theory of distinct types of “impulsive” behaviors: A meta-analysis of self-report and behavioral measures. ''Psychological Bulletin, 140''(2), 374–408. https://doi.org/10.1037/a0034418}}

{{Hanging indent|Shulman, E. P., Smith, A. R., Silva, K., Icenogle, G., Duell, N., Chein, J., &amp; Steinberg, L. (2016). The dual systems model: Review, reappraisal, and reaffirmation. ''Developmental Cognitive Neuroscience, 17'', 103–117. https://doi.org/10.1016/j.dcn.2015.12.010}}

{{Hanging indent|Siraj, R., Najam, B., &amp; Ghazal, S. (2021). Sensation seeking, peer influence, and risk-taking behavior in adolescents. ''Education Research International, 2021'', 8403024. https://doi.org/10.1155/2021/8403024}}

{{Hanging indent|Steinberg, L. (2010). A dual systems model of adolescent risk-taking. ''Developmental Psychobiology, 52''(3), 216–224. https://doi.org/10.1002/dev.20445}}

{{Hanging indent|Türkmen, İ., Rodoplu, N., Üner, B. S., Esmer, Ş. C., Altan-Atalay, A., &amp; Ece, B. (2023). When the UPPS-P model of impulsivity meets a revised approach: The development and validation of the TRUE Multidimensional Impulsivity Scale. ''Journal of Personality Assessment, 105''(3), 355–370. https://doi.org/10.1080/00223891.2022.2093730}}

{{Hanging indent|Whiteside, S. P., &amp; Lynam, D. R. (2001). The five factor model and impulsivity: Using a structural model of personality to understand impulsivity. ''Personality and Individual Differences, 30''(4), 669–689. https://doi.org/10.1016/S0191-8869(00)00064-7}}

{{Hanging indent|Zuckerman, M., &amp; Kuhlman, D. M. (2000). Personality and risk-taking: Common biosocial factors. ''Journal of Personality, 68''(6), 999–1029. https://doi.org/10.1111/1467-6494.00124}}

==External links==
* [https://dictionary.apa.org/sensation-seeking-scale APA Dictionary of Psychology – Sensation-Seeking Scale]
* [https://onlinelibrary.wiley.com/doi/full/10.1002/9781405186407.wbiecs029 Sensation Seeking – Zuckerman] {{ic|Move academic sources to citations/references}}
* [https://www.impulsivity.org/measurement/upps_p/ UPPS-P Impulsive Behavior Scale]

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[[Category:Motivation and emotion/Book/Sensation-seeking]]</text>
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&lt;div align=center&gt;Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].&lt;br&gt;[[Motivation and emotion/About/Staff|Seek approval]] for any changes.&lt;br&gt;Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).&lt;/div&gt;
__TOC__

{{RoundBoxTop|theme=2}}
[[File: Beer Cantus.jpg|right|thumb|250px|'''Figure 1.''' Social drinking can involve similar observable behaviours despite differences in the psychological processes underlying an individual's decision to participate.]]

'''Imagine this:'''

At a university party, two students are offered an unfamiliar alcoholic beverage. The first accepts immediately, without hesitation, considering the possible consequences. The second pauses but deliberately chooses to try it because the experience is new and exciting. From the outside, their behaviour looks almost identical: both accept the drink. Psychologically, however, the processes motivating their decisions may be quite different.
{{RoundBoxBottom}}

Impulsivity and sensation seeking are related but distinct psychological constructs that can help explain why people engage in seemingly similar behaviours for different reasons. Impulsivity is multidimensional and includes tendencies such as acting without sufficient forethought, whereas sensation seeking reflects the pursuit of novel, exciting, or stimulating experiences (Goh et al., 2020; Ravert &amp; Donnellan, 2021). Consequently, risk taking behaviour does not necessarily indicate that an individual is simply &quot;impulsive&quot;. Understanding the motivation and psychological processes behind the behaviour can provide a more complete explanation of why it occurs.

Distinguishing impulsivity from sensation seeking is particularly essential when considering risk taking behaviour. Different dimensions of impulsivity and sensation seeking are associated with different patterns of health risk behaviour, suggesting that similar actions may arise through varied psychological pathways (Rogers et al., 2021). In the opening scenario, for instance, immediately accepting the drink without considering its consequences may reflect a lack of premeditation, whereas deliberately accepting it for novelty and excitement may more closely reflect sensation seeking. The behavioural outcome is similar, but the motivation is not.

Alcohol use provides a useful real world example of why this distinction matters. Research with university students suggests that sensation seeking and impulsivity can relate to alcohol involvement through different pathways, with sensation seeking more strongly associated with alcohol consumption and impulsivity more closely associated with alcohol related problems (Magid et al., 2007). Identifying these differences can therefore improve understanding of not only whether someone engages in risky behaviour, but also the psychological processes that may contribute to that behaviour and its consequences.

This chapter examines the theoretical and empirical distinction between impulsivity and sensation seeking and evaluates how each may influence behaviour. By examining their conceptual overlap, underlying psychological processes, relationships with risk taking, and associations with alcohol use, the chapter demonstrates why understanding ''why'' a person behaves in a particular way can be as important as observing ''what'' they do.

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

# What is impulsivity and what are its key characteristics?
# What is sensation seeking and how does it differ from impulsivity?
# What psychological processes distinguish impulsivity from sensation seeking?
# How do impulsivity and sensation seeking differentially influence risk-taking behaviour?
# How can these differences help explain alcohol use and related consequences?
{{RoundBoxBottom}}

== Understanding impulsivity ==

Impulsivity is commonly understood as acting without thinking, but psychological research suggests that it is not a single characteristic. Behaviours described as impulsive can result from varied psychological processes, such as acting impetuously during intense emotions, failing to consider future consequences, or struggling to persist with difficult tasks. Research supports this multidimensional understanding, finding that measures labelled as impulsivity assess several related but distinguishable characteristics rather than one unified trait (Berg et al., 2015; Sharma et al., 2014). Thus, understanding why an individual acts impulsively may provide more information than simply labelling the behaviour as impulsive.

=== The UPPS-P model ===

One influential framework for understanding these differences is the UPPS-P model of impulsive personality. The original UPPS model proposed four dimensions: negative urgency, or acting rashly during negative emotion; lack of premeditation, or acting without adequately considering consequences, lack of perseverance, involving difficulty remaining focused on demanding or boring tasks and sensation seeking, involving preference for exciting and novel experiences (Whiteside &amp; Lynam, 2001). The framework was later expanded to distinguish positive urgency, referring to hastely actions during intense positive emotion, from negative urgency (Cyders &amp; Smith, 2008). Consequently, two apparently impulsive decisions may originate from quite different combinations of emotion, planning, persistence and reward seeking.

Experts agree that these components should be measured individually. Network analysis of the UPPS-P found meaningful relationships between its components while also indicating that the dimensions are not interchangeable (Goh et al., 2020). Other research has continued to examine and refine multidimensional measures of impulsivity, demonstrating both the usefulness and continuing complexity of defining the construct (Samiefard et al., 2023; Türkmen et al., 2023). This is an important limitation of the broad term impulsivity: although multidimensional models provide greater precision, disagreement about exactly how impulsivity should be organised and measured remains.

=== Emotion and urgency ===

The distinction between positive and negative urgency further demonstrates why motivation matters. Urgency theory proposes that intense emotional states can increase the likelihood of reckless action, with positive urgency occurring during strongly positive emotion and negative urgency during strongly negative emotion (Cyders &amp; Smith, 2008). This differs from lack of premeditation because a person may ordinarily consider consequences effectively but behave differently when experiencing intense emotion.

The opening party scenario illustrates this distinction. Immediately accepting the unfamiliar drink without adequately considering its consequences may indicate lack of premeditation. If the decision instead occurred during intense excitement at the party, positive urgency might provide another explanation. The observable action alone therefore cannot identify which dimension was responsible.

== Understanding sensation seeking ==

Sensation seeking is strongly correlated to impulsivity but places greater emphasis on the motivation to experience novelty, intensity and stimulation. The construct has traditionally been understood as an individual difference in preference for varied, novel, complex and intense experiences, sometimes accompanied by willingness to accept risk to obtain those experiences (Roberti, 2004; Zuckerman &amp; Kuhlman, 2000). Ultimately indicating that risk itself does not always have to be the person's goal. Instead, risk may be accepted because it accompanies an experience considered sufficiently interesting or rewarding.

=== A motivational perspective ===

This provides an important distinction from other impulsivity dimensions. Someone displaying lack of premeditation may act before adequately considering the consequences, whereas a sensation seeker may recognise the consequences and deliberately decide that the potential stimulation is worthwhile. In the opening scenario, the second student hesitates before accepting the unfamiliar drink but chooses it because the experience is new and exciting. The decision may therefore involve forethought while still being associated with risk.

Sensation seeking should consequently not be treated as inherently dysfunctional. Ravert and Donnellan (2021) found different associations between impulsivity, sensation seeking and psychological well being, supporting the idea that the constructs should not simply be combined into a general tendency towards problematic behaviour. Sensation seeking may encourage exploration and engagement as well as potentially hazardous behaviour, meaning that its consequences depend partly on how and where the need for stimulation is expressed.

=== A theoretical complication ===

An important theoretical complication is that sensation seeking is simultaneously treated as a distinct construct and included as a dimension within the UPPS-P model of impulsivity (Whiteside &amp; Lynam, 2001). The inclusion of sensation seeking within the UPPS-P model does not mean that it is the same as other forms of impulsivity; rather, it is considered one distinct pathway that may contribute to impulsive behaviour. Contrastingly, it demonstrates that the boundaries surrounding the broader concept of impulsivity remain debated and depend partly on how researchers define and measure it. If all sensation seeking were simply impulsivity, there would be little reason to expect the two to show different relationships with behaviour. Evidence that they predict different outcomes can therefore help determine whether distinguishing them is psychologically meaningful.

== Distinguishing impulsivity from sensation seeking ==

[[File:Sensation seeking Vs Impulsivity.png|right|thumb|387px|'''Figure 2'''. Comparison of the UPPS-P dimensions of impulsive behaviour and Zuckerman’s dimensions of sensation seeking, highlighting areas of conceptual overlap and distinction (Goh et al., 2020; Magid et al., 2007; Samiefard et al., 2023). (image created independently using Canva software).]]

Impulsivity and sensation seeking overlap because both can contribute to behaviours involving uncertainty or risk. The key distinction concerns the process motivating the action. Dimensions such as urgency and lack of premeditation emphasise rash action or insufficient regulation, whereas sensation seeking emphasises approach towards novelty, excitement and stimulation (Cyders &amp; Smith, 2008; Zuckerman &amp; Kuhlman, 2000). Similar behaviour can therefore emerge through different psychological pathways.

Research comparing the constructs provides support for this distinction. Magid et al. (2007), found that sensation seeking and impulsivity showed different relationships with alcohol involvement, suggesting that combining them could overlook meaningful differences. Similarly, a meta-analysis found that sensation seeking and impulsivity were both associated with greater risk taking, but sensation seeking showed a somewhat stronger relationship with risky behaviour than impulsivity (Lauriola et al., 2014). These findings support distinguishing the constructs while also demonstrating that neither provides a complete explanation of risky behaviour.

'''Table 1''' 

'''Table – Comparing impulsivity and sensation''' '''seeking''' 

The comparison table summarises the major conceptual differences and similarities between impulsivity and sensation seeking, including their defining characteristics, underlying processes, and relationships with risk taking behaviour.
{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! Feature !! Impulsivity !! Sensation seeking
|-
| '''Core characteristic''' || Tendency toward rash or insufficiently considered action across multiple dimensions || Tendency to seek novel, varied, exciting or stimulating experiences
|-
| '''Key Process''' || Can involve reduced forethought, urgency or behavioural regulation || Motivation toward novelty, excitement and stimulation
|-
|'''Risk Taking'''
|Risk may result from insufficient consideration of consequences or other impulsive tendencies
|Risk may be accepted in pursuit of rewarding or stimulating experiences
|-
|'''UPPS-P'''
|Multidimensional model including positive urgency, negative urgency, lack of premeditation, lack of perseverance and sensation seeking
|Sensation seeking is one distinct dimension within the UPPS-P model
|-
|'''Example'''
|Immediately accepting an unfamiliar drink without considering consequences
|Deliberately trying the drink because the experience is novel and exciting
|-
|'''Behavioural Outcome'''
|Can contribute to health risk, gambling and substance related behaviours
|Can contribute to risk taking, alcohol use and novelty oriented behaviour
|}
Whilst impulsivity and sensation seeking can contribute to similar observable behaviours, their underlying characteristics and psychological processes differ (see Table 1; Goh et al., 2020; Magid et al., 2007).

=== Development and the dual systems model ===

The dual systems model provides another theoretical perspective for understanding this distinction. The model proposes that heightened reward sensitivity develops differently from capacities associated with cognitive control, potentially contributing to increased risk taking during adolescence (Steinberg, 2010). From this perspective, attraction towards rewarding or stimulating experiences and the ability to regulate behaviour are related but separable processes.

Conversely, the model has also been critically reconsidered. Shulman et al. (2016) concluded that evidence broadly supports different developmental trajectories for reward related and cognitive control systems while also highlighting complexities that cannot be captured by a simple imbalance between two systems. Risk taking varies substantially across people and situations, so developmental models should not be interpreted as suggesting that risky behaviour is inevitable or caused by one neural mechanism. The theory is useful for explaining why reward seeking and behavioural control can be distinguished, but it should complement rather than replace personality and contextual explanations.

== Impulsivity, sensation seeking, and risk taking behaviour ==

[[File:Boxing in Uruguay - Palacio Peñarol.jpg|right|thumb|350px|'''Figure 3'''. Activities involving risk and stimulation, such as boxing, illustrate that engagement in risky behaviour does not necessarily indicate impulsivity. The psychological motivation underlying the behaviour may be important for distinguishing impulsivity from sensation seeking.]]

The theoretical distinction becomes particularly useful when considering risk taking behaviour. If impulsivity and sensation seeking represented the same underlying characteristic, they would be expected to show broadly equivalent relationships with risky outcomes. Instead, evidence indicates that different dimensions can be associated with different behaviours and consequences.

Research examining risk taking has found that both sensation seeking and impulsivity are associated with a greater tendency to engage in risky behaviour, although these relationships are relatively modest (Lauriola et al., 2014). This pattern extends across varied types of behaviour, with sensation seeking and impulsivity related traits associated with health risk behaviours (Rogers et al., 2021), adolescent risk taking (Siraj et al., 2021), and speeding behaviour (Sârbescu &amp; Rusu, 2021). More recently, Grubbs et al. (2024) demonstrated that the specific psychological trait involved may also relate to different aspects of risky behaviour. Sensation seeking was associated with whether individuals had engaged in sports wagering, while urgency related dimensions were associated with different patterns of wagering involvement and gambling related problems. 

These findings provide evidence for the theoretical distinction, whilst also requiring cautious interpretation. Personality traits generally explain only part of the variation in complex behaviours, and correlations cannot establish that a trait directly causes an individual to take a particular risk. Social influences, opportunity, emotional state, perceived rewards and the specific type of risk may interact with personality characteristics. Therefore, describing someone simply as a &quot;risk taker&quot; may obscure both the psychological pathway and the context contributing to their behaviour.

== Alcohol use and related consequences ==

Alcohol use provides an especially useful real-world example because drinking and experiencing alcohol related problems are not the same outcome. Sensation seeking may motivate approach towards stimulating social or drinking experiences, whereas other impulsivity dimensions may be more relevant to rash decisions and harmful consequences. This distinction directly reflects the opening scenario: both students accept the same drink, however their reasons for doing so differ.

Magid et al. (2007) found that sensation seeking and impulsivity related differently to alcohol use and alcohol related problems among university students. Broader research evidence supports this outcome specific approach; for instance across 96 studies, Coskunpinar et al. (2013) found that different UPPS dimensions showed different relationships with alcohol outcomes, with urgency dimensions particularly relevant to alcohol related problems. Evidence from individuals entering residential alcohol detoxification also demonstrates clinically relevant relationships between UPPS-P dimensions and substance related characteristics (Kempeneers et al., 2023).

These findings illustrate why psychological explanations should expand beyond asking whether someone is simply &quot;impulsive&quot;. Identifying whether behaviour is motivated primarily by stimulation, emotional urgency, insufficient forethought or another process may provide a more precise understanding of the behaviour. Simultaniously, much of this evidence is correlational and relies on self report measures, so personality should not be interpreted as determining whether an individual will drink or experience alcohol related harm.

=== From explanation to application ===

Understanding different pathways may also have practical implications. Individuals motivated primarily by sensation seeking may benefit from finding safer ways to obtain novelty and stimulation, whereas behaviour associated with urgency may require greater attention to managing intense emotional states before acting. Lack of premeditation is particularly relevant, strategies that introduce time for considering consequences may be more appropriate.

These possibilities illustrate why distinguishing psychological processes can contribute to improving everyday behaviour rather than merely attaching personality labels to people. However, individualised strategies should not be inferred solely from personality scores, and the available evidence does not demonstrate that matching interventions to UPPS-P dimensions will necessarily produce better outcomes. Instead, the distinction provides a framework for understanding why the same behaviour may require different explanations and potentially different approaches to change.

==Figures==
[[File:Sensation seeking Vs Impulsivity.png|thumb|387x387px|'''Figure 2'''. Comparison of the UPPS-P dimensions of impulsive behaviour and Zuckerman’s dimensions of sensation seeking, highlighting areas of conceptual overlap and distinction (Goh et al., 2020; Magid et al., 2007; Samiefard et al., 2023). (image created independently using Canva software).|center]]

==Learning features==
'''Table 1''' 

'''Table – Comparing impulsivity and sensation''' '''seeking''' 

The comparison table summarises the major conceptual differences and similarities between impulsivity and sensation seeking, including their defining characteristics, underlying processes, and relationships with risk taking behaviour.
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
|-
! Feature !! Impulsivity !! Sensation seeking
|-
| '''Core characteristic''' || Tendency toward rash or insufficiently considered action across multiple dimensions || Tendency to seek novel, varied, exciting or stimulating experiences
|-
| '''Key Process''' || Can involve reduced forethought, urgency or behavioural regulation || Motivation toward novelty, excitement and stimulation
|-
|'''Risk Taking'''
|Risk may result from insufficient consideration of consequences or other impulsive tendencies
|Risk may be accepted in pursuit of rewarding or stimulating experiences
|-
|'''UPPS-P'''
|Multidimensional model including positive urgency, negative urgency, lack of premeditation, lack of perseverance and sensation seeking
|Sensation seeking is one distinct dimension within the UPPS-P model
|-
|'''Example'''
|Immediately accepting an unfamiliar drink without considering consequences
|Deliberately trying the drink because the experience is novel and exciting
|-
|'''Behavioural Outcome'''
|Can contribute to health-risk, gambling and substance related behaviours
|Can contribute to risk taking, alcohol use and novelty oriented behaviour
|}
Whilst impulsivity and sensation seeking can contribute to similar observable behaviours, their underlying characteristics and psychological processes differ (see Table 1; Goh et al., 2020; Magid et al., 2007).

'''Quiz: Impulsivity or sensation seeking?'''
&lt;quiz display=&quot;simple&quot;&gt;
{A student is offered an unfamiliar alcoholic drink at a party and immediately accepts without considering the possible consequences. Which characteristic best explains this behaviour?
|type=&quot;()&quot;}

+ Lack of premeditation
- Thrill and adventure seeking
- Experience seeking
- Boredom susceptibility

{A student deliberately chooses to try an unfamiliar activity because they enjoy novelty, excitement, and stimulation. Which construct best explains this motivation?
|type=&quot;()&quot;}

- Lack of perseverance
+ Sensation seeking
- Negative urgency
- Lack of premeditation

{Which statement best describes the distinction between impulsivity and sensation seeking?
|type=&quot;()&quot;}

- Impulsivity and sensation seeking are interchangeable terms for the same psychological construct.
- Sensation seeking always involves acting without considering consequences.
+ Similar observable behaviours can arise from different underlying motivations and psychological processes.
- Only impulsivity is associated with risk taking behaviour.
&lt;/quiz&gt;

== [[Conclusion]] ==
Impulsivity and sensation seeking are related psychological constructs, however should not automatically be treated as interchangeable. Multidimensional models such as the UPPS-P demonstrate that behaviour commonly labelled &quot;impulsive&quot; can arise through different pathways involving emotion, forethought, persistence and attraction towards stimulation. Sensation seeking is particularly important because it overlaps conceptually with impulsivity while emphasising the motivation to pursue novel and exciting experiences.

Research supports the practical value of distinguishing these processes. Sensation seeking and different dimensions of impulsivity show different patterns of association with risk taking, alcohol involvement and other potentially harmful behaviours, although these relationships are generally probabilistic rather than deterministic. Consequently, observable behaviour alone cannot reveal why an individual acted as they did.

The opening scenario illustrates the practical significance of distinguishing between these psychological processes. Accepting an unfamiliar drink may result from acting without considering consequences, seeking an exciting new experience, responding rashly to intense emotion, or a combination of these processes. Understanding why behaviour occurs, rather than simply labelling what occurred, can provide a more useful foundation for understanding and potentially improving everyday decision making.

== See also ==
* [[Motivation and emotion/Book/2011/Sensation seeking|Sensation seeking]] (Book chapter, 2011)
* [[w:Sensation Seeking Scale|Sensation Seeking Scale]] (Wikipedia)

== References ==

{{Hanging indent|Berg, J. M., Latzman, R. D., Bliwise, N. G., &amp; Lilienfeld, S. O. (2015). Parsing the heterogeneity of impulsivity: A meta-analytic review of the behavioral implications of the UPPS for psychopathology. ''Psychological Assessment, 27''(4), 1129–1146. https://doi.org/10.1037/pas0000111}}

{{Hanging indent|Coskunpinar, A., Dir, A. L., &amp; Cyders, M. A. (2013). Multidimensionality in impulsivity and alcohol use: A meta-analysis using the UPPS model of impulsivity. ''Alcoholism: Clinical and Experimental Research, 37''(9), 1441–1450. https://doi.org/10.1111/acer.12131}}

{{Hanging indent|Cyders, M. A., &amp; Smith, G. T. (2008). Emotion-based dispositions to rash action: Positive and negative urgency. ''Psychological Bulletin, 134''(6), 807–828. https://doi.org/10.1037/a0013341}}

{{Hanging indent|Goh, P. K., Lee, C. A., Martel, M. M., Fillmore, M. T., Derefinko, K. J., &amp; Lynam, D. R. (2020). Conceptualizing the UPPS-P model of impulsive personality through network analysis: Key dimensions and general robustness across young adulthood. ''Journal of Personality, 88''(6), 1302–1314. https://doi.org/10.1111/jopy.12572}}

{{Hanging indent|Grubbs, J. B., Connolly, A. J., Floyd, C. G., Kim, H. S., &amp; Kraus, S. W. (2024). Impulsivity and diverse forms of sports wagering in the U.S.: An examination of the UPPS-P model. ''Addictive Behaviors, 156'', 108058. https://doi.org/10.1016/j.addbeh.2024.108058}}

{{Hanging indent|Kempeneers, P., Mreyen, K., Pallincourt, R., Remacle, F., Wildemeersch, G., &amp; Simon, J. (2023). Validation of the UPPS-P Impulsive Behavior Scale and clinical correlates of its scores in French-speaking patients starting a residential detoxification program. ''Indian Journal of Psychological Medicine, 45''(5), 503–510. https://doi.org/10.1177/02537176231157411}}

{{Hanging indent|Lauriola, M., Panno, A., Levin, I. P., &amp; Lejuez, C. W. (2014). Individual differences in risky decision making: A meta-analysis of sensation seeking and impulsivity with the Balloon Analogue Risk Task. ''Journal of Behavioral Decision Making, 27''(1), 20–36. https://doi.org/10.1002/bdm.1784}}

{{Hanging indent|Magid, V., MacLean, M. G., &amp; Colder, C. R. (2007). Differentiating between sensation seeking and impulsivity through their mediated relations with alcohol use and problems. ''Addictive Behaviors, 32''(10), 2046–2061. https://doi.org/10.1016/j.addbeh.2007.01.015}}

{{Hanging indent|Ravert, R. D., &amp; Donnellan, M. B. (2021). Impulsivity and sensation seeking: Differing associations with psychological well-being. ''Applied Research in Quality of Life, 16''(4), 1503–1515. https://doi.org/10.1007/s11482-020-09829-y}}

{{Hanging indent|Roberti, J. W. (2004). A review of behavioral and biological correlates of sensation seeking. ''Journal of Research in Personality, 38''(3), 256–279. https://doi.org/10.1016/S0092-6566(03)00067-9}}

{{Hanging indent|Rogers, M. M., Kelley, K., &amp; McKinney, C. (2021). Trait impulsivity and health risk behaviors: A latent profile analysis. ''Personality and Individual Differences, 171'', 110511. https://doi.org/10.1016/j.paid.2020.110511}}

{{Hanging indent|Samiefard, M., Salehi Fadardi, J., Kareshki, H., &amp; Stacy, A. W. (2023). Validity and reliability of a revised S-UPPS-P Impulsive Behavior Scale: The interplay between impulsivity and working memory. ''Journal of Personality Assessment, 105''(2), 174–186. https://doi.org/10.1080/00223891.2022.2081922}}

{{Hanging indent|Sârbescu, P., &amp; Rusu, A. (2021). Personality predictors of speeding: Anger-aggression and impulsive-sensation seeking. A systematic review and meta-analysis. ''Journal of Safety Research, 77'', 86–98. https://doi.org/10.1016/j.jsr.2021.02.004}}

{{Hanging indent|Sharma, L., Markon, K. E., &amp; Clark, L. A. (2014). Toward a theory of distinct types of “impulsive” behaviors: A meta-analysis of self-report and behavioral measures. ''Psychological Bulletin, 140''(2), 374–408. https://doi.org/10.1037/a0034418}}

{{Hanging indent|Shulman, E. P., Smith, A. R., Silva, K., Icenogle, G., Duell, N., Chein, J., &amp; Steinberg, L. (2016). The dual systems model: Review, reappraisal, and reaffirmation. ''Developmental Cognitive Neuroscience, 17'', 103–117. https://doi.org/10.1016/j.dcn.2015.12.010}}

{{Hanging indent|Siraj, R., Najam, B., &amp; Ghazal, S. (2021). Sensation seeking, peer influence, and risk-taking behavior in adolescents. ''Education Research International, 2021'', 8403024. https://doi.org/10.1155/2021/8403024}}

{{Hanging indent|Steinberg, L. (2010). A dual systems model of adolescent risk-taking. ''Developmental Psychobiology, 52''(3), 216–224. https://doi.org/10.1002/dev.20445}}

{{Hanging indent|Türkmen, İ., Rodoplu, N., Üner, B. S., Esmer, Ş. C., Altan-Atalay, A., &amp; Ece, B. (2023). When the UPPS-P model of impulsivity meets a revised approach: The development and validation of the TRUE Multidimensional Impulsivity Scale. ''Journal of Personality Assessment, 105''(3), 355–370. https://doi.org/10.1080/00223891.2022.2093730}}

{{Hanging indent|Whiteside, S. P., &amp; Lynam, D. R. (2001). The five factor model and impulsivity: Using a structural model of personality to understand impulsivity. ''Personality and Individual Differences, 30''(4), 669–689. https://doi.org/10.1016/S0191-8869(00)00064-7}}

{{Hanging indent|Zuckerman, M., &amp; Kuhlman, D. M. (2000). Personality and risk-taking: Common biosocial factors. ''Journal of Personality, 68''(6), 999–1029. https://doi.org/10.1111/1467-6494.00124}}

==External links==
* [https://dictionary.apa.org/sensation-seeking-scale APA Dictionary of Psychology – Sensation-Seeking Scale]
* [https://onlinelibrary.wiley.com/doi/full/10.1002/9781405186407.wbiecs029 Sensation Seeking – Zuckerman] {{ic|Move academic sources to citations/references}}
* [https://www.impulsivity.org/measurement/upps_p/ UPPS-P Impulsive Behavior Scale]

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      <text bytes="5669" sha1="3xnf5s1rdxjg1t47sr2huj4gldh87q1" xml:space="preserve">== About me ==
Hello Everyone,

I am currently a 3rd year psychology student at [https://www.google.com/search?client=safari&amp;rls=en&amp;q=University+of+canberra&amp;ie=UTF-8&amp;oe=UTF-8 University of Canberra] This semester I am studying [[Motivation and emotion|Motivation and Emotion]] unit.

My Linkedln profile:  https://www.linkedin.com/in/palak-kathiriya-6b7048289/

== Hobbies ==

* Dancing
* Hiking
* Travelling to different countries 
* Painting 
* Cycling 
* Nature exploration
** Birdwatching
** Gardening 

== Book Chapter I'm working on ==
I am working on a really interesting topic for my book chapter. My chapter title is: Positive emotion dysregulation: What is positive emotion dysregulation and how does it affect psychological functioning? 

Link for my book chapter: [[Motivation and emotion/Book/2026/Positive emotion dysregulation|Positive emotion dysregulation]] 

== Social contributions ==

# 12:58 pm, 26 August 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FWarm-glow_giving&amp;diff=2826658&amp;oldid=2826657 Added the template and the title for this page - Title: Warm-glow giving - Why does giving feel good and how does this influence prosocial behaviour? '''('''Book Chapter, 2026)]
# 11:59 am, 26 August 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FPerfectionism_and_procrastination&amp;diff=2826589&amp;oldid=2826579 Fixed spelling error in one of the focus question - Title:  Perfectionism and procrastination - What is the role of perfectionism in procrastination and what can be done about it? (Book Chapter, 2026)]
# 12:28 pm, 26 August 2026: [[Talk:Motivation and emotion/Book/2026/Motivations for using sex work services#Heading casing|Made a suggestion about overview section - Title: Motivations for using sex work services: What motivates use of sex work services? (Book Chapter, 2026)]]
# 2:03 pm, 26 August 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456558 Provided a couple of sources for the development of breathing exercises and relaxation book chapter (Book Chapter, 2026) (UC Learn)]
#8:10 am, 2 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/458145 Commented on discussion forum about how to use GenAI in the unit and what are the expectations if we use GenAI (UC Learn)]
# 10:14 am , 2 September 2026:[https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FSelf-control_and_ego_depletion_recovery&amp;diff=2830323&amp;oldid=2761410 Fixed spelling error in book chapter - Title: Self-control and ego depletion recovery: How do people restore self-control resources after depletion and what factors influence recovery? (Book Chapter, 2025)]
# 10:22 am, 2 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Grit_and_academic_achievement&amp;diff=prev&amp;oldid=2830325 Changed few sentences to make it grammatically better - Title: Grit and academic achievement  What role does grit play in academic achievement and can it be fostered in future students? (Book Chapter, 2025)]
# 10:48 am, 2 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FCancer_screening_and_emotion&amp;diff=2830328&amp;oldid=2823381 Rewrote one paragraph in overview section to make it easier to understand - Title: Cancer screening and emotion: How do emotions such as fear, anxiety, and relief influence cancer screening uptake?(Book Chapter, 2025)]
# 10: 54 am, 2 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FCancer_screening_and_emotion&amp;diff=2830330&amp;oldid=2830328 Added reference to support one claim in overview section - Title: Cancer screening and emotion:How do emotions such as fear, anxiety, and relief influence cancer screening uptake? (Book Chapter, 2025)]
#12:56 pm, 2 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455261 Commented on discussion forum about what interests me more in motivation and emotion unit and what I would like to learn (UC Learn)]
#9:17 pm, 3 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FGrit_and_academic_achievement&amp;diff=2830732&amp;oldid=2830326 Corrected grammar and sentence structure, fixed spelling, removed repetition, and improved wording for clarity and flow - Title: Grit and academic achievement - What role does grit play in academic achievement and can it be fostered in future students? - (Book Chapter, 2025)]
#9:27 pm, 3 September 2026: [[Talk:Motivation and emotion/Book/2026/Outdoor play and children's emotional well-being|Provided suggestion for wikiversity book chapter page and clarified that the user page should be separate than the book chapter - Title: Outdoor play and children's emotional well-being - How does outdoor play influence children's emotional well-being? Overview - (Book Chapter, 2025)]]
#8:28 am, 4 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 Commented on discussion forum about what motivates me and what helps me to keep going if I am not feeling motivated (UC Learn)] 
#8:30 am, 7 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FGrit_and_academic_achievement&amp;diff=2831894&amp;oldid=2830732 Changed few spelling errors, fixed sentence structure and punctuation, shortened some repetitive wording while keeping original ideas - Title- Grit and academic achievement - What role does grit play in academic achievement and can it be fostered in future students ? - (Book Chapter, 2025)]  
#7 September 2026:</text>
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      <text bytes="6050" sha1="7lpregsihtgeyujgzexnjary61nq0rj" xml:space="preserve">== About me ==
Hello Everyone,

I am currently a 3rd year psychology student at [https://www.google.com/search?client=safari&amp;rls=en&amp;q=University+of+canberra&amp;ie=UTF-8&amp;oe=UTF-8 University of Canberra] This semester I am studying [[Motivation and emotion|Motivation and Emotion]] unit.

My Linkedln profile:  https://www.linkedin.com/in/palak-kathiriya-6b7048289/

== Hobbies ==

* Dancing
* Hiking
* Travelling to different countries 
* Painting 
* Cycling 
* Nature exploration
** Birdwatching
** Gardening 

== Book Chapter I'm working on ==
I am working on a really interesting topic for my book chapter. My chapter title is: Positive emotion dysregulation: What is positive emotion dysregulation and how does it affect psychological functioning? 

Link for my book chapter: [[Motivation and emotion/Book/2026/Positive emotion dysregulation|Positive emotion dysregulation]] 

== Social contributions ==

# 12:58 pm, 26 August 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FWarm-glow_giving&amp;diff=2826658&amp;oldid=2826657 Added the template and the title for this page - Title: Warm-glow giving - Why does giving feel good and how does this influence prosocial behaviour? '''('''Book Chapter, 2026)]
# 11:59 am, 26 August 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FPerfectionism_and_procrastination&amp;diff=2826589&amp;oldid=2826579 Fixed spelling error in one of the focus question - Title:  Perfectionism and procrastination - What is the role of perfectionism in procrastination and what can be done about it? (Book Chapter, 2026)]
# 12:28 pm, 26 August 2026: [[Talk:Motivation and emotion/Book/2026/Motivations for using sex work services#Heading casing|Made a suggestion about overview section - Title: Motivations for using sex work services: What motivates use of sex work services? (Book Chapter, 2026)]]
# 2:03 pm, 26 August 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456558 Provided a couple of sources for the development of breathing exercises and relaxation book chapter (Book Chapter, 2026) (UC Learn)]
#8:10 am, 2 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/458145 Commented on discussion forum about how to use GenAI in the unit and what are the expectations if we use GenAI (UC Learn)]
# 10:14 am , 2 September 2026:[https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FSelf-control_and_ego_depletion_recovery&amp;diff=2830323&amp;oldid=2761410 Fixed spelling error in book chapter - Title: Self-control and ego depletion recovery: How do people restore self-control resources after depletion and what factors influence recovery? (Book Chapter, 2025)]
# 10:22 am, 2 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Grit_and_academic_achievement&amp;diff=prev&amp;oldid=2830325 Changed few sentences to make it grammatically better - Title: Grit and academic achievement  What role does grit play in academic achievement and can it be fostered in future students? (Book Chapter, 2025)]
# 10:48 am, 2 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FCancer_screening_and_emotion&amp;diff=2830328&amp;oldid=2823381 Rewrote one paragraph in overview section to make it easier to understand - Title: Cancer screening and emotion: How do emotions such as fear, anxiety, and relief influence cancer screening uptake?(Book Chapter, 2025)]
# 10: 54 am, 2 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FCancer_screening_and_emotion&amp;diff=2830330&amp;oldid=2830328 Added reference to support one claim in overview section - Title: Cancer screening and emotion:How do emotions such as fear, anxiety, and relief influence cancer screening uptake? (Book Chapter, 2025)]
#12:56 pm, 2 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455261 Commented on discussion forum about what interests me more in motivation and emotion unit and what I would like to learn (UC Learn)]
#9:17 pm, 3 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FGrit_and_academic_achievement&amp;diff=2830732&amp;oldid=2830326 Corrected grammar and sentence structure, fixed spelling, removed repetition, and improved wording for clarity and flow - Title: Grit and academic achievement - What role does grit play in academic achievement and can it be fostered in future students? - (Book Chapter, 2025)]
#9:27 pm, 3 September 2026: [[Talk:Motivation and emotion/Book/2026/Outdoor play and children's emotional well-being|Provided suggestion for wikiversity book chapter page and clarified that the user page should be separate than the book chapter - Title: Outdoor play and children's emotional well-being - How does outdoor play influence children's emotional well-being? Overview - (Book Chapter, 2025)]]
#8:28 am, 4 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 Commented on discussion forum about what motivates me and what helps me to keep going if I am not feeling motivated (UC Learn)] 
#8:30 am, 7 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FGrit_and_academic_achievement&amp;diff=2831894&amp;oldid=2830732 Changed few spelling errors, fixed sentence structure and punctuation, shortened some repetitive wording while keeping original ideas - Title- Grit and academic achievement - What role does grit play in academic achievement and can it be fostered in future students ? - (Book Chapter, 2025)]
#8:50 am, 7 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FCancer_screening_and_emotion&amp;diff=2831919&amp;oldid=2830330 Changed few sentences to make it grammatically correct and to maintain sentence flow - Title -Cancer screening and emotion: How do emotions such as fear, anxiety, and relief influence cancer screening uptake? - (Book chapter, 2025)]</text>
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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}
[[File:NASA-HS201427a-HubbleUltraDeepField2014-20140603.jpg|right|thumb|200px|'''Figure 1'''. NASA Hubble Ultra Deep Field]]

; Awe, the awareness of life, 

Have you ever experienced a moment of awe? A moment that felt totally present, or maybe you were amazed at the vastness of space looking up at the stars. Maybe you saw someone do something good for another person. How did this leave you feeling? Did. 


* Wondering whether I should frame it towards the reader in the second person or direct a scenario to illustrate the after effects. Probably do both. 
* Change picture to relevant awe triggering media such as grand canyon, or night sky etc. Or maybe save these for criteria section later for table or interactive media 


* ''Provide a context that can be revisited when explaining the psychological concepts and research later in the chapter.''
* ''Avoid explaining theory or research in detail— the purpose is to illustrate the problem, not solve it.''
* ''Be presented in a [[#Feature box|feature box]].''
* ''Include a relevant image, with a figure caption, to help illustrate the scenario. Cite the figure (e.g., see Figure 1) within the scenario.''

{{RoundBoxBottom}}
*Awe is an emotion 

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

* What is awe as an emotion and experience?
* How does the experience of awe diminish the self?
* What is the effect of a diminished sense of self?
* How can awe be integrated into modern life?
* How can the experience of awe be applied?{{RoundBoxBottom}}
*


== Awe ==

=== Vastness ===

==== Physical ====

===== Nature =====

====== Space ======

==== Conceptual ====

=== Need for Accommodation ===

==== Mental Structures (Schemas) ====


==Applications==

===Community===

*

===Individual===

==== Therapy / Personal Growth ====

===== Humility =====
* presenting more balanced view of personal strengths and weaknesses
* increased acknowledgment of outside forces in one's accomplishments (Stellar et al., 2018)

* epistemic humility = measures of wisdom and moral character 
* positive self-transcendent experiences can be utilised as driving force for better understanding one's decision and perspectives impact others (Kim et al., 2023)

===== Psychedelic Therapies =====


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

'''Table 1''' 

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

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

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

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=&quot;simple&quot;&gt;
{Which of the following is an appraisal of the emotion awe?
|type=&quot;()&quot;}
+ Vastness
- Smallness

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

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

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

==See also==
Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)

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

==References==


APA style example:
{{Hanging indent|1=

Kim, Y., Nusbaum, H. C., &amp; Yang, F. (2023). Going beyond ourselves: The role of self-transcendent experiences in wisdom. Cognition and Emotion, 37(1), 98-116. 

Stellar, J. E., Gordon, A., Anderson, C. L., Piff, P. K., McNeil, G. D., &amp; Keltner, D. (2018). Awe and humility. Journal of personality and social psychology, 114(2), 258.

}}

==External links==
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)

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

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]</text>
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    <revision>
      <id>2831902</id>
      <parentid>2831883</parentid>
      <timestamp>2026-09-06T22:36:59Z</timestamp>
      <contributor>
        <username>Amirrorslens</username>
        <id>3106278</id>
      </contributor>
      <comment>more rearranging of headings and organising of ideas</comment>
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      <text bytes="6746" sha1="ry97t7vl52jrunnjkpwsoru13pciyht" xml:space="preserve">{{title|Awe and the diminished self:&lt;br&gt;How does awe diminish the self and how can this be applied?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=2}}
[[File:NASA-HS201427a-HubbleUltraDeepField2014-20140603.jpg|right|thumb|200px|'''Figure 1'''. NASA Hubble Ultra Deep Field]]

; Awe, the awareness of life, 

Have you ever experienced a moment of awe? A moment that felt totally present, or maybe you were amazed at the vastness of space looking up at the stars. Maybe you saw someone do something good for another person. How did this leave you feeling? Did. 


* Wondering whether I should frame it towards the reader in the second person or direct a scenario to illustrate the after effects. Probably do both. 
* Change picture to relevant awe triggering media such as grand canyon, or night sky etc. Or maybe save these for criteria section later for table or interactive media 


* ''Provide a context that can be revisited when explaining the psychological concepts and research later in the chapter.''
* ''Avoid explaining theory or research in detail— the purpose is to illustrate the problem, not solve it.''
* ''Be presented in a [[#Feature box|feature box]].''
* ''Include a relevant image, with a figure caption, to help illustrate the scenario. Cite the figure (e.g., see Figure 1) within the scenario.''

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

* What is awe as an emotion and experience?
* How does the experience of awe diminish the self?
* What is the effect of a diminished sense of self?
* How can awe be integrated into modern life?
* How can the experience of awe be applied?{{RoundBoxBottom}}{{RoundBoxTop|theme=1}}
'''QUESTIONS AND NOTES FOR SELF'''

* Where do I fit discussions of the Self in here? {{RoundBoxBottom}}

== Awe ==

=== Vastness ===

==== Physical ====

===== &gt; Other People =====

====== &gt;&gt; Acts of Talent or Skill ======

====== &gt;&gt; Acts of Virtue or Humanness ======
- updating wordview link

===== &gt; Nature =====
- smallness effect link

- eclipse: seeking connection post link

====== &gt;&gt; Space ======
- smallness effect link 

==== Conceptual ====

===== &gt; Learning =====
- updating wordview link

===== &gt; Religion =====
- smallness effect link 

- seeking connection post link

====== &gt;&gt; Buddhism / Awareness ''(see also)'' ======

===== &gt; The Arts =====

===== &gt; Psychedelics =====
- ego-death 

- oneness (link to buddhism), LINK TO SELF

=== Need for Accommodation ===

==== Smallness ====
- astronaut effect 

==== Profoundness ====

==== Connectedness ====
- seeking connection after feelings of smallness

===== Mental Structures (Schemas) =====

==== Failures to Accommodate ====

===== Fear =====
- threat-based awe (Keltner and Haidt)

- nihilism -&gt; depression 

===== Trauma =====
- dissociation (near death experiences)

- denial
==Applications==

===Community===

*

===Individual===

==== Therapy / Personal Growth ====

* GESTALT THERAPY
** present moment 
** inner child work

===== Humility ''(Rework heading and how this fits into other sections)'' =====
* presenting more balanced view of personal strengths and weaknesses
* increased acknowledgment of outside forces in one's accomplishments (Stellar et al., 2018)

* epistemic humility = measures of wisdom and moral character 
* positive self-transcendent experiences can be utilised as driving force for better understanding one's decision and perspectives impact others (Kim et al., 2023)

===== Psychedelic Therapies =====

* MDMA therapies for depression 
* LSD and psylocibin guided therapies 


&lt;nowiki&gt;--------------------------------------------------------------------------------------------------------------------------------------------------------------------&lt;/nowiki&gt;

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

'''Table 1''' 

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

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

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

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=&quot;simple&quot;&gt;
{Which of the following is an appraisal of the emotion awe?
|type=&quot;()&quot;}
+ Vastness
- Smallness

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

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

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

==See also==
Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)

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

==References==
{{Hanging indent|1=

Kim, Y., Nusbaum, H. C., &amp; Yang, F. (2023). Going beyond ourselves: The role of self-transcendent experiences in wisdom. Cognition and Emotion, 37(1), 98-116. 

Stellar, J. E., Gordon, A., Anderson, C. L., Piff, P. K., McNeil, G. D., &amp; Keltner, D. (2018). Awe and humility. Journal of personality and social psychology, 114(2), 258.

}}

==External links==
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)

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

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]</text>
      <sha1>ry97t7vl52jrunnjkpwsoru13pciyht</sha1>
    </revision>
    <revision>
      <id>2831905</id>
      <parentid>2831902</parentid>
      <timestamp>2026-09-06T22:40:07Z</timestamp>
      <contributor>
        <username>Amirrorslens</username>
        <id>3106278</id>
      </contributor>
      <comment>introduction of self heading</comment>
      <origin>2831905</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6925" sha1="sab91pgc5x7xu8j0szugqzvjpe4z2d4" xml:space="preserve">{{title|Awe and the diminished self:&lt;br&gt;How does awe diminish the self and how can this be applied?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=2}}
[[File:NASA-HS201427a-HubbleUltraDeepField2014-20140603.jpg|right|thumb|200px|'''Figure 1'''. NASA Hubble Ultra Deep Field]]

; Awe, the awareness of life, 

Have you ever experienced a moment of awe? A moment that felt totally present, or maybe you were amazed at the vastness of space looking up at the stars. Maybe you saw someone do something good for another person. How did this leave you feeling? Did. 


* Wondering whether I should frame it towards the reader in the second person or direct a scenario to illustrate the after effects. Probably do both. 
* Change picture to relevant awe triggering media such as grand canyon, or night sky etc. Or maybe save these for criteria section later for table or interactive media 


* ''Provide a context that can be revisited when explaining the psychological concepts and research later in the chapter.''
* ''Avoid explaining theory or research in detail— the purpose is to illustrate the problem, not solve it.''
* ''Be presented in a [[#Feature box|feature box]].''
* ''Include a relevant image, with a figure caption, to help illustrate the scenario. Cite the figure (e.g., see Figure 1) within the scenario.''

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

* What is awe as an emotion and experience?
* How does the experience of awe diminish the self?
* What is the effect of a diminished sense of self?
* How can awe be integrated into modern life?
* How can the experience of awe be applied?{{RoundBoxBottom}}{{RoundBoxTop|theme=1}}
'''QUESTIONS AND NOTES FOR SELF'''

* Where do I fit discussions of the Self in here? {{RoundBoxBottom}}

== Awe ==

=== Vastness ===

==== Physical ====

===== &gt; Other People =====

====== &gt;&gt; Acts of Talent or Skill ======

====== &gt;&gt; Acts of Virtue or Humanness ======
- updating wordview link

===== &gt; Nature =====
- smallness effect link

- eclipse: seeking connection post link

====== &gt;&gt; Space ======
- smallness effect link 

==== Conceptual ====

===== &gt; Learning =====
- updating wordview link

===== &gt; Religion =====
- smallness effect link 

- seeking connection post link

====== &gt;&gt; Buddhism / Awareness ''(see also)'' ======

===== &gt; The Arts =====

===== &gt; Psychedelics =====
- ego-death 

- oneness (link to buddhism), LINK TO SELF

=== Need for Accommodation ===

==== Smallness ====
- astronaut effect 

==== Profoundness ====

==== Connectedness ====
- seeking connection after feelings of smallness

===== Mental Structures (Schemas) =====

==== Failures to Accommodate ====

===== Fear =====
- threat-based awe (Keltner and Haidt)

- nihilism -&gt; depression 

===== Trauma =====
- dissociation (near death experiences)

- denial
==The Self / Perception ==
- discussion of what the self is 

- introduction of schemas 

- perception 

- ego death dissolving perception, awe experiences diminishing the self 

==Applications==

===Community===

*

===Individual===

==== Therapy / Personal Growth ====

* GESTALT THERAPY
** present moment 
** inner child work

===== Humility ''(Rework heading and how this fits into other sections)'' =====
* presenting more balanced view of personal strengths and weaknesses
* increased acknowledgment of outside forces in one's accomplishments (Stellar et al., 2018)

* epistemic humility = measures of wisdom and moral character 
* positive self-transcendent experiences can be utilised as driving force for better understanding one's decision and perspectives impact others (Kim et al., 2023)

===== Psychedelic Therapies =====

* MDMA therapies for depression 
* LSD and psylocibin guided therapies 


&lt;nowiki&gt;--------------------------------------------------------------------------------------------------------------------------------------------------------------------&lt;/nowiki&gt;

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

'''Table 1''' 

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

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

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

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=&quot;simple&quot;&gt;
{Which of the following is an appraisal of the emotion awe?
|type=&quot;()&quot;}
+ Vastness
- Smallness

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

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

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

==See also==
Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)

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

==References==
{{Hanging indent|1=

Kim, Y., Nusbaum, H. C., &amp; Yang, F. (2023). Going beyond ourselves: The role of self-transcendent experiences in wisdom. Cognition and Emotion, 37(1), 98-116. 

Stellar, J. E., Gordon, A., Anderson, C. L., Piff, P. K., McNeil, G. D., &amp; Keltner, D. (2018). Awe and humility. Journal of personality and social psychology, 114(2), 258.

}}

==External links==
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)

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

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]</text>
      <sha1>sab91pgc5x7xu8j0szugqzvjpe4z2d4</sha1>
    </revision>
    <revision>
      <id>2831906</id>
      <parentid>2831905</parentid>
      <timestamp>2026-09-06T22:41:07Z</timestamp>
      <contributor>
        <username>Amirrorslens</username>
        <id>3106278</id>
      </contributor>
      <comment>source for global meditation being correlated with lower crime rates</comment>
      <origin>2831906</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6994" sha1="q60ilg1n93cnlcx7hkbcm96wm56n6pq" xml:space="preserve">{{title|Awe and the diminished self:&lt;br&gt;How does awe diminish the self and how can this be applied?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=2}}
[[File:NASA-HS201427a-HubbleUltraDeepField2014-20140603.jpg|right|thumb|200px|'''Figure 1'''. NASA Hubble Ultra Deep Field]]

; Awe, the awareness of life, 

Have you ever experienced a moment of awe? A moment that felt totally present, or maybe you were amazed at the vastness of space looking up at the stars. Maybe you saw someone do something good for another person. How did this leave you feeling? Did. 


* Wondering whether I should frame it towards the reader in the second person or direct a scenario to illustrate the after effects. Probably do both. 
* Change picture to relevant awe triggering media such as grand canyon, or night sky etc. Or maybe save these for criteria section later for table or interactive media 


* ''Provide a context that can be revisited when explaining the psychological concepts and research later in the chapter.''
* ''Avoid explaining theory or research in detail— the purpose is to illustrate the problem, not solve it.''
* ''Be presented in a [[#Feature box|feature box]].''
* ''Include a relevant image, with a figure caption, to help illustrate the scenario. Cite the figure (e.g., see Figure 1) within the scenario.''

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

* What is awe as an emotion and experience?
* How does the experience of awe diminish the self?
* What is the effect of a diminished sense of self?
* How can awe be integrated into modern life?
* How can the experience of awe be applied?{{RoundBoxBottom}}{{RoundBoxTop|theme=1}}
'''QUESTIONS AND NOTES FOR SELF'''

* Where do I fit discussions of the Self in here? {{RoundBoxBottom}}

== Awe ==

=== Vastness ===

==== Physical ====

===== &gt; Other People =====

====== &gt;&gt; Acts of Talent or Skill ======

====== &gt;&gt; Acts of Virtue or Humanness ======
- updating wordview link

===== &gt; Nature =====
- smallness effect link

- eclipse: seeking connection post link

====== &gt;&gt; Space ======
- smallness effect link 

==== Conceptual ====

===== &gt; Learning =====
- updating wordview link

===== &gt; Religion =====
- smallness effect link 

- seeking connection post link

====== &gt;&gt; Buddhism / Awareness ''(see also)'' ======

===== &gt; The Arts =====

===== &gt; Psychedelics =====
- ego-death 

- oneness (link to buddhism), LINK TO SELF

=== Need for Accommodation ===

==== Smallness ====
- astronaut effect 

==== Profoundness ====

==== Connectedness ====
- seeking connection after feelings of smallness

===== Mental Structures (Schemas) =====

==== Failures to Accommodate ====

===== Fear =====
- threat-based awe (Keltner and Haidt)

- nihilism -&gt; depression 

===== Trauma =====
- dissociation (near death experiences)

- denial
==The Self / Perception ==
- discussion of what the self is 

- introduction of schemas 

- perception 

- ego death dissolving perception, awe experiences diminishing the self 

==Applications==

===Community===

*global meditation bringing down crime rates and violence? need source

===Individual===

==== Therapy / Personal Growth ====

* GESTALT THERAPY
** present moment 
** inner child work

===== Humility ''(Rework heading and how this fits into other sections)'' =====
* presenting more balanced view of personal strengths and weaknesses
* increased acknowledgment of outside forces in one's accomplishments (Stellar et al., 2018)

* epistemic humility = measures of wisdom and moral character 
* positive self-transcendent experiences can be utilised as driving force for better understanding one's decision and perspectives impact others (Kim et al., 2023)

===== Psychedelic Therapies =====

* MDMA therapies for depression 
* LSD and psylocibin guided therapies 


&lt;nowiki&gt;--------------------------------------------------------------------------------------------------------------------------------------------------------------------&lt;/nowiki&gt;

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

'''Table 1''' 

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

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

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

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=&quot;simple&quot;&gt;
{Which of the following is an appraisal of the emotion awe?
|type=&quot;()&quot;}
+ Vastness
- Smallness

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

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

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

==See also==
Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)

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

==References==
{{Hanging indent|1=

Kim, Y., Nusbaum, H. C., &amp; Yang, F. (2023). Going beyond ourselves: The role of self-transcendent experiences in wisdom. Cognition and Emotion, 37(1), 98-116. 

Stellar, J. E., Gordon, A., Anderson, C. L., Piff, P. K., McNeil, G. D., &amp; Keltner, D. (2018). Awe and humility. Journal of personality and social psychology, 114(2), 258.

}}

==External links==
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)

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

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]</text>
      <sha1>q60ilg1n93cnlcx7hkbcm96wm56n6pq</sha1>
    </revision>
    <revision>
      <id>2831924</id>
      <parentid>2831906</parentid>
      <timestamp>2026-09-06T22:54:12Z</timestamp>
      <contributor>
        <username>Amirrorslens</username>
        <id>3106278</id>
      </contributor>
      <comment>adding in reference list</comment>
      <origin>2831924</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10634" sha1="d3ooagimuqas1dcqmudsy2y2uoy7otj" xml:space="preserve">{{title|Awe and the diminished self:&lt;br&gt;How does awe diminish the self and how can this be applied?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=2}}
[[File:NASA-HS201427a-HubbleUltraDeepField2014-20140603.jpg|right|thumb|200px|'''Figure 1'''. NASA Hubble Ultra Deep Field]]

; Awe, the awareness of life, 

Have you ever experienced a moment of awe? A moment that felt totally present, or maybe you were amazed at the vastness of space looking up at the stars. Maybe you saw someone do something good for another person. How did this leave you feeling? Did. 


* Wondering whether I should frame it towards the reader in the second person or direct a scenario to illustrate the after effects. Probably do both. 
* Change picture to relevant awe triggering media such as grand canyon, or night sky etc. Or maybe save these for criteria section later for table or interactive media 


* ''Provide a context that can be revisited when explaining the psychological concepts and research later in the chapter.''
* ''Avoid explaining theory or research in detail— the purpose is to illustrate the problem, not solve it.''
* ''Be presented in a [[#Feature box|feature box]].''
* ''Include a relevant image, with a figure caption, to help illustrate the scenario. Cite the figure (e.g., see Figure 1) within the scenario.''

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

* What is awe as an emotion and experience?
* How does the experience of awe diminish the self?
* What is the effect of a diminished sense of self?
* How can awe be integrated into modern life? i.e. How can we trigger or experience everyday moments of awe?
* How can the experience of awe be applied for social and individual good?{{RoundBoxBottom}}{{RoundBoxTop|theme=1}}
'''QUESTIONS AND NOTES FOR SELF'''

* Where do I fit discussions of the Self in here? {{RoundBoxBottom}}

== Awe ==

=== Vastness ===

==== Physical ====

===== &gt; Other People =====

====== &gt;&gt; Acts of Talent or Skill ======

====== &gt;&gt; Acts of Virtue or Humanness ======
- updating wordview link

===== &gt; Nature =====
- smallness effect link

- See also previous book chapter: [[Motivation and emotion/Book/2026/Awe and nature|Awe and nature]]

- eclipse: seeking connection post link

====== &gt;&gt; Space ======
- smallness effect link 

==== Conceptual ====

===== &gt; Learning =====
- updating wordview link

===== &gt; Religion =====
- smallness effect link 

- seeking connection post link

====== &gt;&gt; Buddhism / Awareness ''(see also)'' ======

===== &gt; The Arts =====

===== &gt; Psychedelics =====
- ego-death 

- oneness (link to buddhism), LINK TO SELF

=== Need for Accommodation ===

==== Smallness ====
- [[wikipedia:Overview_effect|Overview effect]] 

==== Profoundness ====

==== Connectedness ====
- seeking connection after feelings of smallness

===== Mental Structures (Schemas) =====

==== Failures to Accommodate ====

===== Fear =====
- threat-based awe (Keltner and Haidt)

- [[wikipedia:Nihilism|Nihilism]] -&gt; depression 

===== Trauma =====
- dissociation (near death experiences)

- denial
==The Self / Perception ==
- discussion of what the self is 

- introduction of schemas 

- perception 

- ego death dissolving perception, awe experiences diminishing the self 

==Applications==

===Community===

*global meditation bringing down crime rates and violence? need source

===Individual===

==== Therapy / Personal Growth ====

* GESTALT THERAPY
** present moment 
** inner child work

===== Humility ''(Rework heading and how this fits into other sections)'' =====
* presenting more balanced view of personal strengths and weaknesses
* increased acknowledgment of outside forces in one's accomplishments (Stellar et al., 2018)

* epistemic humility = measures of wisdom and moral character 
* positive self-transcendent experiences can be utilised as driving force for better understanding one's decision and perspectives impact others (Kim et al., 2023)

===== Psychedelic Therapies =====

* MDMA therapies for depression 
* LSD and psylocibin guided therapies 


&lt;nowiki&gt;--------------------------------------------------------------------------------------------------------------------------------------------------------------------&lt;/nowiki&gt;

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

'''Table 1''' 

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

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

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

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=&quot;simple&quot;&gt;
{Which of the following is an appraisal of the emotion awe?
|type=&quot;()&quot;}
+ Vastness
- Smallness

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

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

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

==See also==
Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)

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

==References==
{{Hanging indent|1=

Arvidson, P. S. (2022). Reverent Awe and the Field of Consciousness. Human Studies, 45(3), 397-416. 

Bai, Y., Maruskin, L. A., Chen, S., Gordon, A. M., Stellar, J. E., McNeil, G. D., Peng, K., &amp; Keltner, D. (2017). Awe, the diminished self, and collective engagement: Universals and cultural variations in the small self. Journal of personality and social psychology, 113(2), 185. 

Cavallaro, R. M., Church, M. H., Giddens, B. J., &amp; Rivera, G. N. (2025). Complex effects of awe on meaning in life and true self-knowledge. Self and Identity, 24(3), 189-216. 

Chen, S. K., &amp; Mongrain, M. (2021). Awe and the interconnected self. The Journal of Positive Psychology, 16(6), 770-778. 

Edwards, M. E., Mendenhall, K., Sanders, C., &amp; King, L. A. (2026). Small but still significant: Awe and the self. Personality and Social Psychology Bulletin, 52(9), 3032-3045. 

Gao, R. (2026). From awe to pro-environmental behavior-a meta-analysis of the relationship between awe and pro-environmental behavior. The Journal of Positive Psychology, 21(5), 958-970. 

Jiang, T., Hicks, J. A., Yuan, W., Yin, Y., Needy, L., &amp; Vess, M. (2024). The unique nature and psychosocial implications of awe. Nature Reviews Psychology, 3(7), 475-488. 

Jiang, T., &amp; Sedikides, C. (2022). Awe motivates authentic-self pursuit via self-transcendence: Implications for prosociality. Journal of personality and social psychology, 123(3), 576. 

Kim, Y., Nusbaum, H. C., &amp; Yang, F. (2023). Going beyond ourselves: The role of self-transcendent experiences in wisdom. Cognition and Emotion, 37(1), 98-116. 

Li, R., Hou, Z., Zhang, C., Xu, Q., &amp; Nie, A. (2024). A meta-analysis examining the relationship between awe and prosocial behavior. Current Psychology, 43(29), 24702-24711. 

Lucht, A., &amp; van Schie, H. T. (2024). The evolutionary function of awe: A review and integrated model of seven theoretical perspectives. Emotion Review, 16(1), 46-63. 

McMann, G. B. (2025). Role of Vastness and Accommodation of Awe in Personal Change and Growth Grand Canyon University]. 

Perez, K. A., Lench, H. C., Thompson, C. G., &amp; North, S. (2023). Experimental elicitations of awe: A meta-analysis. Cognition and Emotion, 37(1), 18-33. 

Piff, P. K., Dietze, P., Feinberg, M., Stancato, D. M., &amp; Keltner, D. (2015). Awe, the small self, and prosocial behavior. Journal of personality and social psychology, 108(6), 883. 

Piff, P. K., Singhal, I., &amp; Bai, Y. (2025). Bridging me to we: Awe is a conduit to cohesive collectives. Current Opinion in Psychology, 62, 101979. 

Rivera, G. N., Vess, M., Hicks, J. A., &amp; Routledge, C. (2020). Awe and meaning: Elucidating complex effects of awe experiences on meaning in life. European Journal of Social Psychology, 50(2), 392-405. 

Shiota, M. N., Keltner, D., &amp; Mossman, A. (2007). The nature of awe: Elicitors, appraisals, and effects on self-concept. Cognition and Emotion, 21(5), 944-963. 

Shukla, S. (2021). Indian classical music, awe, and healing. The Humanistic Psychologist, 49(3), 355. 

Stellar, J. E., Gordon, A., Anderson, C. L., Piff, P. K., McNeil, G. D., &amp; Keltner, D. (2018). Awe and humility. Journal of personality and social psychology, 114(2), 258. 

Sturm, V. E., Datta, S., Roy, A. R., Sible, I. J., Kosik, E. L., Veziris, C. R., Chow, T. E., Morris, N. A., Neuhaus, J., &amp; Kramer, J. H. (2022). Big smile, small self: Awe walks promote prosocial positive emotions in older adults. Emotion, 22(5), 1044. 

Tanhan, F., DENİZ, M., &amp; Akgün, G. (2022). Awe Therapy: Fundamentals, Formulation and Usage Area Awe Terapi: Temelleri, Formülasyonu ve Kullanım Alanları. Turkish Psychological Counseling and Guidance Journal, 12(65). 

Tanhan, F., Deniz, M. E., &amp; Akgün, G. E. (2022). Awe Therapy: Fundamentals, formulation and usage area. Turkish Psychological Counseling and Guidance Journal, 12(65), 300-319.

}}

==External links==
* [https://self-transcendence.org/theory Self-transendence] (Self-transcendence.org)

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

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      <text bytes="10705" sha1="fj6q829by1npxjmu86x56g6ewlq3pw1" xml:space="preserve">{{title|Awe and the diminished self:&lt;br&gt;How does awe diminish the self and how can this be applied?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=2}}
[[File:NASA-HS201427a-HubbleUltraDeepField2014-20140603.jpg|right|thumb|200px|'''Figure 1'''. NASA Hubble Ultra Deep Field]]

; Awe, the awareness of life, 

Have you ever experienced a moment of awe? A moment that felt totally present, or maybe you were amazed at the vastness of space looking up at the stars. Maybe you saw someone do something good for another person. How did this leave you feeling? Did. 


* Wondering whether I should frame it towards the reader in the second person or direct a scenario to illustrate the after effects. Probably do both. 
* Change picture to relevant awe triggering media such as grand canyon, or night sky etc. Or maybe save these for criteria section later for table or interactive media 


* ''Provide a context that can be revisited when explaining the psychological concepts and research later in the chapter.''
* ''Avoid explaining theory or research in detail— the purpose is to illustrate the problem, not solve it.''
* ''Be presented in a [[#Feature box|feature box]].''
* ''Include a relevant image, with a figure caption, to help illustrate the scenario. Cite the figure (e.g., see Figure 1) within the scenario.''

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

* What is awe as an emotion and experience?
* How does the experience of awe diminish the self?
* What is the effect of a diminished sense of self?
* How can awe be integrated into modern life? i.e. How can we trigger or experience everyday moments of awe?
* How can the experience of awe be applied for social and individual good?{{RoundBoxBottom}}{{RoundBoxTop|theme=1}}
'''QUESTIONS AND NOTES FOR SELF'''

* Where do I fit discussions of the Self in here? {{RoundBoxBottom}}

== Awe ==

=== Vastness ===

==== Physical ====

===== &gt; Other People =====

====== &gt;&gt; Acts of Talent or Skill ======

====== &gt;&gt; Acts of Virtue or Humanness ======
- updating wordview link

===== &gt; Nature =====
- smallness effect link

- See also previous book chapter: [[Motivation and emotion/Book/2026/Awe and nature|Awe and nature]]

- eclipse: seeking connection post link

====== &gt;&gt; Space ======
- smallness effect link 

==== Conceptual ====

===== &gt; Learning =====
- updating wordview link

===== &gt; Religion =====
- smallness effect link 

- seeking connection post link

====== &gt;&gt; Buddhism / Awareness ''(see also)'' ======

===== &gt; The Arts =====

===== &gt; Psychedelics =====
- ego-death 

- oneness (link to buddhism), LINK TO SELF

=== Need for Accommodation ===

==== Smallness ====
- [[wikipedia:Overview_effect|Overview effect]] 

==== Profoundness ====

==== Connectedness ====
- seeking connection after feelings of smallness

===== Mental Structures (Schemas) =====

==== Failures to Accommodate ====

===== Fear =====
- threat-based awe (Keltner and Haidt)

- [[wikipedia:Nihilism|Nihilism]] -&gt; depression 

===== Trauma =====
- dissociation (near death experiences)

- denial
==The Self / Perception ==
- discussion of what the self is 

- introduction of schemas 

- perception 

- ego death dissolving perception, awe experiences diminishing the self 

==Applications==

===Community===

*global meditation bringing down crime rates and violence? need source

===Individual===

==== Therapy / Personal Growth ====

* GESTALT THERAPY
** present moment 
** inner child work

===== Humility ''(Rework heading and how this fits into other sections)'' =====
* presenting more balanced view of personal strengths and weaknesses
* increased acknowledgment of outside forces in one's accomplishments (Stellar et al., 2018)

* epistemic humility = measures of wisdom and moral character 
* positive self-transcendent experiences can be utilised as driving force for better understanding one's decision and perspectives impact others (Kim et al., 2023)

===== Psychedelic Therapies =====

* MDMA therapies for depression 
* LSD and psylocibin guided therapies 


&lt;nowiki&gt;--------------------------------------------------------------------------------------------------------------------------------------------------------------------&lt;/nowiki&gt;

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

'''Table 1''' 

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

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

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

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=&quot;simple&quot;&gt;
{Which of the following is an appraisal of the emotion awe?
|type=&quot;()&quot;}
+ Vastness
- Smallness

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

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

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

==See also==
Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)

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

==References==
{{Hanging indent|1=

Arvidson, P. S. (2022). Reverent Awe and the Field of Consciousness. Human Studies, 45(3), 397-416. 

Bai, Y., Maruskin, L. A., Chen, S., Gordon, A. M., Stellar, J. E., McNeil, G. D., Peng, K., &amp; Keltner, D. (2017). Awe, the diminished self, and collective engagement: Universals and cultural variations in the small self. Journal of personality and social psychology, 113(2), 185. 

Cavallaro, R. M., Church, M. H., Giddens, B. J., &amp; Rivera, G. N. (2025). Complex effects of awe on meaning in life and true self-knowledge. Self and Identity, 24(3), 189-216. 

Chen, S. K., &amp; Mongrain, M. (2021). Awe and the interconnected self. The Journal of Positive Psychology, 16(6), 770-778. 

Edwards, M. E., Mendenhall, K., Sanders, C., &amp; King, L. A. (2026). Small but still significant: Awe and the self. Personality and Social Psychology Bulletin, 52(9), 3032-3045. 

Gao, R. (2026). From awe to pro-environmental behavior-a meta-analysis of the relationship between awe and pro-environmental behavior. The Journal of Positive Psychology, 21(5), 958-970. 

Jiang, T., Hicks, J. A., Yuan, W., Yin, Y., Needy, L., &amp; Vess, M. (2024). The unique nature and psychosocial implications of awe. Nature Reviews Psychology, 3(7), 475-488. 

Jiang, T., &amp; Sedikides, C. (2022). Awe motivates authentic-self pursuit via self-transcendence: Implications for prosociality. Journal of personality and social psychology, 123(3), 576. 

Kim, Y., Nusbaum, H. C., &amp; Yang, F. (2023). Going beyond ourselves: The role of self-transcendent experiences in wisdom. Cognition and Emotion, 37(1), 98-116. 

Li, R., Hou, Z., Zhang, C., Xu, Q., &amp; Nie, A. (2024). A meta-analysis examining the relationship between awe and prosocial behavior. Current Psychology, 43(29), 24702-24711. 

Lucht, A., &amp; van Schie, H. T. (2024). The evolutionary function of awe: A review and integrated model of seven theoretical perspectives. Emotion Review, 16(1), 46-63. 

McMann, G. B. (2025). Role of Vastness and Accommodation of Awe in Personal Change and Growth Grand Canyon University]. 

Perez, K. A., Lench, H. C., Thompson, C. G., &amp; North, S. (2023). Experimental elicitations of awe: A meta-analysis. Cognition and Emotion, 37(1), 18-33. 

Piff, P. K., Dietze, P., Feinberg, M., Stancato, D. M., &amp; Keltner, D. (2015). Awe, the small self, and prosocial behavior. Journal of personality and social psychology, 108(6), 883. 

Piff, P. K., Singhal, I., &amp; Bai, Y. (2025). Bridging me to we: Awe is a conduit to cohesive collectives. Current Opinion in Psychology, 62, 101979. 

Rivera, G. N., Vess, M., Hicks, J. A., &amp; Routledge, C. (2020). Awe and meaning: Elucidating complex effects of awe experiences on meaning in life. European Journal of Social Psychology, 50(2), 392-405. 

Shiota, M. N., Keltner, D., &amp; Mossman, A. (2007). The nature of awe: Elicitors, appraisals, and effects on self-concept. Cognition and Emotion, 21(5), 944-963. 

Shukla, S. (2021). Indian classical music, awe, and healing. The Humanistic Psychologist, 49(3), 355. 

Stellar, J. E., Gordon, A., Anderson, C. L., Piff, P. K., McNeil, G. D., &amp; Keltner, D. (2018). Awe and humility. Journal of personality and social psychology, 114(2), 258. 

Sturm, V. E., Datta, S., Roy, A. R., Sible, I. J., Kosik, E. L., Veziris, C. R., Chow, T. E., Morris, N. A., Neuhaus, J., &amp; Kramer, J. H. (2022). Big smile, small self: Awe walks promote prosocial positive emotions in older adults. Emotion, 22(5), 1044. 

Tanhan, F., DENİZ, M., &amp; Akgün, G. (2022). Awe Therapy: Fundamentals, Formulation and Usage Area Awe Terapi: Temelleri, Formülasyonu ve Kullanım Alanları. Turkish Psychological Counseling and Guidance Journal, 12(65). 

Tanhan, F., Deniz, M. E., &amp; Akgün, G. E. (2022). Awe Therapy: Fundamentals, formulation and usage area. Turkish Psychological Counseling and Guidance Journal, 12(65), 300-319.

}}

==External links==
* [https://self-transcendence.org/theory Self-transendence] (Self-transcendence.org)
* [https://fitmind.org/ Ancient wisdom + modern science] (Fitmind.org)

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

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      <text bytes="25694" sha1="a09fkgnwud69vvqktv22z6vq3cc1rws" xml:space="preserve">{{Bibliography}}
See also [[w:Bibliography of film by genre]], [[w:List of books on films]], [[w:Category:Books about film]] and [[s:Category:Works about film]]

This part of the [[Universal Bibliography]] is a bibliography of cinema.

Bibliography
*George Rehrauer. The Macmillan Film Bibliography. [https://books.google.com/books?id=DmcoAAAAMAAJ]
*Malte Hagener and Michael Töteberg. Film – An International Bibliography. Verlag JB Metzler. 2002. [https://books.google.co.uk/books?id=4r28DQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*James Monaco and Susan Schenker. Books about Film: A Bibliographical Checklist. New York Zoetrope. 1976. [https://books.google.com/books?id=-xzgAAAAMAAJ]
*Jack C Ellis, Charles Derry and Sharon Kern. The Film Book Bibliography, 1940-1975. Scarecrow Press. 1979. [https://books.google.com/books?id=BnWuAAAAIAAJ]
*Robert A Armour. Film: A Reference Guide. 1980. [https://books.google.co.uk/books?id=8X5ZAAAAMAAJ]
*Frank Manchel. Film Study: An Analytical Bibliography. 1990. [https://books.google.co.uk/books?id=BebEAji_wH4C&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 1]. [https://books.google.co.uk/books?id=ID4E3Lm8TsgC&amp;pg=PA953#v=onepage&amp;q&amp;f=false vol 2].
**Film Study: A Resource Guide. Fairleigh Dickinson University Press. 1973. [https://books.google.com/books?id=yzrgAAAAMAAJ]
*The Film Index: A Bibliography. [https://books.google.co.uk/books?id=UM4SAQAAMAAJ]
*Richard Dyer MacCann and Edward S Perry. The New Film Index: A Bibliography of Magazine Articles in English, 1930-1970. E P Dutton and Company. 1975. [https://books.google.com/books?id=FksOAQAAMAAJ] 
*Brian Reis. Australian Film: A Bibliography. Mansell. London and Washington. [https://books.google.co.uk/books?id=IP8PAQAAMAAJ]
*Carl Vincent, Riccardo Redi and Franco Venturini (eds). Bibliografia Generale Del Cinema. [[w:it:Edizioni dell'Ateneo|Edizioni dell'Ateneo]]. Rome. 1953.
**General Bibliography of Motion Pictures. Arno Press. [https://books.google.co.uk/books?id=qv1TAAAAMAAJ]

General
*Magill's Survey of Cinema

Series
*Screen Series. A Zwemmer Limited, London. A S Barnes &amp; Co. New York. (eg Arne Svensson. Japan. 1971. [https://books.google.co.uk/books?id=W4RZAAAAMAAJ])
*World Cinema. Flicks Books. [https://books.google.co.uk/books?id=Im9ZAAAAMAAJ vol 1]. [https://books.google.co.uk/books?id=7TxNAQAAIAAJ vol 2]. [https://books.google.co.uk/books?id=pS9AAQAAIAAJ vol 4]. [https://books.google.co.uk/books?id=AvjoDrhajOcC&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 5]. [https://books.google.co.uk/books?id=yAInAQAAIAAJ]

Periodicals

See also [[w:List of film periodicals]]
*International Index to Film Periodicals. [https://books.google.co.uk/books?id=0axkAAAAMAAJ 1974]. 
*Linda Batty. Retrospective Index to Film Periodicals, 1930-1971. R R Bowker Company. [https://books.google.co.uk/books?id=kcsUAQAAIAAJ]
*East-West Film Journal [https://books.google.co.uk/books?id=3T8bAQAAIAAJ] (began December 1986)

Annuals
*Magill's Cinema Annual. [https://books.google.co.uk/books?id=LXAsctC3wasC 1983] (1982 films). [https://books.google.co.uk/books?id=V5XSO0pJmUUC 1986] (1985 films).
*Picturegoer Film Annual. [https://books.google.co.uk/books?id=yhM6AQAAIAAJ for 1950-1951]. 
*The Motion Picture Annual. [https://books.google.co.uk/books?id=UhUIAQAAMAAJ 1989].
*Boy's Cinema Annual. Amalgamated Press. [https://books.google.co.uk/books?id=QVfych4dj54C 1939].
*International Film Annual [https://books.google.co.uk/books?id=D4I3AAAAIAAJ No 3]
*The British Film Annual. Winchester Publications. [https://books.google.co.uk/books?id=QSMPAQAAMAAJ 1949].
*The Western Film Annual [https://books.google.co.uk/books?id=_kwoXXrpJU4C]

Yearbooks
*Film Daily Year Book of Motion Pictures. [https://books.google.co.uk/books?id=qJMHAQAAIAAJ 1969].

Years
*Edgar Anstey, &quot;The Cinema&quot; (1944) 172 The Spectator 10 (No 6028: 7 January 1944). Includes &quot;Review of the Year&quot;.

History
*Arthur F McClure. Research Guide to Film History. R &amp; E Publishers. 1983. [https://books.google.co.uk/books?id=iYcjAQAAIAAJ]

Film reviews
*Film Review Index. Oryx Press.
**Volume 1: 1882-1949 [https://books.google.co.uk/books?id=EDngAAAAMAAJ]
*Index to Critical Film Reviews in British and American Film Periodicals. Burt Franklin &amp; Co. [https://books.google.co.uk/books?id=fM0UAQAAIAAJ]
*The New York Times Film Reviews [https://books.google.co.uk/books?id=_E350jJ-Ui4C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*[[w:Variety Film Reviews|Variety's Film Reviews]] [https://books.google.co.uk/books?id=62xZAAAAMAAJ]
*Landers Film Reviews [https://books.google.co.uk/books?id=7d3jAAAAMAAJ]
*[[w:Harrison's Reports and Film Reviews|Harrison's Reports and Film Reviews]] [https://books.google.co.uk/books?id=FFSDzDveXHgC]

Writing
*Timothy Corrigan. A Short Guide to Writing about Film. 2004. [https://books.google.co.uk/books?id=er8qAQAAIAAJ] 

Reading
*James Monaco. How to Read a Film: The Art, Technology, Language, History, and Theory of Film and Media. 1981. [https://books.google.co.uk/books?id=inRZAAAAMAAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

World and national
*Kevin Rockett and John Hill. National Cinemas and World Cinema. 2006. [https://books.google.co.uk/books?id=pudkAAAAMAAJ]

World
*Elkan Allan (comp). A Guide to World Cinema. Whittet Books. 1985. [https://books.google.co.uk/books?id=nb8dAAAAMAAJ]
*Rob Stone, Paul Cooke, Stephanie Dennison and Alex Marlow-Mann (eds). The Routledge Companion to World Cinema. [https://books.google.co.uk/books?id=DnE3DwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Geoffrey Nowell-Smith. The Oxford History of World Cinema. 1996. Paperback. 1997. [https://books.google.co.uk/books?id=MZwVDAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*David Robinson. World Cinema: A Short History. Eyre Methuen. 1973. [https://books.google.co.uk/books?id=EH9ZAAAAMAAJ]
*William Luhr (ed). World Cinema Since 1945. Ungar. New York. 1987. [https://books.google.co.uk/books?id=6gAqAAAAYAAJ]
*James Chapman. Cinemas of the World: Film and Society from 1895 to the Present. 2003. [https://books.google.co.uk/books?id=SMYo4Abel2EC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Linda Badley (ed). Traditions in World Cinema. 2006. [https://books.google.co.uk/books?id=tpYkDQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Kate Gamm. Teaching World Cinema. British Film Institute. 2004. [https://books.google.co.uk/books?id=PmJZAAAAMAAJ]
*Shekhar Deshpande and Meta Mazaj. World Cinema: A Critical Introduction. 2018. [https://books.google.co.uk/books?id=qFFHDwAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*John Hill and Pamela Church Gibson. World Cinema: Critical Approaches. 2000. [https://books.google.co.uk/books?id=SUKcAQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Lúcia Nagib, Chris Perriam and Rajinder Dudrah (eds). Theorizing World Cinema. 2012. [https://books.google.co.uk/books?id=cgNQEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

British and foreign
*Jerry Vermilye (ed). 500 Best British and Foreign Films to Buy, Rent, Or Videotape. William Morrow. New York. 1988. [https://books.google.co.uk/books?id=91NZAAAAMAAJ]

Foreign
*Foreign Films: A Guide to Nearly 500 Films on Videocassette by Foreign Directors. CineBooks. 1989. [https://books.google.co.uk/books?id=NrtZAAAAYAAJ]
*James Reid Paris. Classic Foreign Films: From 1960 to Today. Carol Publishing Group. 1993. [https://books.google.co.uk/books?id=PAQIAQAAMAAJ]
*Michael F Mayer. Foreign Films on American Screens. Arco. 1965. [https://books.google.co.uk/books?id=-2ZZAAAAMAAJ]
*Kerry Segrave. Foreign Films in America: A History. 2004. [https://books.google.co.uk/books?id=LVVp0omSDBIC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Foreign language
*Foreign Language Films. (Magill's Survey of Cinema). [https://books.google.co.uk/books?id=33xZAAAAMAAJ vol 1].
*Foreign Language Films. Visual Aids Service. Division of University Extension. University of Illinois. [https://books.google.co.uk/books?id=T_5PAQAAMAAJ 1964-1966]. [https://books.google.co.uk/books?id=Tv5PAQAAMAAJ 1970-1973].
*Michael S Barrett. Foreign Language Films and the Oscar: The Nominees and Winners, 1948-2017. McFarland &amp; Company. 2018. [https://books.google.co.uk/books?id=P5NoDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Bibliography of Asian cinema
*John A Lent. &quot;Asian Cinema: A Selected International Bibliography&quot;. [https://books.google.co.uk/books?id=05RIAQAAIAAJ]
**&quot;Part I: East Asia, Featuring Japan&quot; (1984) 36 Journal of Film and Video 75 (No 3: Summer 1984). &quot;Japan&quot; is at p 81.
**&quot;Part II: Southeast and South Asia, plus Taiwan and Korea&quot; (1985) 37 Journal of Film and Video 76 (No 3: Spring 1985)

Asian
*Tom Vick. Asian Cinema: A Field Guide. HarperCollins. [https://books.google.co.uk/books?id=YpIaAQAAIAAJ]
*Aaron Han Joon Magnan-Park, Gina Marchetti and See Kam Tan (eds). The Palgrave Handbook of Asian Cinema. 2018. [https://books.google.co.uk/books?id=MQ92DwAAQBAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]
*Zhen Zhang, Sangjoon Lee, Debashree Mukherjee and Intan Paramaditha (eds). The Routledge Companion to Asian Cinemas. 2024. [https://books.google.co.uk/books?id=bwYDEQAAQBAJ&amp;pg=PA1995#v=onepage&amp;q&amp;f=false]
*Dimitris Eleftheriotis and Gary Needham. Asian Cinemas: A Reader and Guide. 2006. [https://books.google.co.uk/books?id=tPqgEQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Olivia Khoo. Asian Cinema: A Regional View. 2021. [https://books.google.co.uk/books?id=vvCgEQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Stephen Teo. The Asian Cinema Experience: Styles, spaces, theory. Routledge. 2013. [https://books.google.co.uk/books?id=2sHZz-XUR2oC#v=onepage&amp;q&amp;f=false]
*John A Lent. The Asian Film Industry. University of Texas Press. 1990. [https://books.google.co.uk/books?id=JkkqAAAAYAAJ]
*Yau Shuk-ting and Kinnia (eds). East Asian Cinema and Cultural Heritage: From China, Hong Kong, Taiwan to Japan and South Korea. 2011. [https://books.google.co.uk/books?id=UeLHAAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Routledge Handbook of South Asian Cinemas. 2026. [https://books.google.co.uk/books?id=QEyWEQAAQBAJ&amp;pg=PA6#v=onepage&amp;q&amp;f=false]
*Jose F Lacaba (ed). The Films of ASEAN. 2000. [https://books.google.co.uk/books?id=DI6dq64VNDkC]

Periodicals, Asian cinema
*Asian Cinema [https://books.google.co.uk/books?id=W4saAQAAIAAJ]
*[[w:Cinemaya|Cinemaya]] [https://books.google.co.uk/books?id=3pMHAQAAIAAJ]
*South Asian Cinema [https://books.google.co.uk/books?id=0eVkAAAAMAAJ] (began February 2001)

Annuals, Asian cinema
*Asian Film Directory &amp; Who's Who. [https://books.google.co.uk/books?id=0wY6AQAAIAAJ 1952]

India

Hindi

See [[w:Bibliography of Hindi cinema]]

Japanese and Korean
*Justin Bowyer. The Cinema of Japan &amp; Korea. 2004. [https://books.google.co.uk/books?id=FtqUAxsisk0C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Kate E Taylor-Jones. Rising Sun, Divided Land: Japanese and South Korean Filmmakers. 2013. [https://books.google.co.uk/books?id=SfaEAAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Periodicals, Japanese and Korean
*Journal of Japanese and Korean Cinema [https://www.tandfonline.com/journals/rjkc20]

==Japanese==
*Arne Svensson. Japan. (Screen Series). A Zwemmer Limited, London. A S Barnes &amp; Co. New York. 1971. [https://books.google.co.uk/books?id=W4RZAAAAMAAJ]
*Daisuke Miyao (ed). The Oxford Handbook of Japanese Cinema. 2014. [https://books.google.co.uk/books?id=XXD1AQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Joanne Bernardi, Shota T Ogawa (eds). Routledge Handbook of Japanese Cinema. 2021. [https://books.google.co.uk/books?id=xkX1DwAAQBAJ&amp;pg=PA1931#v=onepage&amp;q&amp;f=false]
*Thomas Weisser and Yuko Mihara Weisser. Japanese Cinema: The Essential Handbook. [https://books.google.com/books?id=IrZcSAAACAAJ]
*David Desser. A Companion to Japanese Cinema. 2022. [https://books.google.co.uk/books?id=YWl6EAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Hideaki Fujiki and Alastair Phillips (eds). The Japanese Cinema Book. Bloomsbury, for British Film Institute. 2020. [https://books.google.co.uk/books?id=Zu3cDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Stuart Galbraith and Paul Duncan. Japanese Cinema. Taschen. 2009. ISBN 9783822831564. [https://books.google.co.uk/books?id=rDkFKAAACAAJ]. Catalogue: [https://catalogue.nla.gov.au/catalog/4701384]
*&quot;Japanese Cinema&quot;. Pam Cook (ed). The Cinema Book. British Film Institute. 1985. 3rd Ed: 2007. [https://books.google.co.uk/books?id=TTr8DwAAQBAJ&amp;pg=PA238#v=onepage&amp;q&amp;f=false p 238].
*Martha P Nochimson. &quot;Japan: Screening Feudalism and Modernism&quot;. World on Film: An Introduction. Chapter 5. [https://books.google.co.uk/books?id=DXK5gkQwAs8C&amp;pg=PA195#v=onepage&amp;q&amp;f=false p 195].
*Donald Richie. Japanese Cinema: An Introduction. Oxford University Press.  Oxford and New York. 1990. [https://books.google.co.uk/books?id=k4lZAAAAMAAJ]. Review: Cinemaya [https://books.google.co.uk/books?id=7ZEHAQAAIAAJ]
*Marie Seton, &quot;Japanese Cinema&quot; (1958) [https://books.google.co.uk/books?id=Y5WQS46o0a4C 1] The Living Cinema 189 (No 4: Spring 1958)
*Donald Richie. Japanese Cinema: Film Style and National Character. 1971. [https://books.google.com/books?id=0YlZAAAAMAAJ]
*Joan Mellen. The Waves at Genji's Door: Japan Through Its Cinema. Pantheon Books. 1976. [https://books.google.co.uk/books?id=alC0AAAAIAAJ]
*Joseph L Anderson and Donald Richie. The Japanese Film: Art and Industry. Tuttle. 1959. Evergreen. 1960. Expanded Edition. Princeton University Press. 1982. [https://books.google.co.uk/books?id=C2z3otM-y5kC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Stuart Galbraith IV. The Japanese Filmography: A Complete Reference to 209 Filmmakers and the Over 1250 Films Released in the United States, 1900 through 1994. 1996. [https://books.google.co.uk/books?id=GLxlEQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*John Berra (ed). Directory of World Cinema: Japan. 2010. [https://books.google.co.uk/books?id=tQHsEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
**Directory of World Cinema: Japan 3. 2015. [https://books.google.co.uk/books?id=9QLsEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Abé Markus Nornes and Aaron Gerow. Research Guide to Japanese Film Studies. 2009. [https://books.google.co.uk/books?id=5UONCwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Keiko I McDonald. Reading a Japanese Film: Cinema in Context. 2006. [https://books.google.co.uk/books?id=ICqSfjUqIpMC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

*David Bordwell, &quot;Our Dream Cinema: Western Historiography and the Japanese Film&quot; (1979) Film Reader, [https://books.google.co.uk/books?id=bp-RAAAAIAAJ No 4], p 45.

*Mitsuyo Wada-Marciano. Japanese Cinema in the Digital Age. 2012. [https://books.google.co.uk/books?id=3F4EEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

*Arthur Nolletti and David Desser. Reframing Japanese Cinema: Authorship, Genre, History. Indiana University Press. 1992. [https://books.google.co.uk/books?id=6Q1jAAAAMAAJ]
*Laura Lee. Japanese Cinema Between Frames. 2017. [https://books.google.co.uk/books?id=c8I9DwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Noel Burch. To the Distant Observer: Form and Meaning in the Japanese Cinema. 1979. [https://books.google.co.uk/books?id=lLtyz275-GYC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Dennis Washburn and Carole Cavanaugh (eds). Word and Image in Japanese Cinema. 2001. [https://books.google.co.uk/books?id=CwZ6SPpmJwQC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Daisuke Miyao. The Aesthetics of Shadow: Lighting and Japanese Cinema. 2013. [https://books.google.co.uk/books?id=80K2AgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Justin Vicari. Japanese Film and the Floating Mind: Cinematic Contemplations of Being. 2016. [https://books.google.co.uk/books?id=CYuwDAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Keiko I McDonald. Cinema East: A Critical Study of Major Japanese Films. Fairleigh Dickinson University Press. Associated University Presses. 1983. [https://books.google.co.uk/books?id=ywxjAAAAMAAJ]
*Alastair Phillips and Julian Stringer. Japanese Cinema: Texts and Contexts. 2007. [https://books.google.co.uk/books?id=53xRa5dwUOUC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Darrell William Davis. Picturing Japaneseness: Monumental Style, National Identity, Japanese Film. Columbia University Press. 1996. ISBN 0-231-10231-3. Review: [https://www.cambridge.org/core/journals/journal-of-asian-studies/article/abs/picturing-japaneseness-monumental-style-national-identity-japanese-film-by-darrell-william-davis-new-york-columbia-university-press-1996-viii-304-pp-1750/7CC73AD51C9A06CA40DF3463CC9D3E7D]
*Barbara Wolf. The Japanese Film. Audio Brandon Films. Mount Vernon, NY. 1976. [https://books.google.co.uk/books?id=qo3SAAAAMAAJ]

Bibliography
*Nornes and Gerow. &quot;Annotated Bibliography for Bibliographic Studies&quot;. Research Guide to Japanese Film Studies. Chapter 4. [https://books.google.co.uk/books?id=5UONCwAAQBAJ&amp;pg=PA72#v=onepage&amp;q&amp;f=false p 72].

Reference
*[https://guides.library.yale.edu/c.php?g=295932&amp;p=1973050 Japanese Reference Materials for Studying Japanese Cinema at Yale University]. Yale Library.

Periodicals

See also [[w:ja:Category:日本の映画雑誌]]. [映画雑誌 = film magazine] [映画機関誌 = film journal]
*Honchi Haruhiko (Japanese: 本地陽彦). Nihon Eiga Zasshi Taitoru Soran (Japanese: 日本映画雑誌タイトル総覧). [[w:ja:ワイズ出版|Waizu Shuppan]]. Tokyo. 2003. [https://books.google.co.uk/books?id=kskvAQAAIAAJ]. Commentary: Research Guide to Japanese Film Studies, [https://books.google.co.uk/books?id=5UONCwAAQBAJ&amp;pg=PA83#v=onepage&amp;q&amp;f=false p 83].
*[https://www.nfaj.go.jp/exhibition/filmmagazines/ 映画雑誌の秘かな愉しみ The Discreet Charm of Film Magazines]. National Film Archive of Japan (NFAJ).
*[https://guides.library.yale.edu/c.php?g=295932&amp;p=1973061 Japanese Reference Materials for Studying Japanese Cinema at Yale University: Film Periodicals]. Yale Library.
*[[w:en:Kinema Junpo|Kinema Junpo]] (Japanese: キネマ旬報) (The Movie Times) [https://books.google.co.uk/books?id=UFKtYBwc5ioC]
*[[w:en:UniJapan Film Quarterly|UniJapan Film Quarterly]] [https://books.google.co.uk/books?id=QIY3AAAAIAAJ]. Catalogue: [https://ci.nii.ac.jp/ncid/AA12490478]

Annuals and year books
*Japanese Films. UniJapan Film. [https://books.google.co.uk/books?id=4LAaAQAAIAAJ 1960]
**Japanese Film [https://books.google.co.uk/books?id=iJUHAQAAIAAJ 1983] [https://books.google.co.uk/books?id=fpYHAQAAIAAJ]
*Cinema Year Book of Japan. [https://books.google.co.uk/books?id=r7W9DZnBbBwC 1938].

History
*Jasper Sharp. Historical Dictionary of Japanese Cinema. 2011. [https://books.google.co.uk/books?id=YQR4EQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Isolde Standish. A New History of Japanese Cinema: A Century of Narrative Film. 2006. [https://books.google.co.uk/books?id=GZxUv4g_icQC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Donald Ritchie. A Hundred Years of Japanese Film: A Concise History, with a Selective Guide to DVDs and Videos. 2001. 2005. [https://books.google.co.uk/books?id=s7-_Gon5-a0C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Yomota Inuhiko. What Is Japanese Cinema? A History. 2014. 2019. [https://books.google.co.uk/books?id=8Il-DwAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*Gerald Mast and Bruce F Kawin. &quot;Japan&quot; in &quot;Cinemas East&quot;. A Short History of the Movies. Allyn and Bacon. 7th Ed: 2000: [https://books.google.co.uk/books?id=AC0IAQAAMAAJ]. pp 403 to 417.
*Aaron Gerow. &quot;From Misemono to Zigomar: A Discursive History of Early Japanese Cinema&quot;. Bean, Kapse and Horak (eds). Silent Cinema and the Politics of Space. 2014. Chapter 6. [https://books.google.co.uk/books?id=7poiAwAAQBAJ&amp;pg=PA157#v=onepage&amp;q&amp;f=false p 157].

20th century
*Beverley Bare Buehrer. Japanese Films: A Filmography and Commentary, 1921-1989. McFarland &amp; Company. 1990. [https://books.google.co.uk/books?id=N6RZAAAAMAAJ]
*Aristides Gazetas. &quot;Post-War Japanese Cinema: 1950-1990&quot;. An Introduction to World Cinema. 2nd Ed. 2008. Chapter 13. [https://books.google.co.uk/books?id=CPuZ-2UtVRwC&amp;pg=PA169#v=onepage&amp;q&amp;f=false p 169].
*Japanese Experimental Film, 1960-1980. American Federation of Arts. [https://books.google.co.uk/books?id=XGUbAQAAIAAJ]
*Yuriko Furuhata. Cinema of Actuality: Japanese Avant-Garde Filmmaking in the Season of Image Politics. 2013. [https://books.google.co.uk/books?id=sDi2AgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false] [covers 1960s and 1970s].
*Outlaw Masters of Japanese Film. 2005. [https://books.google.co.uk/books?id=MbaKDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false] [covers 1950s to 1970s]
*Japanese Cinema: From Kurosawa To Tora-San&quot; (1986) Information Bulletin, February 1986, p 15 [https://books.google.co.uk/books?id=Sw5PAQAAIAAJ]
*Catherine Russell. Classical Japanese Cinema Revisited. 2011. [https://books.google.co.uk/books?id=uv9GAQAAQBAJ&amp;pg=PR4#v=onepage&amp;q&amp;f=false] [covers roughly 1930 to 1960]
*Kyoko Hirano. Mr. Smith Goes to Tokyo: Japanese Cinema Under the American Occupation, 1945-1952. 1992. [https://books.google.co.uk/books?id=6OsKAQAAMAAJ]
*Peter B High. The Imperial Screen: Japanese Film Culture in the Fifteen Years' War, 1931-1945. 2003. [https://books.google.co.uk/books?id=6XiA9DOuvjAC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Naoki Yamamoto. Dialectics without Synthesis: Japanese Film Theory and Realism in a Global Frame. 2020. [https://books.google.co.uk/books?id=lEnrDwAAQBAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false] [Covers 1910s to 1950s].
*Sean O'Reilly (ed). The Advent of Sound in Japanese Cinema: A Handbook. 2025. [https://books.google.co.uk/books?id=vAKbEQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false] [covers the 1930s]
*Mitsuyo Wada-Marciano. Nippon Modern: Japanese Cinema of the 1920s and 1930s. 2008. [https://books.google.co.uk/books?id=dIc0RBYMs9kC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Iwamoto Kenji, &quot;Japanese Cinema Until 1930: A Consideration of its Formal Aspects&quot;. Iris: A Journal of Theory on Image and Sound. No 16, p 9 [https://books.google.co.uk/books?id=zXFhCc7ENAEC]
*David Bordwell, &quot;Visual Style in Japanese Cinema, 1925-1945&quot; (1995) [https://books.google.co.uk/books?id=YqIqAQAAIAAJ 7] Film History 5 to 31 (No 1: Spring 1995)
*Sean D O'Reilly. Re-Viewing the Past: The Uses of History in the Cinema of Imperial Japan. 2018. Paperback Ed: 2020. [https://books.google.co.uk/books?id=fqFiDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

New, contemporary
*Mark Schilling. Contemporary Japanese Film. 1999. [https://books.google.co.uk/books?id=LNQ4EAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Kawamoto Saburo. New Trends in Japanese Cinema. (Orientation Seminars on Japan, No 21). The Japan Foundation, Office for the Japanese Studies Center. [https://books.google.co.uk/books?id=R5IqAQAAIAAJ]
*Tadao Sato. Currents in Japanese Cinema. Kodansha International. 1982. [https://books.google.com/books?id=p-9kAAAAMAAJ]

Genres
*Abe Mark Nornes. Japanese Documentary Film: The Meiji Era Through Hiroshima. 2003. [https://books.google.co.uk/books?id=2JFrwF2LMw4C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*S A Thornton. The Japanese Period Film: A Critical Analysis. 2008. [https://books.google.co.uk/books?id=yhPo95wPz8QC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Alain Silver. The Samurai Film. 1977: [https://books.google.co.uk/books?id=R4BZAAAAMAAJ]. The Overlook Press. 1983: [https://books.google.co.uk/books?id=AH1ZAAAAMAAJ]
*David Desser. The Samurai Films of Akira Kurosawa. UMI Research Press. [https://books.google.com/books?id=AaJZAAAAMAAJ]
*Silver Screen Samurai: The Best of Japan's Samurai Movie Posters. 2004. [https://books.google.co.uk/books?id=tdsuoae7X68C&amp;pg=PA2#v=onepage&amp;q&amp;f=false]
*Stuart Galbraith IV. Japanese Science Fiction, Fantasy and Horror Films. Macfarland. 1994. [https://books.google.co.uk/books?id=2XZREQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Thomas Weisser and Yuko Mihara Weisser. Japanese Cinema Encyclopedia: The Horror, Fantasy, and SciFi films. Vital Books. 1997. [https://books.google.com/books?id=HGSybwAACAAJ]
*Jay McRoy. Japanese Horror Cinema. University of Hawaii Press. Edinburgh University Press. 2005. [https://books.google.co.uk/books?id=XvOgEQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false] Review: Timothy Iles (2007) [https://books.google.co.uk/books?id=rt9KAQAAIAAJ 33] The Journal of Japanese Studies 264
*Colette Balmain. Introduction to Japanese Horror Film. 2008. [https://books.google.co.uk/books?id=POWqBgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Michael Crandol. Ghost in the Well: The Hidden History of Horror Films in Japan. 2021. [https://books.google.co.uk/books?id=mDgfEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Peter C Pugsley. Japanese High School Films: Iconography, Nostalgia and Discipline. 2022. [https://books.google.co.uk/books?id=jPOgEQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Peter C Pugsley. Beyond the High School Film: Reaching Adulthood in Everyday Japanese Cinema. 2026. [https://books.google.co.uk/books?id=7boEEgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Cult
*Patrick Macias. Tokyoscope: The Japanese Cult Film Companion. 2001. [https://books.google.co.uk/books?id=g-0HAQAAMAAJ]

Directors
*Alexander Jacoby. A Critical Handbook of Japanese Film Directors: From the Silent Era to the Present Day. 2008. [https://books.google.co.uk/books?id=RhWNAgAAQBAJ&amp;pg=PA1870#v=onepage&amp;q&amp;f=false]
*Audie Bock. Japanese Film Directors. 1978. Paperback Ed. Kodansha International. 1985. [https://books.google.co.uk/books?id=A6EqAAAAYAAJ]
*Mitsuhiro Yoshimoto. Kurosawa: Film Studies and Japanese Cinema. 2000. [https://books.google.co.uk/books?id=QizaCOjKs-IC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Stars
*Hideaki Fujiki. Making Personas: Transnational Film Stardom in Modern Japan. 2013. [https://books.google.co.uk/books?id=A_gFEAAAQBAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false]

Studios
*Stuart Galbraith IV. The Toho Studios Story: A History and Complete Filmography. 2008. [https://books.google.co.uk/books?id=f7o8pq6G_dYC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Interviews
*Joan Mellen. Voices from the Japanese Cinema. Liveright. New York. 1975. ISBN 0871406047. [https://search.worldcat.org/title/Voices-from-the-Japanese-cinema/oclc/1245912150]

V-Cinema
*Tom Mes. Japanese Film and the Challenge of Video. 2023. [https://books.google.co.uk/books?id=70i7EAAAQBAJ&amp;pg=PA1921#v=onepage&amp;q&amp;f=false]

Film criticism
*Scott Nygren. Time Frames: Japanese Cinema And the Unfolding of History. [https://books.google.co.uk/books?id=PvlgQgAACAAJ]

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  <page>
    <title>Universal Bibliography/Culture</title>
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See [[s:Category:Culture]].

This part of the [[Universal Bibliography]] is a bibliography of culture.

*Terry Eagleton. Culture. Yale University Press. 2016. [https://books.google.co.uk/books?id=z2EdDAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Ben Highmore. Culture. Routledge. 2016. [https://books.google.co.uk/books?id=2teoCgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Chris Jenks. Culture. Routledge. 1993. [https://books.google.co.uk/books?id=6Litru5-ImAC&amp;pg=PP1#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=VcGHAgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Chris Jenks (ed). Culture: Critical Concepts in Sociology. 2003. [https://books.google.co.uk/books?id=VIEbAQAAMAAJ vol 1]. [https://books.google.co.uk/books?id=iIvSvY7HWv8C&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 2]. [https://books.google.co.uk/books?id=ZF1Hk2HytAoC&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 3].
*Craig Calhoun (ed). Culture. (Comparative Social Research: A Research Annual, Volume 11: 1989). JAI Press. 1989. [https://books.google.co.uk/books?id=qvpWAAAAYAAJ]

*Crane. The Production of Culture: Media and the Urban Arts. (Foundations of Popular Culture, vol 1). SAGE Publications. 1992. [https://books.google.co.uk/books?id=DGs5DQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Richard A Peterson. The Production of Culture. (SAGE Contemporary Social Science Issues 33). SAGE Publications. 1976. [https://books.google.co.uk/books?id=DILWAAAAMAAJ].
*Calhoun and Sennett. Practicing Culture. 2007. [https://books.google.co.uk/books?id=NbO4CDIWhn4C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Mead. The Study of Culture at a Distance. 1953. 2000. [https://books.google.co.uk/books?id=5Upv9RZfPe8C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Measuring Culture. Columbia University Press. 2020. [https://books.google.co.uk/books?id=0se_DwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

*Zygmunt Bauman. Culture as Praxis. 1973. Sage. 1999. [https://books.google.co.uk/books?id=7yqa0-s6N24C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Industries
*David Hesmondhalgh. The Cultural Industries. 2nd Ed: 2007. [https://books.google.co.uk/books?id=Tw31nFmGbLgC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Kate Oakley and Justin O'Connor (eds). The Routledge Companion to the Cultural Industries. 2015. [https://books.google.co.uk/books?id=FkisCQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Andrew Beck. Cultural Work: Understanding the Cultural Industries. 2003. [https://books.google.co.uk/books?id=XFuBAgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Industries and production
*Power and Scott. Cultural Industries and the Production of Culture. 2004.  [https://books.google.co.uk/books?id=Pnx_AgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Material culture
*Thomas J Schlereth (ed). Material Culture: A Research Guide. University Press of Kansas. 1985. [https://books.google.co.uk/books?id=Ig9PAAAAMAAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Robert DuPlessis. Material Culture. (Oxford Bibliographies Online Research Guide). 2010. [https://books.google.co.uk/books?id=Y-p4acTurWQC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Popular culture
*Kornhaber. [https://www.theatlantic.com/magazine/archive/2025/06/american-pop-culture-decline/682578/ Is This the Worst-Ever Era of American Pop Culture?]. The Atlantic. 5 May 2025. (June 2025 issue).

Asian
*Carolyn Brown Heinz. Asian Cultural Traditions. 1999: [https://books.google.co.uk/books?id=Ix0XAQAAIAAJ]. Carolyn Brown Heinz and Jeremy A Murray. 2nd Ed: 2019: [https://books.google.co.uk/books?id=n9tdDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false].

Periodicals, Asian
*Asian Culture Quarterly. Asian Cultural Center, Taipei [https://books.google.co.uk/books?id=4PYtAQAAIAAJ]
*Asian Culture: A Quarterly Review. Vietnamese Association for Asian Cultural Relations (Hội Việt Nam Nghiên Cứu Liên Lạc Văn Hoá Á Châu). [https://books.google.co.uk/books?id=g9YbAAAAMAAJ]
*Journal of Asian Culture. Graduate Students in Asian Studies at UCLA. [https://books.google.co.uk/books?id=-HBtAAAAMAAJ]

Asian popular culture
*Anthony YH Fung (ed). Asian Popular Culture: The Global (Dis)continuity. 2013. [https://books.google.co.uk/books?id=Htqw-BHJlnwC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Lorna Fitzsimmons and John A Lent (eds). Asian Popular Culture in Transition. (Routledge Contemporary Asia Series). 2013. [https://books.google.co.uk/books?id=UMZ7eH6dDxkC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*John A Lent and Lorna Fitzsimmons (eds). Asian Popular Culture: New, Hybrid, and Alternate Media. Lexington Books. 2013. [https://books.google.co.uk/books?id=tG6AEQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Yeojin Kim, Dharshani Lakmali Jayasinghe, Hiba Aleem and Karen A Ritzenhoff (eds). Contemporary Asian Popular Culture. Palgrave Macmillan. [https://books.google.co.uk/books?id=G0g9EQAAQBAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false vol 1]. [https://books.google.co.uk/books?id=fZo3EQAAQBAJ&amp;pg=PR1#v=onepage&amp;q&amp;f=false vol 2].

East Asian
*Xiaobing Tang and Stephen Snyder (eds). In Pursuit Of Contemporary East Asian Culture. [https://books.google.co.uk/books?id=dXekDwAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]

Popular culture
*Koichi Iwabuchi, Eva Tsai and Chris Berry (eds). Routledge Handbook of East Asian Popular Culture. 2017. [https://books.google.co.uk/books?id=lCMlDwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false] 
*Seok-Kyeong Hong and Dal Yong Jin (eds). Transnational Convergence of East Asian Pop Culture. 2021. [https://books.google.co.uk/books?id=hbsTEAAAQBAJ&amp;pg=PA2000#v=onepage&amp;q&amp;f=false]

Periodicals
*East Asian Cultural Studies. The Centre for East Asian Cultural Studies, Tokyo. [https://books.google.co.uk/books?id=4OTUAAAAMAAJ]

==Japanese==
*Paul Varley. Japanese Culture. 1984. 4th Ed: 2000: [https://books.google.co.uk/books?id=BvUEzBin61AC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. 
**Japanese Culture: A Short History. 1973. 1977. [https://books.google.co.uk/books?id=bas6AAAAMAAJ]
*Ruth Benedict. The Chrysanthemum and the Sword: Patterns of Japanese Culture. 1946. A Mariner Book. 2005. [https://books.google.co.uk/books?id=R7NpvfYsmU0C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Robert J Smith and Richard K Beardsley (eds). Japanese Culture: Its Development and Characteristics. 1963. [https://books.google.co.uk/books?id=gZFkfPrNErEC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Eiichiro Ishida. Japanese Culture: A Study of Origins and Characteristics. (Translated by Teruko Kachi). 1974. [https://books.google.com/books?id=gztxAAAAMAAJ]
*Pictorial Encyclopedia of Japanese Culture: The Soul and Heritage of Japan. Gakken. 1987. [https://books.google.com/books?id=cNomAQAAMAAJ]
*Setsuko Kojima and Gene A Crane. A Dictionary of Japanese Culture. Chopmen Publishers. [https://books.google.co.uk/books?id=ms_rAAAAMAAJ]
*Joseph Roggendorf (ed). Studies in Japanese Culture. Sophia University. Tokyo. 1963. [https://books.google.co.uk/books?id=VnBwAAAAMAAJ]
**Joseph Roggendorf (ed). Studies in Japanese Culture: Tradition and Experiment. Sophia University. Tokyo. 2nd Ed. 2nd printing. 1965. [https://books.google.co.uk/books?id=GHJwAAAAMAAJ]
*Studies in Japanese Culture. University of Michigan Press. [https://books.google.co.uk/books?id=kxAOAQAAMAAJ]
*Murakami Hyôe and Edward G Seidensticker (eds). Guides to Japanese Culture. Japan Culture Institute. 1977. ISBN 0-87040-403-2 [https://books.google.co.uk/books?id=xiQhhOvtVJEC]
*Chikio Hayashi and Yasumasa Kuroda. Japanese Culture in Comparative Perspective. Praeger. Westport, Connecticut. 1997.  [https://books.google.com/books?id=tTzDEAAAQBAJ]
*Donald H Shively (ed). Tradition and Modernization in Japanese Culture. Princeton University Press. 1971. Paperback. 1976. [https://books.google.co.uk/books?id=MnN9BgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Introduction
*Daniel Sosnoski. Introduction to Japanese Culture. Tuttle. 1996. [https://books.google.co.uk/books?id=kJ3TAgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*T Smibert and C Burns. Art, Nature and Life: An Introduction to Japanese Culture. Educational Media Australia. Melbourne. 1979. Bibliography: [https://books.google.co.uk/books?id=tbYlAQAAIAAJ].

Cultural history
*Shunsuke Tsurumi. A Cultural History of Postwar Japan 1945-1980. Iwanami Shoten. Tokyo. 1984.  Kegan Paul International. 1987. Routledge. 2009. [https://books.google.co.uk/books?id=6HYsBgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*GB Sansom. Japan: A Short Cultural History. 1931. Revised Ed. [https://books.google.co.uk/books?id=ZOpkCwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*John Dougill. Kyoto: A Cultural History. (Cityscapes). Oxford University Press. 2006. [https://books.google.co.uk/books?id=rhMTDAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Nippon No Bunka

[日本の文化 = Nippon No Bunka = Nihon No Bunka = Japanese culture]
*Genshoku Nihon No Bunka (Japanese: 原色日本の文化). Shogakukan (小学館). 1968. [https://books.google.co.uk/books?id=FKwdAQAAMAAJ]. Catalogue: [https://ci.nii.ac.jp/ncid/BN15289454].
*日本文化提要 - Guides to Japanese Culture. 日本文化研究所編集局. 1977. [https://books.google.co.uk/books?id=8noNAQAAMAAJ] [https://books.google.co.uk/books?id=hXcEAAAAMAAJ]. Catalogue: [https://ci.nii.ac.jp/ncid/BN02209055].

Contemporary
*Sandra Buckley. The Encyclopedia of Contemporary Japanese Culture. Routledge. 2002. [https://books.google.co.uk/books?id=3ZKFAgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false] [https://books.google.co.uk/books?id=Wtkm3O3nWXkC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Roger J Davies and Osamu Ikeno (eds). Japanese Mind: Understanding Contemporary Japanese Culture. Tuttle Publishing. 2002. [https://books.google.co.uk/books?id=rADRAgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Modern
*Yoshio Sugimoto. The Cambridge Companion to Modern Japanese Culture. (Cambridge Companions to Culture). 2009. ISBN 9780521880473. [https://books.google.co.uk/books?id=s80AAwAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*Leith Morton. Modern Japanese Culture: The Insider View. Oxford University Press. 2003. ISBN 0195540891. [https://books.google.com/books?id=1XZgQgAACAAJ]

Popular culture
*Hidetoshi Kato (ed). Japanese Popular Culture. Charles E Tuttle Company. Rutland, Vermont. Tokyo. 1959. [https://books.google.com/books?id=HkVxAAAAMAAJ]
**Richard Gid Powers, Hidetoshi Kato and Bruce Stronach (eds). Handbook of Japanese Popular Culture. Greenwood Press. Westport, Connecticut. 1989. [https://books.google.co.uk/books?id=tuRwAAAAMAAJ] 
*Alisa Freedman and Toby Slade (eds). Introducing Japanese Popular Culture. [https://books.google.co.uk/books?id=UBFFDwAAQBAJ&amp;pg=PA1963#v=onepage&amp;q&amp;f=false]. Alisa Freedman (ed). 2nd Ed: 2023: [https://books.google.co.uk/books?id=WuC0EAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false].
*Timothy J Craig (ed). Japan Pop! Inside the World of Japanese Popular Culture. ME Sharpe. 2000. [https://books.google.co.uk/books?id=Vvw5WQ0crLoC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*E Taylor Atkins. A History of Popular Culture in Japan: From the Seventeenth Century to the Present. Bloomsbury Academic. 2017: [https://books.google.co.uk/books?id=DK41DwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]. 2nd Ed: 2023: [https://books.google.co.uk/books?id=hGuHEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false].
*Douglas Slaymaker. A Century of Popular Culture in Japan. [https://books.google.co.uk/books?id=H_dxAAAAMAAJ]
*John Whittier Treat. Contemporary Japan and Popular Culture. University of Hawaii Press. 1996. [https://books.google.co.uk/books?id=iuYwAQAAIAAJ]
*D P Martinez (ed). The Worlds of Japanese Popular Culture: Gender, Shifting Boundaries and Global Cultures. Cambridge University Press. 1998. [https://books.google.co.uk/books?id=6mqM8m-sJY4C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Nissim Kadosh Otmazgin. Regionalizing Culture: The Political Economy of Japanese Popular Culture in Asia. University of Hawaii Press. 2014. [https://books.google.co.uk/books?id=vVgEEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*William W Kelly (ed). Fanning the Flames: Fans and Consumer Culture in Contemporary Japan. 2004. [https://books.google.co.uk/books?id=Y_LmaLo4190C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Forum Mithani and Griseldis Kirsch (eds). Handbook of Japanese Media and Popular Culture in Transition. 2022. 2025. [https://books.google.co.uk/books?id=IECMEQAAQBAJ&amp;pg=PA2005#v=onepage&amp;q&amp;f=false]
*Matthew Allen and Rumi Sakamoto (eds). Popular Culture, Globalization and Japan. 2006. [https://books.google.co.uk/books?id=IVxBHv1olywC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Arts and culture
*Nelly Delay. Art and Culture of Japan. (Discoveries). Harry N Abrams. 1999.  [https://books.google.co.uk/books?id=VlyAILUBFLYC]
*Stephen Addiss, Gerald Groemer and J Thomas Rimer (eds). Traditional Japanese Arts and Culture: An Illustrated Sourcebook. University of Hawaii Press. 2006. [https://books.google.co.uk/books?id=TZcBEAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Leisure
*Sepp Linhart and Sabine Fruhstuck (eds). The Culture of Japan as Seen through Its Leisure. State University of New York Press. 1998. [https://books.google.co.uk/books?id=Ev_n7VaEpUoC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Culture and customs
*Noriko Kamachi. Culture and Customs of Japan. (Culture and Customs of Asia: ISSN 1097-0738). 1999. [https://books.google.co.uk/books?id=2cvWAAAAMAAJ]

Series
*Japanese Culture in the Meiji Era

Culture and behaviour
*Takie Sugiyama Lebra and William P. Lebra (eds). Japanese Culture and Behavior: Selected Readings. 1974. Revised Ed: 1986: [https://books.google.co.uk/books?id=g8-BGRKwWXoC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

==Korean==
*John H Koo and Andrew C Nahm (eds). An Introduction to Korean Culture. Hollym. [https://books.google.co.uk/books?id=975xAAAAMAAJ]
*Joanne Miyang Cho and Lee M Roberts (eds). Korean Culture in the Global Age: K-Pop, K-Drama, K-Film, and K-Literature. 2025. [https://books.google.co.uk/books?id=2ftgEQAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]
*Richard Saccone. The Business of Korean Culture. Hollym. 1994. [https://books.google.co.uk/books?id=7ji2AAAAIAAJ]

Periodicals
*Korean Culture. Korean Cultural Service. ISSN 0270-1618.

==Latin American==
History
*Pedro Henríquez Ureña. A Concise History of Latin American Culture. Frederick A Praeger. 1966. [https://books.google.co.uk/books?id=yZxoAAAAMAAJ]

Contemporary
*C Gail Guntermann (ed). Contemporary Latin American Culture: Unity and Diversity. 1984. [https://books.google.co.uk/books?id=FjUcAQAAIAAJ]
*George M Foster (ed). Readings in Contemporary Latin American Culture: An Anthropological Sourcebook. Selected Academic Readings. [https://books.google.co.uk/books?id=a89AAAAAIAAJ]
*Contemporary Latin American Culture. (Middle American Research Institute, Publication No 25). Tulane University. 1968. [https://books.google.co.uk/books?id=YNNpAAAAMAAJ]

Modern
*John King (ed). The Cambridge Companion to Modern Latin American Culture. 2004. [https://books.google.co.uk/books?id=BE30cHBvjM8C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Anthropology
*Emilio Willems. Latin American Culture: An Anthropological Synthesis. Harper &amp; Row. [https://books.google.co.uk/books?id=mn8WAAAAYAAJ]

Teaching
*Gloria Contreras. Latin American Culture Studies: Information and Materials for Teaching about Latin America. Institute of Latin American Studies, University of Texas at Austin. [https://books.google.co.uk/books?id=kn9qAAAAMAAJ]

Cultural studies
*Ana del Sarto, Alicia Ríos and Abril Trigo (eds). The Latin American Cultural Studies Reader. 2004.[https://books.google.co.uk/books?id=NW1CXsOKRc8C&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Stephen Hart and Richard Young. Contemporary Latin American Cultural Studies. Hodder Arnold. 2003. Routledge. 2014. [https://books.google.co.uk/books?id=o7TpAgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

[[Category:Culture]]</text>
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  <page>
    <title>User:Amirrorslens</title>
    <ns>2</ns>
    <id>331815</id>
    <revision>
      <id>2831875</id>
      <parentid>2831087</parentid>
      <timestamp>2026-09-06T21:59:17Z</timestamp>
      <contributor>
        <username>Amirrorslens</username>
        <id>3106278</id>
      </contributor>
      <comment>/* About Me */ updating book chapter context, as well as employment context</comment>
      <origin>2831875</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2357" sha1="ba2xskvnmlz6r15iw2ayxihvl9gbkqh" xml:space="preserve">==About Me==
Hi there! My name is Amira Killeen and I am currently studying a Bachelors of Science in Psychology at University of Canberra. I am in my fourth year, and have one more year of part-time study to go before I intend to undertake either a Masters of Social Work or Masters of Counselling. 

Prior to commencing Psychology at UC, I was studying a Bachelors of Science (Advanced)(Honours), with a major in Physics and Astrophysics.  

I am currently employed as a Student Services Officer in the Student Centre at UC, as well as with AspireUC as part of Student Equity and Participation. We deliver community-based outreach programs to schools across the Snowy Monaro region and other rural areasm to increase awareness and aspirations for young people towards Higher Education and other career pathways.  

In my spare time, I enjoy going to dubstep gigs, bush doofs and rabbit hole-ing on Wikipedia. 

==Book Chapter==
I am writing my book chapter on: ''[[Motivation and emotion/Book/2026/Awe and the diminished self|Awe and the diminished self]] - How does awe diminish the self and how can this be applied?''  as part of the ongoing project to develop a book on the application of psychological science to improve human life as an assessment exercise for [[Motivation and emotion]].  

==Social Contributions==

# '''13/08/2026''' '''-''' Created discord server for external study support, posted on UC Learn as open invite to fellow students. See here: https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455151
# '''04/09/2026''' '''-''' Suggested possible external link resource for ''&quot;Competence motivation in self-determination theory&quot;''. See here: [[Talk:Motivation and emotion/Book/2026/Competence motivation in self-determination theory#c-Amirrorslens-20260903175000-External Link Suggestion]]
# '''04/09/2026 -''' Left a starter article on discussion page for book chapter ''&quot;How does the need for competence function within self-determination theory to shape motivation and behaviour?&quot;'' See here: [[Talk:Motivation and emotion/Book/2026/Competence motivation in self-determination theory#c-Amirrorslens-20260903201100-Article !]]
# '''04/09/2026 -''' Put up a UC Learn discussion post for students to exchange and request specific feedback. See here: https://uclearn.canberra.edu.au/courses/20143/discussion_topics/459230</text>
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  <page>
    <title>Bully Metric Math and Mnemonics</title>
    <ns>0</ns>
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      <id>2831852</id>
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      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Heliosphere Mnemonics */</comment>
      <origin>2831852</origin>
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      <format>text/x-wiki</format>
      <text bytes="9695" sha1="16pux6z0cldn5u2l99lfskkdg84gsf5" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20 \pi parsecs = 60^4 AU&lt;/math&gt;.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).


&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

The following mnemonics indicate a typical distance of naked-eye stars and the time required for the Sun to travel that distance:

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 51,200 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,R_{\odot} &amp;\sim {512 \times 10^{10}} \text{ ls} \\
&amp;\sim 51,200 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,\tau_{R\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>16pux6z0cldn5u2l99lfskkdg84gsf5</sha1>
    </revision>
    <revision>
      <id>2831853</id>
      <parentid>2831852</parentid>
      <timestamp>2026-09-06T20:33:21Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Heliosphere Mnemonics */</comment>
      <origin>2831853</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="9653" sha1="9gifgey97027qsr2230qs2t82ryodl7" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).


&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

The following mnemonics indicate a typical distance of naked-eye stars and the time required for the Sun to travel that distance:

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 51,200 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,R_{\odot} &amp;\sim {512 \times 10^{10}} \text{ ls} \\
&amp;\sim 51,200 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,\tau_{R\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>9gifgey97027qsr2230qs2t82ryodl7</sha1>
    </revision>
    <revision>
      <id>2831854</id>
      <parentid>2831853</parentid>
      <timestamp>2026-09-06T20:35:05Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Heliosphere Mnemonics */</comment>
      <origin>2831854</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="9652" sha1="qxpnd2i6yw6ilyh0lovgpijzyo6204g" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

The following mnemonics indicate a typical distance of naked-eye stars and the time required for the Sun to travel that distance:

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 51,200 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,R_{\odot} &amp;\sim {512 \times 10^{10}} \text{ ls} \\
&amp;\sim 51,200 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,\tau_{R\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>qxpnd2i6yw6ilyh0lovgpijzyo6204g</sha1>
    </revision>
    <revision>
      <id>2831855</id>
      <parentid>2831854</parentid>
      <timestamp>2026-09-06T20:40:36Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Naked-Eye Star Mnemonics */</comment>
      <origin>2831855</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10062" sha1="gbmcmj30rcj358dkbx2p3nuf0642d6r" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 51,200 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,R_{\odot} &amp;\sim {512 \times 10^{10}} \text{ ls} \\
&amp;\sim 51,200 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,\tau_{R\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>gbmcmj30rcj358dkbx2p3nuf0642d6r</sha1>
    </revision>
    <revision>
      <id>2831857</id>
      <parentid>2831855</parentid>
      <timestamp>2026-09-06T20:46:22Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Naked-Eye Star Mnemonics */</comment>
      <origin>2831857</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10087" sha1="cdnfg9p84n85ak1imti50jd2qjo5nes" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 51,200 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,R_{\odot} &amp;\sim {512 \times 10^{10}} \text{ ls} \\
&amp;\sim 51,200 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,\tau_{R\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>cdnfg9p84n85ak1imti50jd2qjo5nes</sha1>
    </revision>
    <revision>
      <id>2831858</id>
      <parentid>2831857</parentid>
      <timestamp>2026-09-06T20:47:44Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Naked-Eye Star Mnemonics */</comment>
      <origin>2831858</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10086" sha1="j2a6m33gyx7rqit4wgysrfrzp3ptk1t" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp; \approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 51,200 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,R_{\odot} &amp;\sim {512 \times 10^{10}} \text{ ls} \\
&amp;\sim 51,200 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,\tau_{R\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>j2a6m33gyx7rqit4wgysrfrzp3ptk1t</sha1>
    </revision>
    <revision>
      <id>2831859</id>
      <parentid>2831858</parentid>
      <timestamp>2026-09-06T20:50:08Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Naked-Eye Star Mnemonics */</comment>
      <origin>2831859</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10112" sha1="ne5deitap4xi8n6gm895q7zw9r826pw" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp; \approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\approx \frac{20 \pi \times 16^{8}}{60^4 \times 215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 51,200 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,R_{\odot} &amp;\sim {512 \times 10^{10}} \text{ ls} \\
&amp;\sim 51,200 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,\tau_{R\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>ne5deitap4xi8n6gm895q7zw9r826pw</sha1>
    </revision>
    <revision>
      <id>2831860</id>
      <parentid>2831859</parentid>
      <timestamp>2026-09-06T20:51:52Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Naked-Eye Star Mnemonics */</comment>
      <origin>2831860</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10111" sha1="90c32428xvxqta0hug62920x1hyf15w" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp;\approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\approx \frac{20 \pi \times 16^{8}}{60^4 \times 215} \text{ AU} \\ 
&amp;\approx 96.85 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 51,200 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,R_{\odot} &amp;\sim {512 \times 10^{10}} \text{ ls} \\
&amp;\sim 51,200 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,\tau_{R\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>90c32428xvxqta0hug62920x1hyf15w</sha1>
    </revision>
    <revision>
      <id>2831861</id>
      <parentid>2831860</parentid>
      <timestamp>2026-09-06T20:53:45Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Naked-Eye Star Mnemonics */</comment>
      <origin>2831861</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10097" sha1="dvjj7y9af37b994c0c8dq00brc9add4" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp;\approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\approx \frac{20 \pi \times 16^{8}}{60^4 \times 215} \text{ AU} \\ 
&amp;\approx 96.85 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 51,200 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,R_{\odot} &amp;\sim {512 \times 10^{10}} \text{ ls} \\
&amp;\sim 51,200 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,\tau_{R\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>dvjj7y9af37b994c0c8dq00brc9add4</sha1>
    </revision>
    <revision>
      <id>2831862</id>
      <parentid>2831861</parentid>
      <timestamp>2026-09-06T20:55:04Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Naked-Eye Star Mnemonics */</comment>
      <origin>2831862</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10096" sha1="a8302vgs5inhio3v4sbrmesh9noamca" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp;\approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\approx \frac{20 \pi \times 16^{8}}{60^4 \times 215} \text{ AU} \\ 
&amp;\approx 96.85 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499} \text{ AU} \\
&amp;\approx 97.2 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 51,200 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,R_{\odot} &amp;\sim {512 \times 10^{10}} \text{ ls} \\
&amp;\sim 51,200 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,\tau_{R\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>a8302vgs5inhio3v4sbrmesh9noamca</sha1>
    </revision>
    <revision>
      <id>2831867</id>
      <parentid>2831862</parentid>
      <timestamp>2026-09-06T21:05:44Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Milky Way Mnemonics */</comment>
      <origin>2831867</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10096" sha1="but9nx7sui51senw8uoho5xrg9uss32" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp;\approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\approx \frac{20 \pi \times 16^{8}}{60^4 \times 215} \text{ AU} \\ 
&amp;\approx 96.85 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499} \text{ AU} \\
&amp;\approx 97.2 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 51,200 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,\tau_{R\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,R_{\odot} &amp;\sim {512 \times 10^{10}} \text{ ls} \\
&amp;\sim 51,200 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>but9nx7sui51senw8uoho5xrg9uss32</sha1>
    </revision>
    <revision>
      <id>2831868</id>
      <parentid>2831867</parentid>
      <timestamp>2026-09-06T21:12:47Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Naked-Eye Star Mnemonics */</comment>
      <origin>2831868</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10090" sha1="tev4qyekehj5o300n4aiqe8rovqt8f0" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp;\approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\approx \frac{20 \pi \times 16^{8}}{60^4 \times 215} \text{ AU} \\ 
&amp;\approx 96.85 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499} \text{ AU} \\
&amp;\approx 97.2 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 50,000 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,t_{\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,R_{\odot} &amp;\sim {512 \times 97.65} \text{ ls} \\
&amp;\sim 50,000 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>tev4qyekehj5o300n4aiqe8rovqt8f0</sha1>
    </revision>
    <revision>
      <id>2831869</id>
      <parentid>2831868</parentid>
      <timestamp>2026-09-06T21:13:47Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Milky Way Mnemonics */</comment>
      <origin>2831869</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10090" sha1="lzrvys6d8hy732xyhlxneyzysq0fq2l" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp;\approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\approx \frac{20 \pi \times 16^{8}}{60^4 \times 215} \text{ AU} \\ 
&amp;\approx 96.85 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499} \text{ AU} \\
&amp;\approx 97.2 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 50,000 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,t_{\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,R_{\odot} &amp;\sim {512 \times 97.65} \text{ pc} \\
&amp;\sim 50,000 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>lzrvys6d8hy732xyhlxneyzysq0fq2l</sha1>
    </revision>
    <revision>
      <id>2831870</id>
      <parentid>2831869</parentid>
      <timestamp>2026-09-06T21:23:48Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Milky Way Mnemonics */</comment>
      <origin>2831870</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10090" sha1="3sj1u7mzav9nw4z3tq1gi4jceia0m71" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp;\approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\approx \frac{20 \pi \times 16^{8}}{60^4 \times 215} \text{ AU} \\ 
&amp;\approx 96.85 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499} \text{ AU} \\
&amp;\approx 97.2 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 50,000 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,t_{\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,d_{\odot} &amp;\sim {512 \times 97.65} \text{ pc} \\
&amp;\sim 50,000 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 10&lt;sup&gt;10&lt;/sup&gt; light-seconds per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.602232&lt;/sup&gt; ≈ 397,951 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.602232&lt;/sup&gt; ≈ 24,871.9 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.602232&lt;/sup&gt; ≈ 1,554.50 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.602232&lt;/sup&gt; ≈ 49,744 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.602232&lt;/sup&gt; ≈ 1.518064 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>3sj1u7mzav9nw4z3tq1gi4jceia0m71</sha1>
    </revision>
    <revision>
      <id>2831872</id>
      <parentid>2831870</parentid>
      <timestamp>2026-09-06T21:37:03Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Is the Bully system internally consistent? */</comment>
      <origin>2831872</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10077" sha1="ay4yr4cvu78bwqxbns6p98vu6y27x17" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp;\approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\approx \frac{20 \pi \times 16^{8}}{60^4 \times 215} \text{ AU} \\ 
&amp;\approx 96.85 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499} \text{ AU} \\
&amp;\approx 97.2 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 50,000 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,t_{\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,d_{\odot} &amp;\sim {512 \times 97.65} \text{ pc} \\
&amp;\sim 50,000 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>ay4yr4cvu78bwqxbns6p98vu6y27x17</sha1>
    </revision>
    <revision>
      <id>2831873</id>
      <parentid>2831872</parentid>
      <timestamp>2026-09-06T21:41:56Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Is the Bully system internally consistent? */</comment>
      <origin>2831873</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10303" sha1="3ym0kvobokwipd558tmbulfayid2eev" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp;\approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\approx \frac{20 \pi \times 16^{8}}{60^4 \times 215} \text{ AU} \\ 
&amp;\approx 96.85 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499} \text{ AU} \\
&amp;\approx 97.2 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 50,000 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,t_{\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,d_{\odot} &amp;\sim {512 \times 97.65} \text{ pc} \\
&amp;\sim 50,000 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Is the Bully system internally consistent? ====
In Figure 3e, the Sun is shown to travel roughly 51,200 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps (213 million years). However, the Bully Galactic Calendar shown in Figure 3f assumes exactly 52,000 parsecs of orbital travel per 2&lt;sup&gt;41&lt;/sup&gt; timestamps, introducing a distinct discrepancy in both galactic scale and calculated orbital velocity.

Because the long-term orbital dynamics of the Sun are subject to complex gravitational perturbations, standard stellar movement is neither perfectly uniform nor entirely predictable. Consequently, the Sun's true orbital velocity remains a subject of ongoing discovery and refinement. The conjectured values used in Figure 3e and Figure 3f should be viewed as '''practical assumptions''' rather than a reflection of a stable, long-term physical reality; the idealized Bully Calendar is a '''conceptual model''' designed to help visualize the immense scale of the galactic orbit.

The table in '''Figure 4d''' illustrates how scaling the assumed baseline velocity from 1 solar radius per Bully timestamps up to 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps aligns the highest digits with rounded integer multiples of the parsec length.

{| class=&quot;wikitable&quot; style=&quot;margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;&quot;

|+ style=&quot;font-weight: bold; margin-bottom: 8px;&quot; | '''Figure 4d''': Distance Conversions to Parsecs

! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt;Bully Timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 1 solar radius per Bully timestamp&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 100 parsecs per 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps&lt;/small&gt;
! style=&quot;background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 3px;&quot; | &lt;small&gt; Orbital distance in parsecs assuming 52,000 parsecs per 2&lt;sup&gt;41&lt;/sup&gt; Bully timestamps&lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;11&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;18.597453&lt;/sup&gt; ≈ 396,635 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.6438562&lt;/sup&gt; ≈ 409,600 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;18.666224&lt;/sup&gt; ≈ 416,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;10&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;14.597453&lt;/sup&gt; ≈ 24,789.7 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.6438562&lt;/sup&gt; ≈ 25,600.0 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;14.666224&lt;/sup&gt; ≈ 26,000.0 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;9&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 1,549.36 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.6438562&lt;/sup&gt; ≈ 1,600.00 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;10.666224&lt;/sup&gt; ≈ 1,625.00 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''16&lt;sup&gt;8&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;10.597453&lt;/sup&gt; ≈ 96.8348 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.6438562&lt;/sup&gt; ≈ 100.0000 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;6.666224&lt;/sup&gt; ≈ 101.5625 &lt;/small&gt;

|- style=&quot;background-color: #e6f2ff;{{Text color default}}; font-weight: bold;&quot;
! colspan=&quot;4&quot; style=&quot;text-align: left; padding: 8px;&quot; | Off Nominal Values

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;41&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;15.597453&lt;/sup&gt; ≈ 49,579 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.6438562&lt;/sup&gt; ≈ 51,200 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;15.666224&lt;/sup&gt; ≈ 52,000 &lt;/small&gt;

|-
| style=&quot;text-align: left; padding: 8px;&quot; | '''2&lt;sup&gt;26&lt;/sup&gt;'''
| &lt;small&gt;2&lt;sup&gt;0.597453&lt;/sup&gt; ≈ 1.513043 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.6438562&lt;/sup&gt; ≈ 1.562500 &lt;/small&gt;
| &lt;small&gt;2&lt;sup&gt;0.666224&lt;/sup&gt; ≈ 1.586914 &lt;/small&gt;
|}

== References ==
{{reflist}}</text>
      <sha1>3ym0kvobokwipd558tmbulfayid2eev</sha1>
    </revision>
    <revision>
      <id>2831877</id>
      <parentid>2831873</parentid>
      <timestamp>2026-09-06T22:01:59Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <origin>2831877</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6626" sha1="269s5hgxlkeopahwarfdyb86q3tbo7r" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp;\approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\approx \frac{20 \pi \times 16^{8}}{60^4 \times 215} \text{ AU} \\ 
&amp;\approx 96.85 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499} \text{ AU} \\
&amp;\approx 97.2 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way is roughly 50,000 parsecs and is completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,t_{\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,d_{\odot} &amp;\sim {512 \times 97.65} \text{ pc} \\
&amp;\sim 50,000 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;

== References ==
{{reflist}}</text>
      <sha1>269s5hgxlkeopahwarfdyb86q3tbo7r</sha1>
    </revision>
    <revision>
      <id>2831926</id>
      <parentid>2831877</parentid>
      <timestamp>2026-09-06T23:04:27Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Milky Way Mnemonics */</comment>
      <origin>2831926</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6634" sha1="9gjhcen5w0bsjovtry6eavo0zk6m5lp" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp;\approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\approx \frac{20 \pi \times 16^{8}}{60^4 \times 215} \text{ AU} \\ 
&amp;\approx 96.85 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499} \text{ AU} \\
&amp;\approx 97.2 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way assumed to be roughly 50,000 parsecs and completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,t_{\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,d_{\odot} &amp;\sim {512 \times 97.65} \text{ pc} \\
&amp;\sim 50,000 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;

== References ==
{{reflist}}</text>
      <sha1>9gjhcen5w0bsjovtry6eavo0zk6m5lp</sha1>
    </revision>
    <revision>
      <id>2831930</id>
      <parentid>2831926</parentid>
      <timestamp>2026-09-06T23:35:03Z</timestamp>
      <contributor>
        <username>~2026-48171-60</username>
        <id>3110678</id>
      </contributor>
      <comment>/* Naked-Eye Star Mnemonics */</comment>
      <origin>2831930</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6634" sha1="jvrfptdfami7ody5uvt775iiztf1way" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

The following mnemonics help one remember the approximate length of the solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;) in terms of [[W:light-second|light-seconds]] (ls), [[W:astronomical units|astronomical units]] (AU), and [[W:parsecs|parsecs]] (pc):
&lt;div style=&quot;background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #AA8080;&quot;&gt;
:&lt;math&gt;
1\text{ AU} \approx 499 \text{ ls} \approx 215 \, R_{\odot} 
&lt;/math&gt;
:&lt;math&gt;
100\text{ pc} \sim 10^{10} \text{ ls} \sim 16^{8} \, R_{\odot}
&lt;/math&gt;
&lt;/div&gt;
&amp;hairsp;

=== Solar Radius Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|center|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3,055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second]&lt;ref&gt;{{cite journal |last1=Eilers |first1=Anna-Christina |last2=Hogg |first2=David W. |last3=Rix |first3=Hans-Walter |last4=Ness |first4=Melissa |title=The Circular Velocity Curve of the Milky Way from 5 to 25 kpc |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=120 |year=2019 |doi=10.3847/1538-4357/aaf648 |arxiv=1810.09466}}&lt;/ref&gt; where 299,792.458 kilometers = 1 light-second. 

During each 3,055-second period (&lt;math&gt;t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;d_{\odot}&lt;/math&gt;) of a little over 2.33 light-seconds, which is slightly more than one solar radius (&lt;math&gt;R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
t_{\odot} \equiv 3,055 \text{ seconds}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
d_{\odot} &amp;\equiv \frac{3,055 \times 229}{299,792.458} \text{ ls} \\
&amp;\approx 2.333598 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
R_{\odot} &amp;\equiv \frac{695,700}{299,792.458} \text{ ls} \\
&amp;\approx 2.320605 \text{ ls}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \approx \frac{499}{215} \text{ ls} \approx 2.3209 \text{ ls}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
R_{\odot} \sim \frac{10^{10}}{16^{8}} \text{ ls} \approx 2.33 \text{ ls}
&lt;/math&gt;
&amp;hairsp;

=== Heliosphere Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|center|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16&lt;sup&gt;4&lt;/sup&gt; Bully timestamps.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit.

During each 6.344-year period (&lt;math&gt;16^{4}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{4}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 65,536 solar radii (&lt;math&gt;16^{4}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,t_{\odot} &amp;\equiv 16^{4} \times 3,055 \text{ s} \\
&amp;\approx 6.344 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,d_{\odot} &amp;\equiv \frac{16^{4} \times 3,055 \times 229}{149,597,870.7} \text{ AU} \\
&amp;\approx 306.479348 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\equiv \frac{16^{4} \times 695,700}{149,597,870.7} \text{ AU}\\
&amp; \approx 304.773022 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\approx \frac{16^{4}}{215} \text{ AU} \\ &amp;\approx 304.82 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{4}\,R_{\odot} &amp;\sim \frac{10^{10}}{499 \times 16^{4}} \text{ AU} \\
&amp;\approx 305.8 \text{ AU}
\end{align}
&lt;/math&gt;
&amp;hairsp;

=== Naked-Eye Star Mnemonics ===
[[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of naked-eye stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 10&lt;sup&gt;10&lt;/sup&gt; light-seconds, which is the distance the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16&lt;sup&gt;8&lt;/sup&gt; Bully timestamps. The included stacked histogram shows that a large percentage of naked-eye stars are within this travel distance of the sun, 97.156 parsecs or 10&lt;sup&gt;10&lt;/sup&gt; light-seconds.]]

Assume a solar radius of 695,700 kilometers and velocity of [https://arxiv.org/abs/1810.09466 229.0 ± 0.2 kilometers per second] where 149,597,870.7 kilometers = 1 astronomical unit and &lt;math&gt;20\,\pi&lt;/math&gt; parsecs = &lt;math&gt;60^4&lt;/math&gt; astronomical units.

During each 415,792-year period (&lt;math&gt;16^{8}\,t_{\odot}&lt;/math&gt;), the Sun travels a distance (&lt;math&gt;16^{8}\,d_{\odot}&lt;/math&gt;) of a little over 306 astronomical units, which is slightly more than 4,294,967,296 solar radii (&lt;math&gt;16^{8}\,R_{\odot}&lt;/math&gt;).

&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,t_{\odot} &amp;\equiv 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 415,792 \text{ years}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,d_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 3,055 \times 229}{60^4 \times 149,597,870.7} \text{ pc} \\
&amp;\approx 97.376915 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\equiv \frac{20 \pi \times 16^{8} \times 695,700}{60^4 \times 149,597,870.7} \text{ pc}\\
&amp;\approx 96.834768 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\approx \frac{20 \pi \times 16^{8}}{60^4 \times 215} \text{ pc} \\ 
&amp;\approx 96.85 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
16^{8}\,R_{\odot} &amp;\sim \frac{20 \pi \times 10^{10}}{60^4 \times 499} \text{ pc} \\
&amp;\approx 97.2 \text{ pc}
\end{align}
&lt;/math&gt;
&amp;hairsp;

==== Milky Way Mnemonics ====
[[File:Milky_Way_map_by_Gaia_High_Density_Grid.jpg|thumb|center|600px|'''Figure 3e''': Division of the Milky Way into 32 equal polar sectors (yellow grid).]]

The Sun's full orbital path around the Milky Way assumed to be roughly 50,000 parsecs and completed in roughly 212.8 million years.

&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,t_{\odot} &amp;\equiv 512 \times 16^{8} \times 3,055 \text{ s} \\
&amp;\approx 212.8 \text{ million years} \\
\end{align}
&lt;/math&gt;
&amp;hairsp;
:&lt;math&gt;
\begin{align}
512 \times 16^{8}\,d_{\odot} &amp;\sim {512 \times 97.65} \text{ pc} \\
&amp;\sim 50,000 \text{ parsecs}
\end{align}
&lt;/math&gt;
&amp;hairsp;

== References ==
{{reflist}}</text>
      <sha1>jvrfptdfami7ody5uvt775iiztf1way</sha1>
    </revision>
  </page>
  <page>
    <title>Universal Bibliography/Television</title>
    <ns>0</ns>
    <id>331837</id>
    <revision>
      <id>2831817</id>
      <parentid>2831760</parentid>
      <timestamp>2026-09-06T16:04:13Z</timestamp>
      <contributor>
        <username>James500</username>
        <id>297601</id>
      </contributor>
      <comment>/* Japanese */ Add</comment>
      <origin>2831817</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="12798" sha1="mrscz83ditpj21n7p6fczc9ld3ts73c" xml:space="preserve">{{Bibliography}}
See [[w:Category:Books about television]] and [[w:Category:Works about television]]

This part of the [[Universal Bibliography]] is a bibliography of television.

Bibliography
*Mary Cassata and Thomas Skill. Television: A Guide to the Literature. Oryx Press. 1985. [https://books.google.com/books?id=4jdGAAAAMAAJ]
*Felix Chin. Cable Television: A Comprehensive Bibliography. IFI/Plenum. New York. 1978. [https://books.google.com/books?id=flBHAQAAIAAJ]
*William Saffady. High Definition Television: A Bibliography. Meckler. 1990. [https://books.google.com/books?id=_Ssbwbn1QbAC]
*James E Sudalnik and Victoria A Kuhl (comps). High-Definition Television: An Annotated Multidisciplinary Bibliography, 1981-1992. [https://books.google.co.uk/books?id=0Q3DEAAAQBAJ]
*George Shiers (comp). Early Television: A Bibliographic Guide to 1940. 1997. [https://books.google.co.uk/books?id=YLcJBAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*A Partial Bibliography of Television. [https://books.google.co.uk/books?id=HpBt18StMuwC]

Bibliography and terminology
*Television: Terminology, Bibliography. [https://books.google.com/books?id=WiRzbHou3k0C]

Encyclopedias
*Horace Newcomb (ed). Encyclopedia of Television. 1997. 2004. 2nd Ed. Routledge. 2013. [https://books.google.co.uk/books?id=NUXIAgAAQBAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*Les Brown's Encyclopedia of Television. 1977. New York Zoetrope. 1982. [https://books.google.co.uk/books?id=gb5kAAAAMAAJ]. 3rd Ed: 1992. [https://books.google.co.uk/books?id=07EYAAAAIAAJ]
*Les Brown. The New York Times Encyclopedia of Television. 1977. [https://books.google.co.uk/books?id=4L1kAAAAMAAJ]
*Stanley Kempner. Television Encyclopedia. Fairchild Publishing Company. 1948. [https://books.google.com/books?id=Gk9LAAAAMAAJ]
*Vincent Terrace. Encyclopedia of Television Series, Pilots and Specials. [https://books.google.co.uk/books?id=AKlgjBCPPnsC&amp;pg=PA1#v=onepage&amp;q&amp;f=false]

Periodicals
*Television. Television Magazine Corporation. [https://books.google.co.uk/books?id=rOgWAQAAMAAJ]
**Television Magazine. Frederick Kugel Company. [https://books.google.co.uk/books?id=Beg84qwbyhcC]. Commentary: [https://books.google.co.uk/books?id=29LVAAAAMAAJ]
*Television Quarterly. National Academy of Television Arts and Sciences. [https://books.google.co.uk/books?id=A1cZAAAAIAAJ]
*Television Age. Television Editorial Corp Publication Office. [https://books.google.co.uk/books?id=27qiEDXrT3wC]
*Journal of the Television Society [https://books.google.co.uk/books?id=RYuaAAAAIAAJ]

Annuals
*World Guide to Television. [https://books.google.co.uk/books?id=15EHAQAAMAAJ 1999].

Almanacs
*International Television Almanac. Quigley. [https://books.google.co.uk/books?id=aRgdAAAAIAAJ]

History
*Anthony Smith (ed). Television: An International History. Oxford University Press. 1995. [https://books.google.co.uk/books?id=KLRkAAAAMAAJ]
*Albert Abramson. The History of Television, 1880 to 1941. McFarland. 1987. [https://books.google.com/books?id=hxlTAAAAMAAJ]

Future
*The Future of Television: A Global Overview of Programming, Advertising, Technology, and Growth. NTC Business Books. 1992. [https://books.google.co.uk/books?id=I04PAQAAMAAJ]

World
*Joseph D Straubhaar. World Television: From Global to Local. 2007. [https://books.google.co.uk/books?id=OP10AwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Shawn Shimpach (ed). The Routledge Companion to Global Television. 2020. [https://books.google.co.uk/books?id=GOK5DwAAQBAJ&amp;pg=PA1950#v=onepage&amp;q&amp;f=false]
*Wilson P Dizard. Television: a World View. Syracuse University Press. 1966. [https://books.google.co.uk/books?id=J7dkAAAAMAAJ]
*John Sinclair (ed). Contemporary World Television. [Graeme Turner (assoc ed)]. British Film Institute. 2004. [https://books.google.com/books?id=2iLuAAAAMAAJ] 
*Tony Verna. Global Television: How to Create Effective Television for the Future. [https://books.google.co.uk/books?id=Q7FkAAAAMAAJ] [https://books.google.co.uk/books?id=3cfhEAAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]

France and the rest of the world
*Hervé Michel. La Télévision en France et dans le monde. [[w:Presses Universitaires de France|Presses Universitaires de France]]. Deposited March 1989. ISBN 2130701655. [https://books.google.co.uk/books?id=mb3_EAAAQBAJ&amp;pg=PA3#v=onepage&amp;q&amp;f=false]

United Kingdom
*Rob Young. The Magic Box: Viewing Britain Through the Rectangular Window. [https://books.google.co.uk/books?id=fH8NEAAAQBAJ&amp;pg=PA1#v=onepage&amp;q&amp;f=false]. Review: [https://www.theguardian.com/books/2021/aug/13/the-magic-box-by-rob-young-review-a-spirited-history-of-television]

Magazines
*The Radio Times
*TV Times

Newspaper television reviews etc

United Kingdom
*A A Gill. Paper View: The Best of the Sunday Times Television Columns.

*&quot;Choice&quot; or &quot;Television and Radio Choice&quot; in &quot;Television and Radio&quot;. 1991.  Middle of newspaper. The page number of the listings is given on the front page. These reviews are printed in the body of the listings, and not in a separate column.
*&quot;Choice&quot; or &quot;TV Choice&quot; in &quot;Television and Radio&quot;. The Times. 1992. These reviews are printed in the body of the listings, and not in a separate column. These reviews are printed on the last page of the &quot;Life &amp; Times&quot; section of the newspaper, for issues of the newspaper where &quot;Life &amp; Times&quot; is a separate section. Otherwise they are printed in the middle of newspaper.
*&quot;Choice&quot; or &quot;TV Choice&quot; in &quot;Television and Radio&quot;. The Times. 1992 to 1993. Penultimate page of newspaper. These reviews are printed in the body of the listings, and not in a separate column.
*&quot;Choice&quot;. The Times. 1993 to 1997. Mondays to Fridays. Penultimate page of newspaper.
*&quot;Television Choice&quot;. The Times. 1997 onwards. Mondays to Fridays. Third page from back of newspaper.
*&quot;Review&quot;. The Times. 1994 onwards. Mondays to Fridays. Penultimate page of newspaper.
*There are reviews in:
**The Independent, The Guardian, The Financial Times, and The Daily Telegraph

Netherlands
*&quot;TV: Films Video&quot; in &quot;televisie en radio woensdag&quot;. Limburgs Dagblad.
*&quot;show&quot;. Limburgs Dagblad.

Music
*Tele-Tunes

Black and white
*[https://www.theguardian.com/commentisfree/2018/nov/09/black-white-television-viewers-colour Black and white TVs are a lo-fi rebuke to a world gone wrong]. The Guardian. 9 November 2018.

Japanese and American
*Leroy W Gardner, &quot;A Content Analysis of Japanese and American Television&quot;, 6 Journal of Broadcasting 45 (No 1: Winter 1961-1962) [https://books.google.co.uk/books?id=Wlb1a3tWofAC]

Asian
*Jinna Tay and Graeme Turner (eds). Television Histories in Asia: Issues and Contexts. 2015. [https://books.google.co.uk/books?id=IxU-CgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

==Japanese==
*Jacques Mousseau. &quot;La télévision au Japon&quot; (1984) Communication et langages. No 59. pp 87 to 101. [[w:es:Dialnet|Dialnet]]: [https://dialnet.unirioja.es/servlet/articulo?codigo=5564949]. [[w:Persée (web portal)|Persée]]: [https://www.persee.fr/doc/colan_0336-1500_1984_num_59_1_1603]
*La Télévision au Japon. Problèmes audiovisuels. INA/Documentation Française. No 5. February 1982.
*Mitsuhiro Yoshimoto, Eva Tsai and JungBong Choi (eds). Television, Japan, and Globalization. 2010. [https://books.google.co.uk/books?id=wx-NCwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Toru Yamamoto. &quot;The Growth of Television in Japan&quot;. Studies of Broadcasting. No 2. March 1964. pp 81 to 126. [https://books.google.co.uk/books?lr=&amp;id=Cl0sC0WefuUC]
*Masaki Ikuta. &quot;The Characteristics of the Growth of Television in Japan&quot;. Studies of Broadcasting. No 4. March 1966. pp 5 to 22. [https://books.google.co.uk/books?lr=&amp;id=JwxQAQAAMAAJ]
*&quot;Twenty Years of Television in Japan&quot;. Studies of Broadcasting. No 10. March 1974. [https://books.google.com/books?id=BRN7GpQke2IC] [https://books.google.co.uk/books?id=JTwmkgrpOQwC]
**Akira Fujitake. &quot;Trends in the Studies of Television in Japan&quot;. pp 5 to 28.
*Jun Yoshida. &quot;Development of Television and Changes in TV Viewing Habits in Japan&quot;. Studies of Broadcasting. (Thirty Years of TV Viewing). 1983. [https://books.google.co.uk/books?id=LfuuXs9U6t4C No 22]. 1986. pp 127 to 54.
*Norimichi Fujiwara. &quot; Televiewing of Japanese People&quot;. Studies of Broadcasting. No 7. March 1969. pp 59 to 104. [https://books.google.co.uk/books?id=8N0UlMSjlrMC]
*Jayson Makoto Chun. A Nation of a Hundred Million Idiots? A Social History of Japanese Television, 1953 - 1973. 2007. [https://books.google.co.uk/books?id=9miRAgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*S Sasao, &quot;The History of Television in Japan&quot; (1961) 9 Journal of the Television Society 436 to 443 (No 11: July to September 1961) [https://books.google.co.uk/books?id=pmUPAAAAIAAJ]
*&quot;The Slow March of Progress: Japanese Television&quot;. The Economist. 15 July 1995. pp 49 to 50.
*William Horsley. &quot;Japan's conformist television&quot;. The Listener. (vol 94, no 2424). 18 September 1975. p 366. [https://books.google.co.uk/books?id=_NVBAQAAIAAJ]
*Terebi Bangumi No 40 Nen. (Japanese: テレビ番組の40年). [English: 40 Years of Television Programmes]. [[w:ja:日本放送出版協会|NHK Shuppan]]. Tokyo. 1994. ISBN 4-14-080192. [https://books.google.co.uk/books?id=DqQvAQAAIAAJ]

Genres

Drama

[テレビドラマ = Television drama]
*Jonathan Clements and Motoko Tamamuro. The Dorama Encyclopedia: A Guide to Japanese TV Drama Since 1953. Stone Bridge Press. 2003. [https://books.google.co.uk/books?id=z7I-VyCfZdQC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*T Makita. &quot;Television Drama and the Japanese Culture: with special emphasis on the historical drama&quot;. Studies of Broadcasting. No 10. pp 57 to 76. [https://books.google.co.uk/books?id=JTwmkgrpOQwC]
*Terebi Dorama Zenshi: 1953-1994: TV Gaido. (Japanese: テレビドラマ全史 1953-1994 TV ガイド). [English: Complete History of Japanese Television Drama: 1953-1994: TV Guide]. Tokyo News Mook. [[w:ja:東京ニュース通信社|Tokyo News Service]]. 1994. [https://books.google.co.uk/books?id=HCEQAQAAMAAJ]. Catalogue: [https://www.library.pref.kyoto.jp/opw/OPW/OPWSRCHTYPE.CSP?ReloginFlag=1&amp;BID=B10300776&amp;DB=LIB&amp;FROMFLG=1] [https://www.library.pref.kyoto.jp/bib/?B10300776]
*Masunori Sata and Hideo Hirahara (eds). Kazuhiko Gotō, Hideo Hirahara, Katsumi Oyama and Masunori Sata. A History of Japanese Television Drama: Modern Japan and the Japanese. Japan Association of Broadcasting Art. Tokyo. 1991. Catalogue: [https://search.worldcat.org/title/A-History-of-Japanese-television-drama-:-modern-Japan-and-the-Japanese/oclc/1341882698]. Commentary: [https://books.google.co.uk/books?id=C7RZAAAAMAAJ].
**Japanese title: 日本テレビドラマ戦後史. Cataglogue: [https://ndlsearch.ndl.go.jp/books/R100000136-I1971149384770108736].
*Hiromu Toriyama (鳥山拡). Nihon Terebi Dorama-shi (Japanese: 日本テレビドラマ史). [English: History of Japanese Television Drama]. Eijinsha (映人社). Tokyo. 25 September 1986. ISBN 4-87100-213-6. [https://books.google.co.uk/books?id=pIYSAQAAMAAJ].
*Nobuo Harada (原田信男). Terebi Dorama 30 Nen. (Japanese: テレビドラマ 30年). [[w:ja:読売新聞社|Yomiuri Shinbun-sha]]. 1983. [https://books.google.co.uk/books?id=k_1IAAAAMAAJ]

Drama periodicals
*ドラマ from 映人社. Commentary: [https://www.library.pref.kyoto.jp/?pickupkiji=103969 こんな記事、読めます　No.42『ドラマ』]. [https://natalie.mu/eiga/news/557392]. Catalogue: [https://ci.nii.ac.jp/ncid/AN0035884X]

Other genres
*Hakan Ergül. Popularizing Japanese TV: The Cultural, Economic, and Emotional Dimensions of Infotainment Discourse. 2019. [https://books.google.co.uk/books?id=Hfh1DwAAQBAJ&amp;pg=PA1942#v=onepage&amp;q&amp;f=false]
*Jose Maria De Vera. Educational Television in Japan. Sophia University.  Tokyo. Charles E Tuttle Company. Tokyo and Rutland. 1967. [https://books.google.co.uk/books?id=_6gcAAAAMAAJ]

Audience
*Yoshida. &quot;Trends in Television Audience Survey in Japan&quot;. (Twenty Years of Television in Japan). Studies of Broadcasting. No 10. March 1974. pp 29 to 44. [https://books.google.com/books?id=BRN7GpQke2IC] [https://books.google.co.uk/books?id=JTwmkgrpOQwC]
*Jun Yoshida. &quot;Japanese TV Audiences as seen from Surveys&quot;. Studies of Broadcasting. No 18. 1982. p 115. [https://books.google.co.uk/books?id=ZaoeHmpNpTsC]

Okinawan diaspora
*Taku Suzuki, &quot;Viewing Nations, Narrating Hybridity: Okinawan Diasporic Subjectivity and Japanese Satellite Telecasts in Colonia Okinawa, Bolivia&quot; (2005) 14(1) Diaspora: A Journal of Transnational Studies 75 to 107 [https://books.google.co.uk/books?id=cbIpAQAAIAAJ]

Periodicals

See [[w:ja:テレビ情報誌]] and [[w:ja:Category:日本のテレビ情報誌]]

Newspaper television reviews etc

*&quot;Today's Choice&quot; in &quot;TV/Radio&quot;. The Japan Times.

Archives and listings
*[https://www.nhk.or.jp/archives/ NHK Archives]. [https://www.nhk.or.jp/archives/chronicle/ Chronicle]. [https://www.nhk.or.jp/archives/chronicle/timetable/ Timetables].

[[Category:Television]]</text>
      <sha1>mrscz83ditpj21n7p6fczc9ld3ts73c</sha1>
    </revision>
  </page>
  <page>
    <title>User talk:Cfm490</title>
    <ns>3</ns>
    <id>331866</id>
    <revision>
      <id>2831935</id>
      <parentid>2831584</parentid>
      <timestamp>2026-09-07T00:46:04Z</timestamp>
      <contributor>
        <username>The Citer</username>
        <id>3110681</id>
      </contributor>
      <comment>/* Welcome */ Reply</comment>
      <origin>2831935</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2491" sha1="255t5rxylzrz6ev5i6lxlz5oq3gpl0w" xml:space="preserve">==Welcome==
{{Robelbox|theme=9|title='''[[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]],  Cfm490!'''|width=100%}}
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See you around Wikiversity! ---- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 21:23, 5 September 2026 (UTC)&lt;/div&gt;
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:And don't misbehave. [[User:The Citer|The Citer]] ([[User talk:The Citer|discuss]] • [[Special:Contributions/The Citer|contribs]]) 00:46, 7 September 2026 (UTC)</text>
      <sha1>255t5rxylzrz6ev5i6lxlz5oq3gpl0w</sha1>
    </revision>
  </page>
  <page>
    <title>French/Conversation/A1/Restaurant</title>
    <ns>0</ns>
    <id>331877</id>
    <revision>
      <id>2831955</id>
      <parentid>2831744</parentid>
      <timestamp>2026-09-07T06:05:13Z</timestamp>
      <contributor>
        <username>ShakespeareFan00</username>
        <id>6645</id>
      </contributor>
      <minor />
      <origin>2831955</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3742" sha1="63140zrkncr1gqzahrer20sc2e59jpo" xml:space="preserve">== 1 ==
Server: '''Bonjour, une table pour combien de personnes ?'''
{{green|bɔ̃ʒuʁ yn tabl puʁ kɔ̃bjɛ̃ də pɛʁsɔn}}
''Hello, a table for how many people?''

Customer: '''Bonjour, une table pour deux, s'il vous plaît.'''
{{green|bɔ̃ʒuʁ yn tabl puʁ dø sil vu plɛ}}
''Hello, a table for two, please.''

Server: '''Voici le menu. Vous avez choisi ?'''
{{green|vwasi lə məny vuzave ʃwazi}}
''Here is the menu. Have you chosen?''

Customer: '''Oui, je voudrais le poulet et une salade.'''
{{green|wi ʒə vudʁɛ lə pulɛ e yn salad}}
''Yes, I would like the chicken and a salad.''

== 2 ==

Server: '''Bonsoir, avez-vous réservé une table ?'''
{{green|bɔ̃swaʁ avevu ʁezɛʁve yn tabl}}
''Good evening, do you have a reservation?''

Customer: '''Non, mais je voudrais une table pour deux.'''
{{green|nɔ̃ mɛ ʒə vudʁɛ yn tabl puʁ dø}}
''No, but I would like a table for two.''

Server: '''Voulez-vous boire quelque chose pour commencer ?'''
{{green|vulevu bwaʁ kɛlkə ʃoz puʁ kɔmɑ̃se}}
''Would you like something to drink to start?''

Customer: '''L'addition, s'il vous plaît, quand vous pourrez.'''
{{green|ladisjɔ̃ sil vu plɛ kɑ̃ vu puʁʁe}}
''The bill, please, whenever you can.''

== 3 ==
Server: '''Bonjour, avez-vous une préférence pour la table ?'''
{{green|bɔ̃ʒuʁ avevu yn pʁefeʁɑ̃s puʁ la tabl}}
''Hello, do you have a preference for the table?''

Customer: '''Une table près de la fenêtre, si possible.'''
{{green|yn tabl pʁɛ də la fənɛtʁ si pɔsibl}}
''A table near the window, if possible.''

Server: '''Je vous recommande le plat du jour.'''
{{green|ʒə vu ʁəkɔmɑ̃d lə pla dy ʒuʁ}}
''I recommend the dish of the day.''

Customer: '''Parfait, et un verre de vin rouge, merci.'''
{{green|paʁfɛ e œ̃ vɛʁ də vɛ̃ ʁuʒ mɛʁsi}}
''Perfect, and a glass of red wine, thank you.''

== 4 ==
Server: '''Bonsoir, souhaitez-vous un apéritif avant de commander ?'''
{{green|bɔ̃swaʁ swɛtevu œ̃n‿apeʁitif avɑ̃ də kɔmɑ̃de}}
''Good evening, would you like an aperitif before ordering?''

Customer: '''Non merci, je suis prêt à commander maintenant.'''
{{green|nɔ̃ mɛʁsi ʒə sɥi pʁɛ a kɔmɑ̃de mɛ̃tnɑ̃}}
''No thanks, I'm ready to order now.''

Server: '''Avez-vous des allergies alimentaires à signaler ?'''
{{green|avevu dez‿alɛʁʒi alimɑ̃tɛʁ a siɲale}}
''Do you have any food allergies to mention?''

Customer: '''Oui, je suis allergique aux fruits de mer.'''
{{green|wi ʒə sɥiz‿alɛʁʒik o fʁɥi də mɛʁ}}
''Yes, I'm allergic to seafood.''

== 5 ==
Server: '''Est-ce que tout va bien avec votre repas ?'''
{{green|ɛskə tu va bjɛ̃ avɛk vɔtʁ ʁəpa}}
''Is everything going well with your meal?''

Customer: '''Oui, c'est délicieux, merci beaucoup.'''
{{green|wi sɛ delisjø mɛʁsi boku}}
''Yes, it's delicious, thank you very much.''

Server: '''Voulez-vous voir la carte des desserts ?'''
{{green|vulevu vwaʁ la kaʁt de desɛʁ}}
''Would you like to see the dessert menu?''

Customer: '''Non merci, juste l'addition, s'il vous plaît.'''
{{green|nɔ̃ mɛʁsi ʒyst ladisjɔ̃ sil vu plɛ}}
''No thanks, just the bill, please.''

== 6 ==
Server: '''Puis-je débarrasser votre assiette ?'''
{{green|pɥiʒ debaʁase vɔtʁ asjɛt}}
''May I clear your plate?''

Customer: '''Oui, allez-y, c'était très bon.'''
{{green|wi alezi setɛ tʁɛ bɔ̃}}
''Yes, go ahead, it was very good.''

Server: '''Souhaitez-vous un café pour terminer ?'''
{{green|swɛtevu œ̃ kafe puʁ tɛʁmine}}
''Would you like a coffee to finish?''

Customer: '''Oui, un café et l'addition, merci.'''
{{green|wi œ̃ kafe e ladisjɔ̃ mɛʁsi}}
''Yes, a coffee and the bill, thank you.''

[[Category:French Conversations A1]]</text>
      <sha1>63140zrkncr1gqzahrer20sc2e59jpo</sha1>
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  </page>
  <page>
    <title>French/Conversation/A1/Taxi</title>
    <ns>0</ns>
    <id>331878</id>
    <revision>
      <id>2831956</id>
      <parentid>2831750</parentid>
      <timestamp>2026-09-07T06:26:53Z</timestamp>
      <contributor>
        <username>ShakespeareFan00</username>
        <id>6645</id>
      </contributor>
      <minor />
      <origin>2831956</origin>
      <model>wikitext</model>
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      <text bytes="3909" sha1="4d2442657jp7r7szbyqpfofuk2yhtch" xml:space="preserve">== 1 ==
Driver: '''Bonjour, où voulez-vous aller aujourd'hui ?'''
{{green|bɔ̃ʒuʁ u vulevu ale oʒuʁdɥi}}
''Hello, where would you like to go today?''

Passenger: '''À l'aéroport, s'il vous plaît, je suis pressé.'''
{{green|a laeʁɔpɔʁ sil vu plɛ ʒə sɥi pʁese}}
''To the airport, please, I'm in a hurry.''

Driver: '''Pas de problème, ça prendra environ vingt minutes.'''
{{green|pa də pʁɔblɛm sa pʁɑ̃dʁa ɑ̃viʁɔ̃ vɛ̃t minyt}}
''No problem, it will take about twenty minutes.''

Passenger: '''Merci, vous pouvez déposer les bagages ici ?'''
{{green|mɛʁsi vu puve depoze le bagaʒ isi}}
''Thank you, can you drop the bags here?''

== 2 ==
Driver: '''Bonsoir, montez, je vous emmène où ?'''
{{green|bɔ̃swaʁ mɔ̃te ʒə vuz‿amɛn u}}
''Good evening, hop in, where am I taking you?''

Passenger: '''Au centre-ville, près de la gare, merci.'''
{{green|o sɑ̃tʁəvil pʁɛ də la gaʁ mɛʁsi}}
''To the city center, near the station, thank you.''

Driver: '''Il y a beaucoup de circulation ce soir.'''
{{green|il i a boku də siʁkylasjɔ̃ sə swaʁ}}
''There's a lot of traffic tonight.''

Passenger: '''Ce n'est pas grave, prenez votre temps.'''
{{green|sə nɛ pa gʁav pʁəne vɔtʁ tɑ̃}}
''That's fine, take your time.''
== 3 ==
Driver: '''Bonsoir, avez-vous une adresse précise ?'''
{{green|bɔ̃swaʁ avevu yn adʁɛs pʁesiz}}
''Good evening, do you have a specific address?''

Passenger: '''Oui, voici l'adresse sur mon téléphone.'''
{{green|wi vwasi ladʁɛs syʁ mɔ̃ telefɔn}}
''Yes, here's the address on my phone.''

Driver: '''D'accord, le trajet coûtera environ quinze euros.'''
{{green|dakɔʁ lə tʁaʒɛ kutʁa ɑ̃viʁɔ̃ kɛ̃z øʁo}}
''Okay, the ride will cost about fifteen euros.''

Passenger: '''Très bien, je paierai par carte bancaire.'''
{{green|tʁɛ bjɛ̃ ʒə pɛʁe paʁ kaʁt bɑ̃kɛʁ}}
''Very well, I'll pay by credit card.''

== 4 ==
Driver: '''Bonjour, c'est votre première fois dans cette ville ?'''
{{green|bɔ̃ʒuʁ sɛ vɔtʁ pʁəmjɛʁ fwa dɑ̃ sɛt vil}}
''Hello, is this your first time in this city?''

Passenger: '''Oui, je viens d'arriver, je découvre encore.'''
{{green|wi ʒə vjɛ̃ daʁive ʒə dekuvʁ ɑ̃kɔʁ}}
''Yes, I just arrived, I'm still exploring.''

Driver: '''Combien vous dois-je pour la course ?'''
{{green|kɔ̃bjɛ̃ vu dwaʒ puʁ la kuʁs}}
''How much do I owe you for the ride?''

Passenger: '''Ça fait quinze euros, vous pouvez payer en carte.'''
{{green|sa fɛ kɛ̃z øʁo vu puve peje ɑ̃ kaʁt}}
''That's fifteen euros, you can pay by card.''

== 5 ==
Driver: '''Bonjour, vous connaissez le chemin le plus rapide ?'''
{{green|bɔ̃ʒuʁ vu kɔnese lə ʃəmɛ̃ lə ply ʁapid}}
''Hello, do you know the fastest way?''

Passenger: '''Non, faites confiance à votre GPS.'''
{{green|nɔ̃ fɛt kɔ̃fjɑ̃s a vɔtʁ ʒepeɛs}}
''No, just trust your GPS.''

Driver: '''Il y a des travaux, on va contourner.'''
{{green|il i a de tʁavo ɔ̃ va kɔ̃tuʁne}}
''There's construction, we'll go around.''

Passenger: '''Pas de souci, prenez le temps qu'il faut.'''
{{green|pa də susi pʁəne lə tɑ̃ kil fo}}
''No worries, take the time you need.''

== 6 ==
Driver: '''Bonsoir, il fait froid ce soir, non ?'''
{{green|bɔ̃swaʁ il fɛ fʁwa sə swaʁ nɔ̃}}
''Good evening, it's cold tonight, isn't it?''

Passenger: '''Oui, très froid, pouvez-vous monter le chauffage ?'''
{{green|wi tʁɛ fʁwa puvevu mɔ̃te lə ʃofaʒ}}
''Yes, very cold, can you turn up the heat?''

Driver: '''Bien sûr, dites-moi si c'est suffisant.'''
{{green|bjɛ̃ syʁ ditmwa si sɛ syfizɑ̃}}
''Of course, tell me if that's enough.''

Passenger: '''C'est parfait maintenant, merci beaucoup pour votre gentillesse.'''
{{green|sɛ paʁfɛ mɛ̃tnɑ̃ mɛʁsi boku puʁ vɔtʁ ʒɑ̃tijɛs}}
''That's perfect now, thank you very much for your kindness.''

[[Category:French Conversations A1]]</text>
      <sha1>4d2442657jp7r7szbyqpfofuk2yhtch</sha1>
    </revision>
  </page>
  <page>
    <title>Differential equations/Slope fields</title>
    <ns>0</ns>
    <id>331881</id>
    <revision>
      <id>2831777</id>
      <timestamp>2026-09-06T13:45:30Z</timestamp>
      <contributor>
        <username>IanVG</username>
        <id>2918363</id>
      </contributor>
      <comment>Created page with &quot;Slope fields are representations of (usually) distinct, non-overlapping, solution curves for system of differential equations. A vector field is a map of vectors corresponding with the specific location in the domain of solutions.&quot;</comment>
      <origin>2831777</origin>
      <model>wikitext</model>
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      <text bytes="230" sha1="mn0yhigil1vmhplilh09uike90ukiix" xml:space="preserve">Slope fields are representations of (usually) distinct, non-overlapping, solution curves for system of differential equations. A vector field is a map of vectors corresponding with the specific location in the domain of solutions.</text>
      <sha1>mn0yhigil1vmhplilh09uike90ukiix</sha1>
    </revision>
    <revision>
      <id>2831785</id>
      <parentid>2831777</parentid>
      <timestamp>2026-09-06T13:56:08Z</timestamp>
      <contributor>
        <username>IanVG</username>
        <id>2918363</id>
      </contributor>
      <minor />
      <comment>IanVG moved page [[Slope Fields]] to [[Differential equations/Slope fields]]: I accidentally forgot to add the parent page</comment>
      <origin>2831777</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="230" sha1="mn0yhigil1vmhplilh09uike90ukiix" xml:space="preserve">Slope fields are representations of (usually) distinct, non-overlapping, solution curves for system of differential equations. A vector field is a map of vectors corresponding with the specific location in the domain of solutions.</text>
      <sha1>mn0yhigil1vmhplilh09uike90ukiix</sha1>
    </revision>
    <revision>
      <id>2831787</id>
      <parentid>2831785</parentid>
      <timestamp>2026-09-06T13:58:09Z</timestamp>
      <contributor>
        <username>IanVG</username>
        <id>2918363</id>
      </contributor>
      <origin>2831787</origin>
      <model>wikitext</model>
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      <text bytes="430" sha1="3wos25uj9ca3fc6s0sg2wjhfpnbq8p3" xml:space="preserve">Slope fields are representations of (usually) distinct, non-overlapping, solution curves for system of differential equations. A vector field is a map of vectors corresponding with the specific location in the domain of solutions.

The figure below shows one example of a vector field. Vector fields can help you obtain a sense of the possible solutions.

[[File:Isotropic_vector_field_example.svg|Isotropic vector field example]]</text>
      <sha1>3wos25uj9ca3fc6s0sg2wjhfpnbq8p3</sha1>
    </revision>
    <revision>
      <id>2831793</id>
      <parentid>2831787</parentid>
      <timestamp>2026-09-06T14:31:26Z</timestamp>
      <contributor>
        <username>IanVG</username>
        <id>2918363</id>
      </contributor>
      <comment>changed image</comment>
      <origin>2831793</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="528" sha1="1gl8ehpa7069bmdzj0zqne4kxkidsgy" xml:space="preserve">Slope fields are representations of (usually) distinct, non-overlapping, solution curves for system of differential equations. A vector field is a map of vectors corresponding with the specific location in the domain of solutions.

The figure below shows one example of a vector field. Vector fields can help you obtain a sense of the possible solutions.
[[File:Normalized_isotropic_vector_field_dxdt_x_dydt_y.svg|left|frame|Normalized isotropic vector field (isotropic direction field) of a first-order differential equation.]]</text>
      <sha1>1gl8ehpa7069bmdzj0zqne4kxkidsgy</sha1>
    </revision>
    <revision>
      <id>2831794</id>
      <parentid>2831793</parentid>
      <timestamp>2026-09-06T14:35:40Z</timestamp>
      <contributor>
        <username>IanVG</username>
        <id>2918363</id>
      </contributor>
      <minor />
      <origin>2831794</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="533" sha1="7064ic5f9hjn1nxt6ahy5loc9rvu988" xml:space="preserve">Slope fields are representations of (usually) distinct, non-overlapping, solution curves for system of differential equations. A vector field is a map of vectors corresponding with the specific location in the domain of solutions.

The figure below shows one example of a vector field. Vector fields can help you obtain a sense of the possible solutions.
[[File:Normalized isotropic vector field dxdt x dydt y tail.svg|left|frame|Normalized isotropic vector field (isotropic direction field) of a first-order differential equation.]]</text>
      <sha1>7064ic5f9hjn1nxt6ahy5loc9rvu988</sha1>
    </revision>
    <revision>
      <id>2831932</id>
      <parentid>2831794</parentid>
      <timestamp>2026-09-06T23:57:00Z</timestamp>
      <contributor>
        <username>MathXplore</username>
        <id>2888076</id>
      </contributor>
      <minor />
      <comment>Added {{[[Template:BookCat|BookCat]]}} using [[User:1234qwer1234qwer4/BookCat.js|BookCat.js]]</comment>
      <origin>2831932</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="546" sha1="nnn0wfwhroafqr6x3bagc2l53sd36wy" xml:space="preserve">Slope fields are representations of (usually) distinct, non-overlapping, solution curves for system of differential equations. A vector field is a map of vectors corresponding with the specific location in the domain of solutions.

The figure below shows one example of a vector field. Vector fields can help you obtain a sense of the possible solutions.
[[File:Normalized isotropic vector field dxdt x dydt y tail.svg|left|frame|Normalized isotropic vector field (isotropic direction field) of a first-order differential equation.]]

{{BookCat}}</text>
      <sha1>nnn0wfwhroafqr6x3bagc2l53sd36wy</sha1>
    </revision>
  </page>
  <page>
    <title>Differential equations/First-order problems</title>
    <ns>0</ns>
    <id>331882</id>
    <revision>
      <id>2831781</id>
      <timestamp>2026-09-06T13:47:55Z</timestamp>
      <contributor>
        <username>IanVG</username>
        <id>2918363</id>
      </contributor>
      <comment>Created page with &quot;Determine and draw the vector fields associated with the following first-order systems:&quot;</comment>
      <origin>2831781</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="87" sha1="7lvsqvrv90lrb0ujp8r4vlubofnhcc1" xml:space="preserve">Determine and draw the vector fields associated with the following first-order systems:</text>
      <sha1>7lvsqvrv90lrb0ujp8r4vlubofnhcc1</sha1>
    </revision>
    <revision>
      <id>2831782</id>
      <parentid>2831781</parentid>
      <timestamp>2026-09-06T13:51:08Z</timestamp>
      <contributor>
        <username>IanVG</username>
        <id>2918363</id>
      </contributor>
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      <text bytes="261" sha1="js6tyhe8emgd4lf8mgg9zv63l5fzo6e" xml:space="preserve">Determine and draw the vector fields associated with the following first-order systems:

# &lt;math&gt;\left\{
\begin{array}{l}
\frac{dx}{dt}=0\\
\frac{dy}{dt}=0
\end{array}
\right.

&lt;/math&gt;
# &lt;math&gt;\begin{cases}
\frac{dx}{dt}=0\\
\frac{dy}{dt}=0
\end{cases}

&lt;/math&gt;</text>
      <sha1>js6tyhe8emgd4lf8mgg9zv63l5fzo6e</sha1>
    </revision>
    <revision>
      <id>2831783</id>
      <parentid>2831782</parentid>
      <timestamp>2026-09-06T13:53:46Z</timestamp>
      <contributor>
        <username>IanVG</username>
        <id>2918363</id>
      </contributor>
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      <text bytes="765" sha1="e4oz2gshzriq1rxhaisbzuybhe96r6x" xml:space="preserve">Determine and draw the vector fields associated with the following first-order systems. Draw enough of each vector field, so you get an idea of the geometric structure of the vector field.

# &lt;math&gt;\left\{
\begin{array}{l}
\frac{dx}{dt}=0\\
\frac{dy}{dt}=0
\end{array}
\right.

&lt;/math&gt;
# &lt;math&gt;\left\{
\begin{array}{l}
\frac{dx}{dt}=1\\
\frac{dy}{dt}=0
\end{array}
\right.

&lt;/math&gt;
# &lt;math&gt;\left\{
\begin{array}{l}
\frac{dx}{dt}=x\\
\frac{dy}{dt}=1
\end{array}
\right.

&lt;/math&gt;
# &lt;math&gt;\left\{
\begin{array}{l}
\frac{dx}{dt}=x\\
\frac{dy}{dt}=y
\end{array}
\right.&lt;/math&gt;
# &lt;math&gt;\left\{
\begin{array}{l}
\frac{dy}{dt}=-v\\
\frac{dv}{dt}=y
\end{array}
\right.

&lt;/math&gt;
# &lt;math&gt;\left\{
\begin{array}{l}
\frac{dx}{dt}=x\\
\frac{dy}{dt}=2y
\end{array}
\right.

&lt;/math&gt;</text>
      <sha1>e4oz2gshzriq1rxhaisbzuybhe96r6x</sha1>
    </revision>
    <revision>
      <id>2831931</id>
      <parentid>2831783</parentid>
      <timestamp>2026-09-06T23:56:55Z</timestamp>
      <contributor>
        <username>MathXplore</username>
        <id>2888076</id>
      </contributor>
      <minor />
      <comment>Added {{[[Template:BookCat|BookCat]]}} using [[User:1234qwer1234qwer4/BookCat.js|BookCat.js]]</comment>
      <origin>2831931</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="778" sha1="e94wm8h36v7ok95zeyyc21bzr5ae95w" xml:space="preserve">Determine and draw the vector fields associated with the following first-order systems. Draw enough of each vector field, so you get an idea of the geometric structure of the vector field.

# &lt;math&gt;\left\{
\begin{array}{l}
\frac{dx}{dt}=0\\
\frac{dy}{dt}=0
\end{array}
\right.

&lt;/math&gt;
# &lt;math&gt;\left\{
\begin{array}{l}
\frac{dx}{dt}=1\\
\frac{dy}{dt}=0
\end{array}
\right.

&lt;/math&gt;
# &lt;math&gt;\left\{
\begin{array}{l}
\frac{dx}{dt}=x\\
\frac{dy}{dt}=1
\end{array}
\right.

&lt;/math&gt;
# &lt;math&gt;\left\{
\begin{array}{l}
\frac{dx}{dt}=x\\
\frac{dy}{dt}=y
\end{array}
\right.&lt;/math&gt;
# &lt;math&gt;\left\{
\begin{array}{l}
\frac{dy}{dt}=-v\\
\frac{dv}{dt}=y
\end{array}
\right.

&lt;/math&gt;
# &lt;math&gt;\left\{
\begin{array}{l}
\frac{dx}{dt}=x\\
\frac{dy}{dt}=2y
\end{array}
\right.

&lt;/math&gt;

{{BookCat}}</text>
      <sha1>e94wm8h36v7ok95zeyyc21bzr5ae95w</sha1>
    </revision>
  </page>
  <page>
    <title>Slope Fields</title>
    <ns>0</ns>
    <id>331883</id>
    <redirect title="Differential equations/Slope fields" />
    <revision>
      <id>2831786</id>
      <timestamp>2026-09-06T13:56:08Z</timestamp>
      <contributor>
        <username>IanVG</username>
        <id>2918363</id>
      </contributor>
      <comment>IanVG moved page [[Slope Fields]] to [[Differential equations/Slope fields]]: I accidentally forgot to add the parent page</comment>
      <origin>2831786</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="49" sha1="993hboz36r0x4winu35a97ewu968p01" xml:space="preserve">#REDIRECT [[Differential equations/Slope fields]]</text>
      <sha1>993hboz36r0x4winu35a97ewu968p01</sha1>
    </revision>
  </page>
  <page>
    <title>OpenStax Introduction to Philosophy</title>
    <ns>0</ns>
    <id>331884</id>
    <revision>
      <id>2831800</id>
      <timestamp>2026-09-06T15:17:43Z</timestamp>
      <contributor>
        <username>Andy?yes</username>
        <id>3006471</id>
      </contributor>
      <comment>Created page with &quot;See also [[OpenStax]]  == &lt;big&gt;OpenStax&lt;/big&gt; &lt;big&gt;Introduction to Philosophy&lt;/big&gt; ==  == Summary == Designed to meet the scope and sequence of your course, ''Introduction to Philosophy'' surveys logic, metaphysics, epistemology, theories of value, and history of philosophy thematically. To provide a strong foundation in global philosophical discourse, diverse primary sources and examples are central to the design, and the text emphasizes engaged reading, critical think...&quot;</comment>
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      <format>text/x-wiki</format>
      <text bytes="715" sha1="jfh8sa19vqpycmnidy3cbqjqk7lqg7v" xml:space="preserve">See also [[OpenStax]]

== &lt;big&gt;OpenStax&lt;/big&gt; &lt;big&gt;Introduction to Philosophy&lt;/big&gt; ==

== Summary ==
Designed to meet the scope and sequence of your course, ''Introduction to Philosophy'' surveys logic, metaphysics, epistemology, theories of value, and history of philosophy thematically. To provide a strong foundation in global philosophical discourse, diverse primary sources and examples are central to the design, and the text emphasizes engaged reading, critical thinking, research, and analytical skill-building through guided activities.

* OpenStax Introduction to Philosophy (original content).  Available as pdf or web view.
* OpenStax Introduction to Philosophy audiobook.  Available as audio textbook.</text>
      <sha1>jfh8sa19vqpycmnidy3cbqjqk7lqg7v</sha1>
    </revision>
    <revision>
      <id>2831801</id>
      <parentid>2831800</parentid>
      <timestamp>2026-09-06T15:18:16Z</timestamp>
      <contributor>
        <username>Andy?yes</username>
        <id>3006471</id>
      </contributor>
      <origin>2831801</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="846" sha1="qdnl105gjjc04bfzcckdmz3e7wskdgc" xml:space="preserve">See also [[OpenStax]]

== &lt;big&gt;OpenStax&lt;/big&gt; &lt;big&gt;Introduction to Philosophy&lt;/big&gt; ==

== Summary ==
Designed to meet the scope and sequence of your course, ''Introduction to Philosophy'' surveys logic, metaphysics, epistemology, theories of value, and history of philosophy thematically. To provide a strong foundation in global philosophical discourse, diverse primary sources and examples are central to the design, and the text emphasizes engaged reading, critical thinking, research, and analytical skill-building through guided activities.

* [https://openstax.org/details/books/introduction-philosophy OpenStax Introduction to Philosophy] (original content).  Available as pdf or web view.
* [https://audileo.com/audiobooks/openstax/introduction-to-philosophy/ OpenStax Introduction to Philosophy audiobook].  Available as audio textbook.</text>
      <sha1>qdnl105gjjc04bfzcckdmz3e7wskdgc</sha1>
    </revision>
    <revision>
      <id>2831802</id>
      <parentid>2831801</parentid>
      <timestamp>2026-09-06T15:19:27Z</timestamp>
      <contributor>
        <username>Andy?yes</username>
        <id>3006471</id>
      </contributor>
      <origin>2831802</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="923" sha1="ra54jym5lhu2irbtmcfvktutem9anv1" xml:space="preserve">See also [[OpenStax]]

== &lt;big&gt;OpenStax&lt;/big&gt; &lt;big&gt;Introduction to Philosophy&lt;/big&gt; ==

== Summary ==
Designed to meet the scope and sequence of your course, ''Introduction to Philosophy'' surveys logic, metaphysics, epistemology, theories of value, and history of philosophy thematically. To provide a strong foundation in global philosophical discourse, diverse primary sources and examples are central to the design, and the text emphasizes engaged reading, critical thinking, research, and analytical skill-building through guided activities.

* [https://openstax.org/details/books/introduction-philosophy OpenStax Introduction to Philosophy] (original content).  Available as pdf or web view.
* [https://audileo.com/audiobooks/openstax/introduction-to-philosophy/ OpenStax Introduction to Philosophy audiobook].  Available as audio textbook.
[[Category:Openstax textbook]]
[[Category:OpenStax]]
[[Category:Philosophy]]</text>
      <sha1>ra54jym5lhu2irbtmcfvktutem9anv1</sha1>
    </revision>
  </page>
  <page>
    <title>OpenStax Principles of Marketing</title>
    <ns>0</ns>
    <id>331885</id>
    <revision>
      <id>2831803</id>
      <timestamp>2026-09-06T15:21:54Z</timestamp>
      <contributor>
        <username>Andy?yes</username>
        <id>3006471</id>
      </contributor>
      <comment>Created page with &quot;See also [[OpenStax]]  == &lt;big&gt;OpenStax&lt;/big&gt; &lt;big&gt;Principles of Marketing&lt;/big&gt; ==  == Summary == ''Principles of Marketing'' is designed to meet the scope and sequence for a one-semester marketing course for undergraduate business majors and minors. ''Principles of Marketing'' provides a solid grounding in the core concepts and frameworks of marketing theory and analysis so that business students interested in a major or minor in marketing will also be prepared for mor...&quot;</comment>
      <origin>2831803</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1244" sha1="2gbu5gjuz4guciqvwshhbzzp88xtwgr" xml:space="preserve">See also [[OpenStax]]

== &lt;big&gt;OpenStax&lt;/big&gt; &lt;big&gt;Principles of Marketing&lt;/big&gt; ==

== Summary ==
''Principles of Marketing'' is designed to meet the scope and sequence for a one-semester marketing course for undergraduate business majors and minors. ''Principles of Marketing'' provides a solid grounding in the core concepts and frameworks of marketing theory and analysis so that business students interested in a major or minor in marketing will also be prepared for more rigorous, upper-level elective courses. Concepts are further reinforced through detailed, diverse, and realistic company and organization scenarios and examples from various industries and geographical locations. To illuminate the meaningful applications and implications of marketing ideas, the book incorporates a modern approach providing connections between topics, solutions, and real-world problems. ''Principles of Marketing'' is modular, allowing flexibility for courses with varied learning outcomes and coverage.

* OpenStax ''Principles of Marketing'' (original content). Available as pdf or web view.
* OpenStax ''Principles of Marketing'' audiobook Available as audio textbook.

[[Category:OpenStax]]
[[Category:Openstax textbook]]
[[Category:Marketing]]</text>
      <sha1>2gbu5gjuz4guciqvwshhbzzp88xtwgr</sha1>
    </revision>
    <revision>
      <id>2831805</id>
      <parentid>2831803</parentid>
      <timestamp>2026-09-06T15:22:28Z</timestamp>
      <contributor>
        <username>Andy?yes</username>
        <id>3006471</id>
      </contributor>
      <origin>2831805</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1369" sha1="e9m7d8d4f24rz4tad59i6arm6ftvsyr" xml:space="preserve">See also [[OpenStax]]

== &lt;big&gt;OpenStax&lt;/big&gt; &lt;big&gt;Principles of Marketing&lt;/big&gt; ==

== Summary ==
''Principles of Marketing'' is designed to meet the scope and sequence for a one-semester marketing course for undergraduate business majors and minors. ''Principles of Marketing'' provides a solid grounding in the core concepts and frameworks of marketing theory and analysis so that business students interested in a major or minor in marketing will also be prepared for more rigorous, upper-level elective courses. Concepts are further reinforced through detailed, diverse, and realistic company and organization scenarios and examples from various industries and geographical locations. To illuminate the meaningful applications and implications of marketing ideas, the book incorporates a modern approach providing connections between topics, solutions, and real-world problems. ''Principles of Marketing'' is modular, allowing flexibility for courses with varied learning outcomes and coverage.

* [https://openstax.org/details/books/principles-marketing OpenStax ''Principles of Marketing''] (original content). Available as pdf or web view.
* [https://audileo.com/audiobooks/openstax/principles-of-marketing/ OpenStax ''Principles of Marketing'' audiobook] Available as audio textbook.

[[Category:OpenStax]]
[[Category:Openstax textbook]]
[[Category:Marketing]]</text>
      <sha1>e9m7d8d4f24rz4tad59i6arm6ftvsyr</sha1>
    </revision>
  </page>
  <page>
    <title>User:Rasalache/sandbox</title>
    <ns>2</ns>
    <id>331886</id>
    <revision>
      <id>2831804</id>
      <timestamp>2026-09-06T15:22:07Z</timestamp>
      <contributor>
        <username>Rasalache</username>
        <id>3110662</id>
      </contributor>
      <comment>Página de testes EBDC</comment>
      <origin>2831804</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="268" sha1="7ndn8dec1o5sm4o975m2ry2s8vv6wd1" xml:space="preserve">'''Quais ações podem colaborar para a construção de Políticas Públicas em Divulgação Científica no Brasil?'''

-Investir na Educação Científica principalmente na formação docente, inicial e continuada;

-Incorporação de Livros de DC no PNLD literário.</text>
      <sha1>7ndn8dec1o5sm4o975m2ry2s8vv6wd1</sha1>
    </revision>
    <revision>
      <id>2831849</id>
      <parentid>2831804</parentid>
      <timestamp>2026-09-06T20:14:45Z</timestamp>
      <contributor>
        <username>Rasalache</username>
        <id>3110662</id>
      </contributor>
      <comment>alteração do texto e referências</comment>
      <origin>2831849</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="453" sha1="lksv0a60rf0n6wqzhnx47v6kjonqam0" xml:space="preserve">'''Quais ações podem colaborar para a construção de Políticas Públicas em Divulgação Científica no Brasil?'''

-Investir na na formação docente, inicial e continuada, considerando as discussões de Educação Científica; [https://www.planalto.gov.br/ccivil_03/_ato2015-2018/2016/decreto/d8752.htm]

-Incorporação de Livros ilustrados de não ficção na Política Nacional do Livro Didático- literário.[https://www.fnde.gov.br/guialivro]</text>
      <sha1>lksv0a60rf0n6wqzhnx47v6kjonqam0</sha1>
    </revision>
    <revision>
      <id>2831850</id>
      <parentid>2831849</parentid>
      <timestamp>2026-09-06T20:15:32Z</timestamp>
      <contributor>
        <username>Rasalache</username>
        <id>3110662</id>
      </contributor>
      <comment>edições de texto</comment>
      <origin>2831850</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="477" sha1="8nt65pxfhz5u5fhqd32uvwo7ecsv10x" xml:space="preserve">'''Quais ações podem colaborar para a construção de Políticas Públicas em Divulgação Científica no Brasil?'''

-Investir na na formação docente, inicial e continuada, considerando as discussões de Educação Científica e de Formação Docente; [https://www.planalto.gov.br/ccivil_03/_ato2015-2018/2016/decreto/d8752.htm]

-Incorporação de Livros ilustrados de não ficção na Política Nacional do Livro Didático- literário.[https://www.fnde.gov.br/guialivro]</text>
      <sha1>8nt65pxfhz5u5fhqd32uvwo7ecsv10x</sha1>
    </revision>
    <revision>
      <id>2831871</id>
      <parentid>2831850</parentid>
      <timestamp>2026-09-06T21:30:32Z</timestamp>
      <contributor>
        <username>Rasalache</username>
        <id>3110662</id>
      </contributor>
      <origin>2831871</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="859" sha1="rb0g5d80eku6binlxuio24qlapbv3a0" xml:space="preserve">'''Quais ações podem colaborar para a construção de Políticas Públicas em Divulgação Científica no Brasil?'''

-Investir na na formação docente, inicial e continuada, considerando as discussões de Educação Científica e de Formação Docente; [https://www.planalto.gov.br/ccivil_03/_ato2015-2018/2016/decreto/d8752.htm]

-Incorporação de Livros ilustrados de não ficção na Política Nacional do Livro Didático- literário.[https://www.fnde.gov.br/guialivro]

'''A ciência com você'''

Série de vídeos em que se apresentam os projetos de extensão da UFSCar, com fomento institucional.  

'''Sonhar com rei dá Leão'''

Dissertação da colega do EBDC 2024 elaborada com base nos protocolos de visitantes de zoológicos e aquários percebendo suas emoções, valorizando as questões culturais do samba.

Em qual instituição? FIOCRUZ</text>
      <sha1>rb0g5d80eku6binlxuio24qlapbv3a0</sha1>
    </revision>
  </page>
  <page>
    <title>OpenStax Principles of Management</title>
    <ns>0</ns>
    <id>331887</id>
    <revision>
      <id>2831807</id>
      <timestamp>2026-09-06T15:24:40Z</timestamp>
      <contributor>
        <username>Andy?yes</username>
        <id>3006471</id>
      </contributor>
      <comment>Created page with &quot;See also [[OpenStax]]  == &lt;big&gt;OpenStax&lt;/big&gt; &lt;big&gt;Principles of Management&lt;/big&gt; ==  == Summary == ''Principles of Management'' is designed to meet the scope and sequence requirements of the introductory course on management. This is a traditional approach to management using the leading, planning, organizing, and controlling approach. Management is a broad business discipline, and the Principles of Management course covers many management areas such as human resource m...&quot;</comment>
      <origin>2831807</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="906" sha1="0o6x68a7jdxotca6fs3diluak9rgxn7" xml:space="preserve">See also [[OpenStax]]

== &lt;big&gt;OpenStax&lt;/big&gt; &lt;big&gt;Principles of Management&lt;/big&gt; ==

== Summary ==
''Principles of Management'' is designed to meet the scope and sequence requirements of the introductory course on management. This is a traditional approach to management using the leading, planning, organizing, and controlling approach. Management is a broad business discipline, and the Principles of Management course covers many management areas such as human resource management and strategic management, as well as behavioral areas such as motivation. No one individual can be an expert in all areas of management, so an additional benefit of this text is that specialists in a variety of areas have authored individual chapters.

* OpenStax ''Principles of Management'' (original content). Available as pdf or web view.
* OpenStax ''Principles of Management'' audiobook Available as audio textbook.</text>
      <sha1>0o6x68a7jdxotca6fs3diluak9rgxn7</sha1>
    </revision>
    <revision>
      <id>2831808</id>
      <parentid>2831807</parentid>
      <timestamp>2026-09-06T15:26:05Z</timestamp>
      <contributor>
        <username>Andy?yes</username>
        <id>3006471</id>
      </contributor>
      <origin>2831808</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1132" sha1="6iwrgty6hprf0fxw0yskziparqebokh" xml:space="preserve">See also [[OpenStax]]

== &lt;big&gt;OpenStax&lt;/big&gt; &lt;big&gt;Principles of Management&lt;/big&gt; ==

== Summary ==
''Principles of Management'' is designed to meet the scope and sequence requirements of the introductory course on management. This is a traditional approach to management using the leading, planning, organizing, and controlling approach. Management is a broad business discipline, and the Principles of Management course covers many management areas such as human resource management and strategic management, as well as behavioral areas such as motivation. No one individual can be an expert in all areas of management, so an additional benefit of this text is that specialists in a variety of areas have authored individual chapters.

* [https://openstax.org/details/books/principles-management OpenStax ''Principles of Management''] (original content). Available as pdf or web view.
* [https://audileo.com/audiobooks/openstax/principles-of-management/ OpenStax ''Principles of Management'' audiobook] Available as audio textbook.
[[Category:Management]]
[[Category:Business]]
[[Category:OpenStax]]
[[Category:Openstax textbook]]</text>
      <sha1>6iwrgty6hprf0fxw0yskziparqebokh</sha1>
    </revision>
  </page>
  <page>
    <title>User talk:Rasalache/sandbox</title>
    <ns>3</ns>
    <id>331888</id>
    <revision>
      <id>2831810</id>
      <timestamp>2026-09-06T15:29:36Z</timestamp>
      <contributor>
        <username>Arleide Rosa</username>
        <id>3110665</id>
      </contributor>
      <comment>/* comentários */ new section</comment>
      <origin>2831810</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="228" sha1="6j8e8rxrr16hqcraoh10q8blb3l6mhu" xml:space="preserve">== comentários ==

ação bastante didática para aplicação nas escolas [[User:Arleide Rosa|Arleide Rosa]] ([[User talk:Arleide Rosa|discuss]] • [[Special:Contributions/Arleide Rosa|contribs]]) 15:29, 6 September 2026 (UTC)</text>
      <sha1>6j8e8rxrr16hqcraoh10q8blb3l6mhu</sha1>
    </revision>
  </page>
  <page>
    <title>OpenStax Business Law I Essentials 2e</title>
    <ns>0</ns>
    <id>331889</id>
    <revision>
      <id>2831811</id>
      <timestamp>2026-09-06T15:30:40Z</timestamp>
      <contributor>
        <username>Andy?yes</username>
        <id>3006471</id>
      </contributor>
      <comment>Created page with &quot;See also [[OpenStax]]  == &lt;big&gt;OpenStax&lt;/big&gt; &lt;big&gt;Business Law I Essentials 2e&lt;/big&gt; ==  == Summary == ''Business Law I Essentials 2e'' is a brief introductory textbook designed to meet the scope and sequence requirements of courses on Business Law or the Legal Environment of Business. The concepts are presented in a streamlined manner, and cover the key concepts necessary to establish a strong foundation in the subject. The textbook follows a traditional approach to th...&quot;</comment>
      <origin>2831811</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="911" sha1="2lvzzsyutzqhqx9h9aasu94m19gc6hs" xml:space="preserve">See also [[OpenStax]]

== &lt;big&gt;OpenStax&lt;/big&gt; &lt;big&gt;Business Law I Essentials 2e&lt;/big&gt; ==

== Summary ==
''Business Law I Essentials 2e'' is a brief introductory textbook designed to meet the scope and sequence requirements of courses on Business Law or the Legal Environment of Business. The concepts are presented in a streamlined manner, and cover the key concepts necessary to establish a strong foundation in the subject. The textbook follows a traditional approach to the study of business law. Each chapter contains learning objectives, explanatory narrative and concepts, references for further reading, and end-of-chapter questions.

* OpenStax ''Business Law I Essentials 2e'' (original content). Available as pdf or web view.
* OpenStax ''Business Law I Essentials 2e'' audiobook Available as audio textbook.

[[Category:Openstax textbook]]
[[Category:OpenStax]]
[[Category:Business]]
[[Category:Law]]</text>
      <sha1>2lvzzsyutzqhqx9h9aasu94m19gc6hs</sha1>
    </revision>
    <revision>
      <id>2831812</id>
      <parentid>2831811</parentid>
      <timestamp>2026-09-06T15:31:15Z</timestamp>
      <contributor>
        <username>Andy?yes</username>
        <id>3006471</id>
      </contributor>
      <origin>2831812</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1049" sha1="gvbnlzc5lkdvu5louu27wst7q74177i" xml:space="preserve">See also [[OpenStax]]

== &lt;big&gt;OpenStax&lt;/big&gt; &lt;big&gt;Business Law I Essentials 2e&lt;/big&gt; ==

== Summary ==
''Business Law I Essentials 2e'' is a brief introductory textbook designed to meet the scope and sequence requirements of courses on Business Law or the Legal Environment of Business. The concepts are presented in a streamlined manner, and cover the key concepts necessary to establish a strong foundation in the subject. The textbook follows a traditional approach to the study of business law. Each chapter contains learning objectives, explanatory narrative and concepts, references for further reading, and end-of-chapter questions.

* [https://openstax.org/details/books/business-law-i-essentials-2e OpenStax ''Business Law I Essentials 2e''] (original content). Available as pdf or web view.
* [https://audileo.com/audiobooks/openstax/business-law-i-essentials-2e/ OpenStax ''Business Law I Essentials 2e'' audiobook] Available as audio textbook.

[[Category:Openstax textbook]]
[[Category:OpenStax]]
[[Category:Business]]
[[Category:Law]]</text>
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==Instructions==
''Please add your request for [[Wikiversity:Interface administrators|interface adminship]] below. Include a short summary of &lt;u&gt;why&lt;/u&gt; you think you should be given the privileges and please refer to your &lt;u&gt;involvement&lt;/u&gt; in other [[Wikimedia]] projects. If you have [[w:Category:Wikipedia functionaries|sysop/bureaucrat]] status at a [[Wikiversity:Sister projects|sister project]], please indicate so as well.''

Please place candidate requests or nominations on a ''subpage'' and ''[[Help:Transclusion|transclude]]'' it here.
{{RoundBoxBottom}}&lt;/div&gt;&lt;includeonly&gt;
{{Wikiversity organization}}
[[Category:Nominations for Interface Adminship|*]]
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== Nominations for Interface Adminship ==
{{clear}}

== See also ==
* [[Wikiversity:Support staff]]</text>
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      <text bytes="9838" sha1="gwpqe46c9fl0xco3nvtlbtzasrfw1wz" xml:space="preserve">[[File:U.S. incarceration rate since 1925.svg|thumb|300px|Figure 1. U.S. prisoners (excluding jails) as a percent of the population: male (dashed red), combined (solid black), female (dotted green), 1925-2023]]

:''The incarceration rate is not related to crime: It's related to people's perception of crime, and that's heavily impacted by the media.''

:This book on ''[[Media Literacy and You]]'' is a combination instruction manual on [[w:Media literacy|media literacy]] and an invitation to you to support collaborative / crowd-sourced research on how to improve the world's understanding of media literacy and how to accelerate its understanding and use globally for the betterment of humanity. 

Parts I and II of this book discuss &quot;The media and political economy&quot; and &quot;The media and war&quot;, respectively. The current Part III considers other issues like climate, immigrants, education, public health, and criminal justice; the latter is the focus of this chapter. 

== Media and incarcerations ==

Figure 1 plots the number of humans in state and federal prisons as a percent of the US population, 1925-2023. The Wikipedia article on &quot;[[w:United States incarceration rate|United States incarceration rate]]&quot;&lt;ref&gt;&quot;[[w:United States incarceration rate]]&quot; accessed 2026-09-06.&lt;/ref&gt; gives various explanations for why the incarceration rate has been so high since the year 2000. However, only one explanation seems to adequately describe why it was so stable at roughly 0.1 percent of the US population in state and federal prisons for the 50 years between 1925 and 1975 and then increased abruptly over the next roughly 25 years before plateauing at roughly 0.5 percent of the population since: 

:''Major corporations bought up the vast majority of the television system in the US, fired nearly all the investigative journalists, and replaced them with the police blotter.''

The public thought that crime was out of control, when there had been no substantive increase in crime. They voted in a generation of politicians promising to &quot;get tough on crime&quot;, and this was the result. 

That article on &quot;United States incarceration rate&quot; offers other explanations for why the US incarceration rate is so high. These include the war on drugs and the for-profit prison industry. However, only the increasing concentration of ownership of the media that has dominated the post-World War II period encouraged people with power to buy the major media and fire nearly all the investigative journalists, as previously mentioned. 

== Social construction of crime == 

Potter and Kappeler (1998) ''Constructing Crime: Perspectives on Making News and Social Problems'' is a collection of research papers on how biases in the news media impact public perceptions of crime and appropriate governmental responses thereto. This is an example of a general problem with human cognition known as &quot;[[w:Social constructionism|social constructionism]]&quot;, with Figure 1 and this discussion of it providing striking documentation of its power, applied to incarcerations.  

The description of the abrupt jump in incarceration rate in the US in last quarter of the twentieth century is eloquently described by Sacco (1998, 2005). 

== International comparison ==

[[File:Prison population rate, World, 2026 (cropped).svg|link=|thumb|upright=1.6|right|Figure 2. Prison population rate. Includes jails too. Click to see yearly slider. Go to reference to hover a country for rate, year, and rate-per-year graph.&lt;ref&gt;Our World in Data (2026).&lt;/ref&gt;]]

The Wikipedia articles on &quot;[[w:List of countries by incarceration rate|List of countries by incarceration rate]]&quot; and [[w:Comparison of United States incarceration rate with other countries|Comparison of United States incarceration rate with other countries]]&lt;ref&gt;Wikipedia articles accessed 2026-09-06.&lt;/ref&gt; both include Figure 2. Both report that the US incarceration rate (including jails, excluded from Figure 1 above) was 542 per 100,000 population in 2023. The former includes a table of &quot;Incarceration rates per 100,000 residents&quot; giving 1,659, 794, 620, 576 and 542 for El Salvador, Cuba, Rwanda, Turkmenistan and the US (1.66, 0.97, 0.62, 0.88 and 0.54 percent of the population), respectively. [[w:World population#Ten most populous countries|The US has the third largest population in the world]], after India and China, but the most prisoners. 

== Evidence based public policy == 

President Trump in his first term signed the [[w:Foundations for Evidence-Based Policymaking Act|Foundations for Evidence-Based Policymaking Act]], which was bipartisan legislation ostensibly mandating evidence-informed public policy.&lt;ref&gt;Nick Hart, President and CEO of the Data Foundation discussed this when interviewed for [[Evidence-informed public policy|&quot;Media &amp; Democracy&quot; 2025-07-31]].&lt;/ref&gt; The evidence is clear:

::''The US Congress is effectively not allowed to consider solid research suppressed by the major media.'' 

For example, studies have evaluated the effect of prison visitations on [[w:recidivism|recidivism]]. Duwe (2011) found that prison visitations generally tended to reduce recidivism, except that &quot;visits from ex-spouses significantly increased the risk.&quot;  Mitchell et al. (2016) estimated a 26 percent reduction in post-release convictions but no effect on arrests. Otsu (2023) reported that family and friends often facilitate stable housing, emotional support, and employment opportunities post release, and convicts incarcerated farther from home tend to have higher rates of recidivism.  

== Likely impact of better media on crime and incarcerations ==

How might the US be different with noncommercial news outlets funded and managed with a firewall that prevented elite interference in the content, as suggested in the section on [[Media Literacy and You#The value of noncommercial news outlets|The value of noncommercial news outlets]] in the landing page / preface of this book on [[Media Literacy and You]]? 

* Most obviously, the recidivism rate would likely be cut by roughly 26 percent and probably substantially more if the media encouraged politicians to seriously consider the available research and invest in more and better research in the future. By contrast, the current media environment amplifies demagogues, whose rhetoric resonates with crowds fed a distorted image of public safety through excessive focus on the police blotter by the major media. These negative impacts are amplified further by social media influencers, who make money from amplifying lies, as documented by DiResta (2026) and others.&lt;ref&gt;More on problems with social media are described in the [[Managing the good and the evils of social media|2026-08-27 interview with DiResta for the 'Media &amp; Democracy']] series of 29-minute interviews syndicated for the Pacifica radio network.&lt;/ref&gt;
* The incarceration rate itself would likely be cut by a factor of 5 or more, at least back to the rate of 0.1 percent of the population during the period prior to 1975, per Figure 1, and probably more. 
* Since most incarcerees have their first negative encounters with law enforcement as teenagers, if the improved media also encouraged 100 percent public funding for quality child care, as described in the chapter below on &quot;[[Media Literacy and You/Education|Education]]&quot;, the actual crime rate would likely fall dramatically. As noted earlier, incarcerations are not a function of crime but of the public's perception of crime, within the range or experience in the US since at least 1925. However, if these reductions in crime were driven by changes in the media, then the reductions in crime could, indeed, contribute to reductions in incarcerations. 

== Exercises ==

''In the following, as previously noted in this book, when talking with others, work to avoid saying, &quot;You're wrong&quot;, because that's likely to offend others and terminate conversations. Instead, ask permission to share contrary perspectives.''

1. Share Figure 1 with others you know and ask their thoughts about the dramatic increase in the US incarceration rate in the last quarter of the twentieth century. 

2. If they do not ascribe it to media biases, ask them about the role of the media in driving that increase. 

3. Unless they mention the economics of for-profit media, note that quoting law enforcement is easy and cheap provided you never offend your news sources, because doing so could make it harder and more expensive to produce news reports. Then ask for comments. 

== See also ==

* [[Media Literacy and You/Substance abuse and addictive behavior]]

== Notes == 
{{reflist}}

== Bibliography == 

* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Grant Duwe (2011-10) &quot;Blessed Be the Social Tie That Binds: The Effects of Prison Visitation on Offender Recidivism&quot;--&gt;{{cite Q|Q141328975}}
* &lt;!-- Meghan M Mitchell, Kallee Spooner, Di Jia, Yan Zhang (2016-12)  The effect of prison visitation on reentry success: A meta-analysis--&gt;{{cite Q|Q141329623}}
* &lt;!--Yuki Otsu (2023-09-11)  Does visitation in prison reduce recidivism?--&gt;{{cite Q|Q141331409}}
* &lt;!--Our World in Data (2026) Prison population rate--&gt;{{cite Q|Q141328499}}
* &lt;!--Gary W. Potter and Victor E. Kappeler (1998-01-31) Constructing Crime: Perspectives on Making News and Social Problems--&gt;{{cite Q|Q135529477}}
* &lt;!--Vincent F. Sacco (1995, 1998) &quot;Media Constructions of Crime--&gt;{{cite Q|Q106878177}}
* &lt;!--Vincent F. Sacco (2005) When Crime Waves--&gt;{{cite Q|Q96344789}}

[[Category:Media literacy]]
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[[Category:Political science]]
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Ever since I wanted to make an article about microkingdoms, people kept complaining about me. In fact, I was added to the Wikipedia:Administrators' noticeboard/Incidents, which goes to show your reputation can get ruined if you want the wrong thing. Annd, you know what happened: I got blocked.
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After my &quot;back-up&quot; account was blocked, I hit a new low: I created Orthokaryote, and when I collabrated with myself, you guessed it: /*&quot;we&quot;*/ got BLOCKED.
==Post second blockage==
After all that, it makes sense of why I'm here. But if you block me, then I will have to move yet again.
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Apparently, a mysterious editor was &quot;Citing&quot; articles but without tracing the source/&quot;cite&quot;. But even then, I was dubbed The Citer and he created an account to make an article about Microkingdoms.

He was almost banned from editing articles, so he made a promise that he would only create articles. It turns out, this is actually edited? Yes, I added a link in Oophaga sylvatica, which is considered editing, but even that made complaints about The Citer.
===Criticism===
Ever since I wanted to make an article about microkingdoms, people kept complaining about me. In fact, I was added to the Wikipedia:Administrators' noticeboard/Incidents, which goes to show your reputation can get ruined if you want the wrong thing. Annd, you know what happened: I got blocked.
==Migration to [https://species.wikimedia.org/wiki/Main_Page Wikispecies]==
After being blocked on Wikipedia, I moved to wikispecies, where I survived much longer. I had a good time up until I made The Other Citer, which marked my downfall.
===Post-Other Citer Blockage===
After my &quot;back-up&quot; account was blocked, I hit a new low: I created Orthokaryote, and when I collabrated with myself, you guessed it: /*&quot;we&quot;*/ got BLOCKED.
==Post second blockage==
After all that, it makes sense of why I'm here. But if you block me, then I will have to move yet again.
==Why don't I just try to request unblock requests?==
You see, it's just easier to move than to waste hours trying to be unblocked.
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Apparently, a mysterious editor was &quot;Citing&quot; articles but without tracing the source/&quot;cite&quot;. But even then, I was dubbed The Citer and I created an account to make an article about Microkingdoms.

I was almost banned from editing articles, so I made a promise that I would only create articles. It turns out, this is actually edited? Yes, I added a link in Oophaga sylvatica, which is considered editing, but even that made complaints about The Citer.
===Criticism===
Ever since I wanted to make an article about microkingdoms, people kept complaining about me. In fact, I was added to the Wikipedia:Administrators' noticeboard/Incidents, which goes to show your reputation can get ruined if you want the wrong thing. Annd, you know what happened: I got blocked.
==Migration to [https://species.wikimedia.org/wiki/Main_Page Wikispecies]==
After being blocked on Wikipedia, I moved to wikispecies, where I survived much longer. I had a good time up until I made The Other Citer, which marked my downfall.
===Post-Other Citer Blockage===
After my &quot;back-up&quot; account was blocked, I hit a new low: I created Orthokaryote, and when I collabrated with myself, you guessed it: /*&quot;we&quot;*/ got BLOCKED.
==Post second blockage==
After all that, it makes sense of why I'm here. But if you block me, then I will have to move yet again.
==Why don't I just try to request unblock requests?==
You see, it's just easier to move than to waste hours trying to be unblocked.
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{{METF/2026
|1=
&lt;!-- Title --&gt;
# Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]]
|2=
&lt;!-- Headings --&gt;
&lt;!-- Heading structure --&gt;
&lt;!-- 1-level --&gt;
# Basic, [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – could benefit from further development, perhaps using a 2-level structure (i.e., use subheadings)
&lt;!-- Alignment with focus questions --&gt;
# Excellent alignment between sub-title, focus questions, and heading structure
|3=
&lt;!-- Overview--&gt;
# Very good
&lt;!-- Scenario --&gt;
# A scenario or case study is presented in a feature box with an image at the start of this section
&lt;!-- Description --&gt;
# A clear description of the problem/topic is planned or presented
&lt;!-- Style --&gt;
# Use 3rd person point of view for main body text (except 1st/2nd person point of view can work within feature boxes for scenarios)
&lt;!-- Focus questions --&gt;
# Focus questions are aligned with sub-title and top-level headings
# Use [https://www.aresearchguide.com/write-in-third-person.html 3rd person perspective], although a case study or feature box could use 1st or 2nd person perspective
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Solid development
# Consider introducing unconscious motivation
# Highlight the most relevant theories and synthesise the best research on the topic; citations do not indicate that a sufficient literature search has been conducted
# Provide more detailed edit summaries
&lt;!-- Scope --&gt;
# The scope is excellent (i.e., not too little/narrow or too big/broad)
&lt;!-- Citation style --&gt;
# Use [https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles APA style 7th edition for citations]
&lt;!-- Other --&gt;
# Use correct capitalisation ([https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style is a &quot;down&quot; style]) – [https://polishedpaper.com/blog/capitalization-apa-style more info]
# Consider using Studiosity Writing Feedback+ or a similar writing-support service (e.g., Grammarly) to improve the quality of written expression and check for grammatical and spelling errors in the book chapter draft.
&lt;!-- Conclusion --&gt;
# Conclusion is well underway
# What are the practical, take-home messages? (address the focus questions)
|5=
&lt;!-- Figure --&gt;
# Excellent - Relevant figure(s) presented, captioned, and cited
&lt;!-- Cite --&gt;
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&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# One in-text [[m:Help:Interwiki linking|interwiki link]] for first mention of key term to [[w:|Wikipedia]]. Also embed links to [[Motivation and emotion/Book|book chapters]].
&lt;!-- Scenarios/examples/case studies --&gt;
Consider incorporating additional scenarios, examples, or case studies to illustrate key concepts. These could build on the Overview scenario or introduce new real-world situations in the main body of the chapter to demonstrate how the concepts apply in practice.
&lt;!-- Quiz --&gt;
# Promising use of quiz question(s)
# Place each quiz question in the most relevant section
&lt;!-- Tables --&gt;
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|7=
&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Insufficient
&lt;!-- Systematic reviews --&gt;
# What are the most relevant systematic reviews/meta-analyses about this topic?
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
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|8=
&lt;!-- Resources --&gt;
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## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
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|9=
&lt;!-- User page --&gt;
# Used effectively
&lt;!-- Description about self --&gt;
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# Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
# A link to the book chapter is provided
|10=
&lt;!-- Social contribution --&gt;
# Good – two out of three types of contributions made with direct link(s) to evidence. The other type of contribution is making:
#* direct improvements to other [[Motivation and emotion/Book|chapters (past or current)]] (valiant attempt - but, overall no changes were made; consider starting with more straightforward text-based changes)
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:22, 7 September 2026 (UTC)</text>
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      </contributor>
      <comment>Created page with &quot;{{Missing information|aspect distincions, formation, and principal parts}} == The Perfect Active Indicative == The perfect tense in Ancient Greek conveys completed aspect, similar to English's present perfect. * λέλυκα: I have loosened&quot;</comment>
      <origin>2831954</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="241" sha1="ar6a0fulht2wauxn4iy8x7vxejwywnl" xml:space="preserve">{{Missing information|aspect distincions, formation, and principal parts}}
== The Perfect Active Indicative ==
The perfect tense in Ancient Greek conveys completed aspect, similar to English's present perfect.
* λέλυκα: I have loosened</text>
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  </page>
  <page>
    <title>Template:AI-generated-section</title>
    <ns>10</ns>
    <id>331898</id>
    <revision>
      <id>2831958</id>
      <timestamp>2026-09-07T06:31:43Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
      </contributor>
      <comment>creating. see original contributors at... https://en.wikiversity.org/w/index.php?title=Template:AI-generated&amp;action=history</comment>
      <origin>2831958</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="420" sha1="bxy7h6xgsyq3zqne0ujf2q5q51aa4mw" xml:space="preserve">{{Ambox
|text = This section includes substantial content generated by [[Wikiversity:Artificial intelligence|artificial intelligence]].
}}&lt;noinclude&gt;{{Documentation}}

==See also==
* [[b:Template:AI-generated|Template:AI-generated]] (Wikibooks)
* [[w:Template:AI-generated|Template:AI-generated]] (Wikipedia)
[[Category:Artificial intelligence]]
&lt;/noinclude&gt;&lt;includeonly&gt;[[Category:AI-generated resources]]&lt;/includeonly&gt;</text>
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    </revision>
    <revision>
      <id>2832001</id>
      <parentid>2831958</parentid>
      <timestamp>2026-09-07T11:00:17Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <comment>/* See also */ +[[Template:AI-generated]]</comment>
      <origin>2832001</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="448" sha1="l6p12xzf4rsckevb79b8soyzap963ny" xml:space="preserve">{{Ambox
|text = This section includes substantial content generated by [[Wikiversity:Artificial intelligence|artificial intelligence]].
}}&lt;noinclude&gt;{{Documentation}}

==See also==
* [[Template:AI-generated]]
* [[b:Template:AI-generated|Template:AI-generated]] (Wikibooks)
* [[w:Template:AI-generated|Template:AI-generated]] (Wikipedia)
[[Category:Artificial intelligence]]
&lt;/noinclude&gt;&lt;includeonly&gt;[[Category:AI-generated resources]]&lt;/includeonly&gt;</text>
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  <page>
    <title>Talk:Harmful Effects and Policy</title>
    <ns>1</ns>
    <id>331900</id>
    <revision>
      <id>2831967</id>
      <timestamp>2026-09-07T06:51:01Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
      </contributor>
      <comment>/* clean up... */ new section</comment>
      <origin>2831967</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="289" sha1="qrr9s7wb2t2rjn3xrq9evj6d2ubyc7u" xml:space="preserve">== clean up... ==

not bad eh? 

https://en.wikiversity.org/w/index.php?title=Harmful_Effects_and_Policy&amp;diff=prev&amp;oldid=2831965

bless up. [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 06:51, 7 September 2026 (UTC)</text>
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  <page>
    <title>User:Buleto</title>
    <ns>2</ns>
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      <timestamp>2026-09-07T10:41:08Z</timestamp>
      <contributor>
        <username>Buleto</username>
        <id>3110702</id>
      </contributor>
      <comment>/* */</comment>
      <origin>2831996</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4340" sha1="ddwrxyi2wxm709ip2ywlchd19jdlon2" xml:space="preserve">{{User page}}
{{DISPLAYTITLE:User:'''Buleto'''}}

&lt;div style=&quot;width:100%; box-sizing:border-box; background:#01411C; border:2px solid #01411C; border-radius:14px; padding:28px 15px; text-align:center; color:#FFFFFF;&quot;&gt;

[[File:Flag of Pakistan.svg|100px|center|border]]

&lt;div style=&quot;font-family:Georgia,serif; font-size:300%; font-weight:bold; letter-spacing:5px; color:#FFFFFF;&quot;&gt;
BULETO
&lt;/div&gt;

&lt;div style=&quot;height:3px; width:90px; background:#FFFFFF; margin:10px auto;&quot;&gt;&lt;/div&gt;

&lt;div style=&quot;font-size:115%; letter-spacing:1px;&quot;&gt;
'''Pakistani Wikimedian · Learner · Contributor'''
&lt;/div&gt;

&lt;div style=&quot;font-size:90%; margin-top:8px;&quot;&gt;
Learning • Teaching • Research • Open Knowledge
&lt;/div&gt;

&lt;/div&gt;

{| style=&quot;width:100%; border-collapse:collapse; margin:15px 0;&quot;
| style=&quot;width:33%; background:#01411C; color:#FFFFFF; text-align:center; padding:16px; border:2px solid #FFFFFF;&quot; |
'''🇵🇰 PAKISTAN'''&lt;br&gt;
Pakistani contributor
| style=&quot;width:34%; background:#FFFFFF; color:#01411C; text-align:center; padding:16px; border:2px solid #01411C;&quot; |
'''📚 WIKIVERSITY'''&lt;br&gt;
Learning &amp; education
| style=&quot;width:33%; background:#01411C; color:#FFFFFF; text-align:center; padding:16px; border:2px solid #FFFFFF;&quot; |
'''🌐 WIKIMEDIA'''&lt;br&gt;
Free knowledge
|}

&lt;div style=&quot;border-left:6px solid #01411C; padding:12px 18px; margin:15px 0; background:#f8faf9;&quot;&gt;

'''Welcome to my Wikiversity user page.'''

I am '''Buleto''', a Pakistani Wikimedia contributor interested in learning, education, health sciences, technology, research, and the development of useful open educational resources.

I believe knowledge becomes more valuable when it is made clear, accessible, verifiable, and freely available to others.

&lt;/div&gt;

== 🎓 About Buleto ==

{| style=&quot;width:100%;&quot;
| style=&quot;width:50%; vertical-align:top; padding:10px;&quot; |
'''🇵🇰 Identity'''

* Pakistani contributor
* Interested in open knowledge
* Wikimedia community participant
* Lifelong learner

| style=&quot;width:50%; vertical-align:top; padding:10px;&quot; |
'''📚 Learning'''

* Nursing &amp; health sciences
* Education
* Science
* Technology
* Research &amp; evidence
|}

== 📖 Areas of interest ==

{| class=&quot;wikitable&quot; style=&quot;width:100%;&quot;
! Area !! Interest
|-
| 🩺 '''Health sciences''' || Nursing, healthcare and related learning
|-
| 🧠 '''Education''' || Learning resources and educational content
|-
| 🔬 '''Science''' || Evidence-based knowledge and research
|-
| 💻 '''Technology''' || Digital tools and Wikimedia technology
|-
| 🇵🇰 '''Pakistan''' || Pakistani knowledge, culture and education
|-
| 🌐 '''Open knowledge''' || Wikimedia and freely accessible learning
|}

== 🏫 Wikiversity ==

On Wikiversity, I am interested in contributing to a collaborative environment where people can:

* Learn together
* Share educational resources
* Improve learning materials
* Organise knowledge
* Explore academic subjects
* Develop freely available educational content

&lt;div style=&quot;background:#01411C; color:#FFFFFF; border-radius:10px; padding:14px; text-align:center; margin:15px 0;&quot;&gt;

'''LEARN · CREATE · SHARE · IMPROVE'''

&lt;/div&gt;

== 🌐 Wikimedia ==

{| class=&quot;wikitable&quot; style=&quot;width:100%; text-align:center;&quot;
! Project !! Purpose
|-
| '''[[Wikipedia]]''' || Free encyclopedia
|-
| '''[[Wikiversity]]''' || Learning and teaching
|-
| '''[[Wikimedia Commons]]''' || Free media
|-
| '''[[Wikidata]]''' || Structured knowledge
|}

== 👤 User links ==

* [[User talk:Buleto|💬 Talk page]]
* [[Special:Contributions/Buleto|✎ Contributions]]
* [[Special:CentralAuth/Buleto|🌐 Global account]]

== 🗣️ Languages ==

{{Babel|en-4}}
{{Clear}}

== 🇵🇰 Pakistani identity ==

&lt;div style=&quot;border:2px solid #01411C; border-radius:10px; padding:15px; text-align:center;&quot;&gt;

[[File:Flag of Pakistan.svg|80px|border]]

'''This user is Pakistani and contributes to Wikimedia's free-knowledge mission.'''

&lt;/div&gt;

== 📬 Contact ==

For Wikiversity-related matters, please leave a message on my [[User talk:Buleto|talk page]].

&lt;div style=&quot;border-top:4px solid #01411C; margin-top:25px; padding:18px; text-align:center;&quot;&gt;

&lt;span style=&quot;font-family:Georgia,serif; font-size:150%; color:#01411C;&quot;&gt;
'''BULETO'''
&lt;/span&gt;

&lt;br&gt;

&lt;span style=&quot;color:#01411C;&quot;&gt;
'''Learn • Share • Serve • Keep knowledge free'''
&lt;/span&gt;

&lt;/div&gt;

{{User:Buleto/signature}}</text>
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  <page>
    <title>User:Buleto/signature</title>
    <ns>2</ns>
    <id>331903</id>
    <revision>
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      <timestamp>2026-09-07T10:41:53Z</timestamp>
      <contributor>
        <username>Buleto</username>
        <id>3110702</id>
      </contributor>
      <comment>/* */</comment>
      <origin>2831997</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="241" sha1="ossccpmlsasi7vhp86e18j9jplxay4x" xml:space="preserve">&lt;span style=&quot;font-family:Georgia,serif; font-size:115%; font-weight:bold; color:#01411C;&quot;&gt;'''[[User:Buleto|Buleto]]'''&lt;/span&gt; &lt;span style=&quot;color:#01411C;&quot;&gt;·&lt;/span&gt; &lt;span style=&quot;font-size:90%; color:#01411C;&quot;&gt;[[User talk:Buleto|talk]]&lt;/span&gt;</text>
      <sha1>ossccpmlsasi7vhp86e18j9jplxay4x</sha1>
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  </page>
  <page>
    <title>User talk:Buleto</title>
    <ns>3</ns>
    <id>331904</id>
    <revision>
      <id>2831998</id>
      <timestamp>2026-09-07T10:44:48Z</timestamp>
      <contributor>
        <username>Buleto</username>
        <id>3110702</id>
      </contributor>
      <comment>/* */</comment>
      <origin>2831998</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3775" sha1="mwu8ejpd356a31q4lq0swshl8fq11vy" xml:space="preserve">{{User talk page}}
{{DISPLAYTITLE:User talk:'''Buleto'''}}

&lt;div style=&quot;width:100%; box-sizing:border-box; background:#01411C; border:2px solid #01411C; border-radius:12px; padding:24px 12px; text-align:center; color:#FFFFFF;&quot;&gt;

[[File:Flag of Pakistan.svg|75px|center|border]]

&lt;div style=&quot;font-family:Georgia,serif; font-size:250%; font-weight:bold; letter-spacing:4px;&quot;&gt;
BULETO
&lt;/div&gt;

&lt;div style=&quot;height:3px; width:80px; background:#FFFFFF; margin:10px auto;&quot;&gt;&lt;/div&gt;

&lt;div style=&quot;font-size:110%;&quot;&gt;
'''User talk page · Wikimedia communication'''
&lt;/div&gt;

&lt;div style=&quot;font-size:90%; margin-top:7px;&quot;&gt;
🇵🇰 Pakistani Wikimedian · Learner · Contributor
&lt;/div&gt;

&lt;/div&gt;

{| style=&quot;width:100%; border-collapse:collapse; margin:15px 0;&quot;
| style=&quot;width:33%; background:#01411C; color:#FFFFFF; text-align:center; padding:14px; border:2px solid #FFFFFF;&quot; |
'''💬 DISCUSS'''&lt;br&gt;
Leave a message
| style=&quot;width:34%; background:#FFFFFF; color:#01411C; text-align:center; padding:14px; border:2px solid #01411C;&quot; |
'''🤝 COLLABORATE'''&lt;br&gt;
Wikimedia matters
| style=&quot;width:33%; background:#01411C; color:#FFFFFF; text-align:center; padding:14px; border:2px solid #FFFFFF;&quot; |
'''📚 CONTRIBUTE'''&lt;br&gt;
Free knowledge
|}

&lt;div style=&quot;border-left:6px solid #01411C; padding:12px 18px; margin:15px 0; background:#f8faf9;&quot;&gt;

'''Welcome to my talk page.'''

This page is for messages, questions, suggestions, and discussions related to my Wikimedia contributions.

If you would like to contact me, please leave a message below. I will respond when I am available.

'''Thank you for keeping discussions constructive, civil, and focused on improving Wikimedia projects.'''

&lt;/div&gt;

== 💬 Leave a message ==

&lt;div style=&quot;border:2px solid #01411C; border-radius:10px; padding:15px; background:#ffffff;&quot;&gt;

'''To start a new discussion, click the &quot;Add topic&quot; button at the top of this page.'''

Please:

* Be clear and specific.
* Assume good faith.
* Keep discussions respectful.
* Provide relevant links or diffs when appropriate.
* Avoid sharing private or sensitive information publicly.

&lt;/div&gt;

== 📌 Current discussions ==

{{User talk:Buleto/Archive}}

== 🤝 Wikimedia collaboration ==

I am happy to discuss:

* Wikipedia and other Wikimedia projects
* Article improvement
* Wikidata and structured data
* Categories and maintenance
* New pages and patrolling
* User assistance and welcoming
* Wikimedia tools and scripts
* Open educational resources
* Pakistan-related knowledge

== 🛠️ Useful links ==

{| class=&quot;wikitable&quot; style=&quot;width:100%; text-align:center;&quot;
! Link !! Purpose
|-
| [[User:Buleto|👤 User page]] || About Buleto
|-
| [[Special:Contributions/Buleto|✎ Contributions]] || My Wikimedia activity
|-
| [[Special:WhatLinksHere/User:Buleto|🔗 What links here]] || Pages linking to my user page
|-
| [[Special:CentralAuth/Buleto|🌐 Global account]] || Global Wikimedia account
|}

== 📚 Communication policy ==

&lt;div style=&quot;background:#f8faf9; border:1px solid #01411C; border-radius:8px; padding:12px;&quot;&gt;

'''Please keep Wikimedia discussions on Wikimedia where possible.'''

For matters concerning my Wikimedia activity, this talk page is generally the best place to contact me.

Personal, confidential, or sensitive information should '''not''' be posted publicly.

&lt;/div&gt;

== 🗄️ Archives ==

Older discussions may be moved to talk-page archives when appropriate.

* [[User talk:Buleto/Archive 1|Archive 1]]

{{DEFAULTSORT:Buleto}}

&lt;div style=&quot;border-top:4px solid #01411C; margin-top:25px; padding:16px; text-align:center;&quot;&gt;

&lt;span style=&quot;font-family:Georgia,serif; font-size:140%; color:#01411C;&quot;&gt;
'''BULETO'''
&lt;/span&gt;

&lt;br&gt;

&lt;span style=&quot;color:#01411C;&quot;&gt;
'''Discuss • Collaborate • Improve • Keep knowledge free'''
&lt;/span&gt;

&lt;/div&gt;</text>
      <sha1>mwu8ejpd356a31q4lq0swshl8fq11vy</sha1>
    </revision>
    <revision>
      <id>2831999</id>
      <parentid>2831998</parentid>
      <timestamp>2026-09-07T10:45:48Z</timestamp>
      <contributor>
        <username>Buleto</username>
        <id>3110702</id>
      </contributor>
      <comment>/* */</comment>
      <origin>2831999</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3769" sha1="tqyrc30xeu1gx9wc04dx4ihxk0jekx5" xml:space="preserve">{{Usertalk}}
{{DISPLAYTITLE:User talk:'''Buleto'''}}

&lt;div style=&quot;width:100%; box-sizing:border-box; background:#01411C; border:2px solid #01411C; border-radius:12px; padding:24px 12px; text-align:center; color:#FFFFFF;&quot;&gt;

[[File:Flag of Pakistan.svg|75px|center|border]]

&lt;div style=&quot;font-family:Georgia,serif; font-size:250%; font-weight:bold; letter-spacing:4px;&quot;&gt;
BULETO
&lt;/div&gt;

&lt;div style=&quot;height:3px; width:80px; background:#FFFFFF; margin:10px auto;&quot;&gt;&lt;/div&gt;

&lt;div style=&quot;font-size:110%;&quot;&gt;
'''User talk page · Wikimedia communication'''
&lt;/div&gt;

&lt;div style=&quot;font-size:90%; margin-top:7px;&quot;&gt;
🇵🇰 Pakistani Wikimedian · Learner · Contributor
&lt;/div&gt;

&lt;/div&gt;

{| style=&quot;width:100%; border-collapse:collapse; margin:15px 0;&quot;
| style=&quot;width:33%; background:#01411C; color:#FFFFFF; text-align:center; padding:14px; border:2px solid #FFFFFF;&quot; |
'''💬 DISCUSS'''&lt;br&gt;
Leave a message
| style=&quot;width:34%; background:#FFFFFF; color:#01411C; text-align:center; padding:14px; border:2px solid #01411C;&quot; |
'''🤝 COLLABORATE'''&lt;br&gt;
Wikimedia matters
| style=&quot;width:33%; background:#01411C; color:#FFFFFF; text-align:center; padding:14px; border:2px solid #FFFFFF;&quot; |
'''📚 CONTRIBUTE'''&lt;br&gt;
Free knowledge
|}

&lt;div style=&quot;border-left:6px solid #01411C; padding:12px 18px; margin:15px 0; background:#f8faf9;&quot;&gt;

'''Welcome to my talk page.'''

This page is for messages, questions, suggestions, and discussions related to my Wikimedia contributions.

If you would like to contact me, please leave a message below. I will respond when I am available.

'''Thank you for keeping discussions constructive, civil, and focused on improving Wikimedia projects.'''

&lt;/div&gt;

== 💬 Leave a message ==

&lt;div style=&quot;border:2px solid #01411C; border-radius:10px; padding:15px; background:#ffffff;&quot;&gt;

'''To start a new discussion, click the &quot;Add topic&quot; button at the top of this page.'''

Please:

* Be clear and specific.
* Assume good faith.
* Keep discussions respectful.
* Provide relevant links or diffs when appropriate.
* Avoid sharing private or sensitive information publicly.

&lt;/div&gt;

== 📌 Current discussions ==

{{User talk:Buleto/Archive}}

== 🤝 Wikimedia collaboration ==

I am happy to discuss:

* Wikipedia and other Wikimedia projects
* Article improvement
* Wikidata and structured data
* Categories and maintenance
* New pages and patrolling
* User assistance and welcoming
* Wikimedia tools and scripts
* Open educational resources
* Pakistan-related knowledge

== 🛠️ Useful links ==

{| class=&quot;wikitable&quot; style=&quot;width:100%; text-align:center;&quot;
! Link !! Purpose
|-
| [[User:Buleto|👤 User page]] || About Buleto
|-
| [[Special:Contributions/Buleto|✎ Contributions]] || My Wikimedia activity
|-
| [[Special:WhatLinksHere/User:Buleto|🔗 What links here]] || Pages linking to my user page
|-
| [[Special:CentralAuth/Buleto|🌐 Global account]] || Global Wikimedia account
|}

== 📚 Communication policy ==

&lt;div style=&quot;background:#f8faf9; border:1px solid #01411C; border-radius:8px; padding:12px;&quot;&gt;

'''Please keep Wikimedia discussions on Wikimedia where possible.'''

For matters concerning my Wikimedia activity, this talk page is generally the best place to contact me.

Personal, confidential, or sensitive information should '''not''' be posted publicly.

&lt;/div&gt;

== 🗄️ Archives ==

Older discussions may be moved to talk-page archives when appropriate.

* [[User talk:Buleto/Archive 1|Archive 1]]

{{DEFAULTSORT:Buleto}}

&lt;div style=&quot;border-top:4px solid #01411C; margin-top:25px; padding:16px; text-align:center;&quot;&gt;

&lt;span style=&quot;font-family:Georgia,serif; font-size:140%; color:#01411C;&quot;&gt;
'''BULETO'''
&lt;/span&gt;

&lt;br&gt;

&lt;span style=&quot;color:#01411C;&quot;&gt;
'''Discuss • Collaborate • Improve • Keep knowledge free'''
&lt;/span&gt;

&lt;/div&gt;</text>
      <sha1>tqyrc30xeu1gx9wc04dx4ihxk0jekx5</sha1>
    </revision>
    <revision>
      <id>2832000</id>
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      <contributor>
        <username>Buleto</username>
        <id>3110702</id>
      </contributor>
      <comment>/* */</comment>
      <origin>2832000</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
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{{DISPLAYTITLE:User talk:'''Buleto'''}}

&lt;div style=&quot;width:100%; box-sizing:border-box; background:#01411C; border:2px solid #01411C; border-radius:12px; padding:24px 12px; text-align:center; color:#FFFFFF;&quot;&gt;

[[File:Flag of Pakistan.svg|75px|center|border]]

&lt;div style=&quot;font-family:Georgia,serif; font-size:250%; font-weight:bold; letter-spacing:4px;&quot;&gt;
BULETO
&lt;/div&gt;

&lt;div style=&quot;height:3px; width:80px; background:#FFFFFF; margin:10px auto;&quot;&gt;&lt;/div&gt;

&lt;div style=&quot;font-size:110%;&quot;&gt;
'''User talk page · Wikimedia communication'''
&lt;/div&gt;

&lt;div style=&quot;font-size:90%; margin-top:7px;&quot;&gt;
🇵🇰 Pakistani Wikimedian · Learner · Contributor
&lt;/div&gt;

&lt;/div&gt;

{| style=&quot;width:100%; border-collapse:collapse; margin:15px 0;&quot;
| style=&quot;width:33%; background:#01411C; color:#FFFFFF; text-align:center; padding:14px; border:2px solid #FFFFFF;&quot; |
'''💬 DISCUSS'''&lt;br&gt;
Leave a message
| style=&quot;width:34%; background:#FFFFFF; color:#01411C; text-align:center; padding:14px; border:2px solid #01411C;&quot; |
'''🤝 COLLABORATE'''&lt;br&gt;
Wikimedia matters
| style=&quot;width:33%; background:#01411C; color:#FFFFFF; text-align:center; padding:14px; border:2px solid #FFFFFF;&quot; |
'''📚 CONTRIBUTE'''&lt;br&gt;
Free knowledge
|}

&lt;div style=&quot;border-left:6px solid #01411C; padding:12px 18px; margin:15px 0; background:#f8faf9;&quot;&gt;

'''Welcome to my talk page.'''

This page is for messages, questions, suggestions, and discussions related to my Wikimedia contributions.

If you would like to contact me, please leave a message below. I will respond when I am available.

'''Thank you for keeping discussions constructive, civil, and focused on improving Wikimedia projects.'''

&lt;/div&gt;

== 💬 Leave a message ==

&lt;div style=&quot;border:2px solid #01411C; border-radius:10px; padding:15px; background:#ffffff;&quot;&gt;

'''To start a new discussion, click the &quot;Add topic&quot; button at the top of this page.'''

Please:

* Be clear and specific.
* Assume good faith.
* Keep discussions respectful.
* Provide relevant links or diffs when appropriate.
* Avoid sharing private or sensitive information publicly.

&lt;/div&gt;

== 📌 Current discussions ==

{{User talk:Buleto/Archive}}

== 🤝 Wikimedia collaboration ==

I am happy to discuss:

* Wikipedia and other Wikimedia projects
* Article improvement
* Wikidata and structured data
* Categories and maintenance
* New pages and patrolling
* User assistance and welcoming
* Wikimedia tools and scripts
* Open educational resources
* Pakistan-related knowledge

== 🛠️ Useful links ==

{| class=&quot;wikitable&quot; style=&quot;width:100%; text-align:center;&quot;
! Link !! Purpose
|-
| [[User:Buleto|👤 User page]] || About Buleto
|-
| [[Special:Contributions/Buleto|✎ Contributions]] || My Wikimedia activity
|-
| [[Special:WhatLinksHere/User:Buleto|🔗 What links here]] || Pages linking to my user page
|-
| [[Special:CentralAuth/Buleto|🌐 Global account]] || Global Wikimedia account
|}

== 📚 Communication policy ==

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'''Please keep Wikimedia discussions on Wikimedia where possible.'''

For matters concerning my Wikimedia activity, this talk page is generally the best place to contact me.

Personal, confidential, or sensitive information should '''not''' be posted publicly.

&lt;/div&gt;

== 🗄️ Archives ==

Older discussions may be moved to talk-page archives when appropriate.

* [[User talk:Buleto/Archive 1|Archive 1]]

{{DEFAULTSORT:Buleto}}

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'''BULETO'''
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&lt;br&gt;

&lt;span style=&quot;color:#01411C;&quot;&gt;
'''Discuss • Collaborate • Improve • Keep knowledge free'''
&lt;/span&gt;

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